tag:blogger.com,1999:blog-30558052669917206012024-03-13T03:26:05.289-05:00Giant Battling Robots-The mathematics and statistics of games-Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.comBlogger315125tag:blogger.com,1999:blog-3055805266991720601.post-60981537971304907392023-10-12T09:44:00.001-05:002023-10-12T09:46:00.711-05:00Flipped coins not fair?<div>It should not be a complete surprise that flipped coins do not exactly meet the ideal of fair 50/50 outcomes. After all the stamp on each side must shift the balance, however slightly. Here researchers find the "up" side when flipped is slightly more likely to be the end result. </div><div>I suspect dice have a similar bias, especially when you don't give them an energetic shake and throw.</div><div><br /></div><div><h1 style="box-sizing: border-box; color: #263238; font-family: Quicksand, sans-serif; font-size: 24px; line-height: 27.28px; margin: 0px;">Flipped coins found not to be as fair as thought</h1></div><div><br /></div><div>https://phys.org/news/2023-10-flipped-coins-fair-thought.html</div><div><br /></div><div><br /></div><div><br /></div> <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-77188400555866634852020-08-09T10:55:00.008-05:002020-08-12T20:28:11.279-05:00Celebrate Roguelikes, October 3rd 2020<div><br /></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left;"><tbody><tr><td style="text-align: center;"><a href="https://img.evbuc.com/https%3A%2F%2Fcdn.evbuc.com%2Fimages%2F107691941%2F464531253973%2F1%2Foriginal.20200804-015511?w=1080&auto=format%2Ccompress&q=75&sharp=10&rect=0%2C0%2C800%2C400&s=f11aeb880f67dca7915ab2c5da4fcced" style="clear: left; display: block; margin-bottom: 1em; margin-left: auto; margin-right: auto; padding: 1em 0px;"><img alt="Celebrate Roguelikes" border="0" data-original-height="400" data-original-width="800" height="160" src="https://img.evbuc.com/https%3A%2F%2Fcdn.evbuc.com%2Fimages%2F107691941%2F464531253973%2F1%2Foriginal.20200804-015511?w=1080&auto=format%2Ccompress&q=75&sharp=10&rect=0%2C0%2C800%2C400&s=f11aeb880f67dca7915ab2c5da4fcced" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: x-small;">Celebrate the rich history and inspiring future of roguelikes <br />with streamed talks and more in our own custom-built<br /> roguelike social space!</span></td></tr></tbody></table><div><div vertical-align:text-top=""><a style="margin-left: 1em; margin-right: 1em;">I don't think I've ever mentioned my love of roguelike games here before. This dates back 40 years and my Sophmore year as a computer science major. The version I played was called "Hack" but as far as I can tell it was an early version of Rogue for the PC - back when Personal Computers were a novel concept! I spent every hour I could spare in the computer lab playing Hack, and nearly flunked my classes that semester because of it. </a></div>
This October comes <a href="https://www.eventbrite.com/e/roguelike-celebration-2020-tickets-115662964039">Roguelike Celebration</a>, an online event with dozens of presentations about Roguelike games. Count me in!<br /><br /><br /></div><div vertical-align:text-top="">The roguelike I am currently playing is a much simplified version called <b><a href="https://shatteredpixel.com/shatteredpd/">Shattered Pixel Dungeon</a></b>, which is a relatively gentle introduction to a complex genre.</div><div vertical-align:text-top=""><a style="margin-left: 1em; margin-right: 1em;"><br /></a></div><div vertical-align:text-top=""><a style="margin-left: 1em; margin-right: 1em;"><br /></a></div><div vertical-align:text-top=""> ~
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</div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com1tag:blogger.com,1999:blog-3055805266991720601.post-7070063432711276852015-11-05T18:31:00.000-06:002015-11-05T18:31:00.070-06:00Tribes Universe games, including Earthseige, are now available free<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivkZx3AimwcIqxaNB_-G75Vqu6gZzC_uyVK40jGUYVCMW8FWuM3lwXAvqNYD3zXItXPs6Bc83s3VmZ8k8AmnYlbuNS85GxhhPnS4nHWsZuYPWTb9sbGjLoIkoS9hIyN_3N-4BTx7Fhc5Y/s1600/earthsiege.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivkZx3AimwcIqxaNB_-G75Vqu6gZzC_uyVK40jGUYVCMW8FWuM3lwXAvqNYD3zXItXPs6Bc83s3VmZ8k8AmnYlbuNS85GxhhPnS4nHWsZuYPWTb9sbGjLoIkoS9hIyN_3N-4BTx7Fhc5Y/s1600/earthsiege.jpg" /></a></div>
I remember downloading and playing the demo for Earthseige, long ago. It seemed like a cool game, and the demo left me wanting more.<br />
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One apocalypse later, the Earth lies in ruin from these heavy metal marauders. You and your squad of HERCULAN warriors must prowl this target-rich wasteland to deliver some heavily mechanized payback. But beware--the Cybrids are an intelligent and relentless enemy. You'll constantly have to train new pilots, develop new tactics, and acquire new weapons to secure an advantage. If not, they'll be hosing your remains out of the cockpit for the next rookie.</blockquote>
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Then I bought <b><a href="https://en.wikipedia.org/wiki/MechWarrior_2:_31st_Century_Combat" target="_blank">Mechwarrior 2</a> </b>and mostly forgot about Earthseige. I recall reading about one of the developers saying they thought Earthseige suffered from the lack of a strong background story like that of the <a href="http://www.sarna.net/wiki/Main_Page" target="_blank">Battletech universe</a>. I actually didn't know that the Tribes games were in the same series as Earthseige, so I guess they did OK without me. You can download all five Tribes games (for free) now at: http://www.tribesuniverse.com/<br />
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Via <a href="http://www.polygon.com/2015/10/30/9646074/tribes-free-downloads-pc-ps2" target="_blank">Polygon News</a><br />
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-36343200892752352982015-08-11T18:18:00.005-05:002021-04-14T21:44:50.453-05:00GBR Collection on Google Plus+<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm2b01fTxOeUWf7u1oDpaaRECBFgYUeDJN9PHJvt_bZPST8J2f8RFutXWR8yi6xwyWYZoPQIh2EFXd4-X5NzSqN2Xnr82ReRHu0hbEHrPhquU0wpItT4KvSAesC8EJKFKjp6kUtCOMTNc/s1600/snakes_and.JPG" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm2b01fTxOeUWf7u1oDpaaRECBFgYUeDJN9PHJvt_bZPST8J2f8RFutXWR8yi6xwyWYZoPQIh2EFXd4-X5NzSqN2Xnr82ReRHu0hbEHrPhquU0wpItT4KvSAesC8EJKFKjp6kUtCOMTNc/s320/snakes_and.JPG" width="320" /></a>I have a <a href="https://plus.google.com/u/0/collection/YE4Gf" target="_blank">collection of games related posts on Google+</a>. Most of these are things I would write about if I could make the time. Stop by and browse a bit.</div><div dir="ltr" style="text-align: left;" trbidi="on"><br /></div><div dir="ltr" style="text-align: left;" trbidi="on">UPDATE: G+ is gone now. I have the collection archived, but it would take some work to make it available again. Maybe ...<br />
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com1tag:blogger.com,1999:blog-3055805266991720601.post-41235530965673883482014-12-19T20:45:00.001-06:002014-12-19T20:45:08.693-06:00Megabots: Not Funded<div dir="ltr" style="text-align: left;" trbidi="on">
<b><a href="https://www.kickstarter.com/projects/megabots/megabots-live-action-giant-robot-combat" target="_blank">Megabots: Giant Fighting Robots</a></b> - an unsuccessful Kickstarter project to develop arena style robot combat. <br />
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So of course I just had to share it. :-)<br />
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-60425896159740181842014-08-07T10:04:00.001-05:002014-08-07T10:04:15.318-05:00Ludology Podcast<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQWpFim46xl6OBE9CKZ57fgCpTPJ1LXyHD6XC4CmnuYqxjrrZ7N7uASZIN2pYZYfLhgYTpCP87lMDuKFR4kSFJrlWui2R1E1yX8Aus7ZJY0UwMr5h7_Z8DlLPNMQeHIQHULsWjkhiYpBo/s1600/Ludology1.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Ludology Podcast" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQWpFim46xl6OBE9CKZ57fgCpTPJ1LXyHD6XC4CmnuYqxjrrZ7N7uASZIN2pYZYfLhgYTpCP87lMDuKFR4kSFJrlWui2R1E1yX8Aus7ZJY0UwMr5h7_Z8DlLPNMQeHIQHULsWjkhiYpBo/s1600/Ludology1.png" title="Ludology Podcast" /></a>I have recently discovered the <b><a href="https://itunes.apple.com/us/podcast/ludology/id419046224?mt=2&i=317188620" target="_blank">Ludology Podcast</a></b>, which has serious discussions about what makes things work, including a bit of informal probability. If you have any interest in game design, it's definitely worth checking out.<br />
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com3tag:blogger.com,1999:blog-3055805266991720601.post-61134269168129432142014-07-17T18:20:00.001-05:002014-07-17T18:27:50.508-05:00New Dice to Move your Mice<div dir="ltr" style="text-align: left;" trbidi="on">
I've going to have to get some of these for my collection, <b>because dice!</b><br />
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More info at <b><a href="http://thedicelab.com/" target="_blank">The Dice Lab</a></b>.<br />
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<iframe allowfullscreen="" frameborder="0" height="270" src="//www.youtube.com/embed/Gnz32BQHNTo" width="480"></iframe><br />
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Visit <b><a href="https://plus.google.com/u/0/+HenrySegerman/posts" target="_blank">+Henry Segerman</a></b> for more mathy goodness. :-) </div>
Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-37640560184172215682012-12-07T07:23:00.001-06:002016-06-09T17:18:22.168-05:00Levi's Double Dice<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqz4oSjHrqOKMOtxhyn7apLqaDE-b46HaNv8zn3mYafX9MOF2sK3KR5XfJN_U0EZB_YKefgMLYMjvW0RZNBPm9W2jJBkSpME-ZHeYvPrb4AKMgY5YBQ1XkESIVaxyiabZgF-qh5O51lus/s1600/Levi_K.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqz4oSjHrqOKMOtxhyn7apLqaDE-b46HaNv8zn3mYafX9MOF2sK3KR5XfJN_U0EZB_YKefgMLYMjvW0RZNBPm9W2jJBkSpME-ZHeYvPrb4AKMgY5YBQ1XkESIVaxyiabZgF-qh5O51lus/s200/Levi_K.jpg" width="200" /></a></div>
Just a quickie - On the new<a href="https://plus.google.com/u/0/communities/103519561214578272000" target="_blank"> G+ Gamecraft community</a> <span style="font-size: x-small;">(and communities are brand new)</span> <b><a href="https://plus.google.com/u/0/106374477644864180661/posts" target="_blank">Levi Kornelsen</a></b> asks the following:<br />
<blockquote class="tr_bq">
<span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;">Okay, so, dice mechanic thing; kind of a "little idea" I keep playing with.</span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;">Consider a character with skills like those in Skyrim - so, ranging generally from 15 - 30 to start, and up to near 100.</span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;">Now, imagine you roll 2d10, and read them as percentile </span><i style="background-color: white; font-family: arial, sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;">both ways.</i><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;"> So, 9,2 is 29 AND 92.</span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;">If you succeed (roll skill or less) one way of reading? Partial success. If you do it both ways? Complete success.</span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;">How does that hit you, overall? Gimmicky or good? </span><a class="ot-hashtag" href="https://plus.google.com/s/%23rpg" style="background-color: white; color: #3366cc; cursor: pointer; font-family: arial, sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px; text-decoration: initial;">#rpg</a><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;"> </span><a class="ot-hashtag" href="https://plus.google.com/s/%23roleplaying" style="background-color: white; color: #3366cc; cursor: pointer; font-family: arial, sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px; text-decoration: initial;">#roleplaying</a><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;"> </span><a class="ot-hashtag" href="https://plus.google.com/s/%23rpggames" style="background-color: white; color: #3366cc; cursor: pointer; font-family: arial, sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px; text-decoration: initial;">#rpggames</a><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12.800000190734863px; line-height: 14.399999618530273px;"> </span></blockquote>
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And here is what the cumulative distribution if Partial and Complete success looks like, assuming you need to roll your skill level or less, and "00" is both "0" and "100":<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWpxRjxAyn2gIzGqOSCDFGIjOJSTts8KZ3cyVMpL4WT854a2vzfOjCsraF9lA1QhNYpWXRHLE5Vaq3LS3-PTCIA670TgxwlD_um7i95y0xQBYAQvUn-sVMRvoWdwaYRzTF99mAMx2A058/s1600/Levi's+Double+Dice.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="237" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWpxRjxAyn2gIzGqOSCDFGIjOJSTts8KZ3cyVMpL4WT854a2vzfOjCsraF9lA1QhNYpWXRHLE5Vaq3LS3-PTCIA670TgxwlD_um7i95y0xQBYAQvUn-sVMRvoWdwaYRzTF99mAMx2A058/s400/Levi's+Double+Dice.png" width="400" /></a></div>
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That's it --- I said it was a quickie!<br />
Edit: Maybe the chart title should be "2D10 Double-Dice". Oh well ...<br />
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com2tag:blogger.com,1999:blog-3055805266991720601.post-30545291032178122482012-11-19T20:39:00.000-06:002012-11-19T20:40:20.384-06:001917 Russian Revolution: Why the Reds Won<div dir="ltr" style="text-align: left;" trbidi="on">
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Battletech fans, examine this photo closely:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwJNdjeX31Q9e6Epoxs4smPiUqwCMxtEl1FllYNSj7azTlkPLtPdk0m8dG7qN5ZdSjgztu_AukFUWNu5aI-Vd77rCAh7x-UTews44wj-TbnlNVR5PcqTqcx_0XSgYwlSPjr1L8JbrtyjY/s1600/1_art-TRANSFORMER3-620x349.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwJNdjeX31Q9e6Epoxs4smPiUqwCMxtEl1FllYNSj7azTlkPLtPdk0m8dG7qN5ZdSjgztu_AukFUWNu5aI-Vd77rCAh7x-UTews44wj-TbnlNVR5PcqTqcx_0XSgYwlSPjr1L8JbrtyjY/s400/1_art-TRANSFORMER3-620x349.jpg" width="400" /></a></div>
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<a href="http://www.theage.com.au/national/education/vce-authorities-apologise-for-phantom-robot-20121119-29lbl.html" target="_blank">Then go read this</a>!<br />
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<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com4tag:blogger.com,1999:blog-3055805266991720601.post-75512845488137874752012-09-21T10:57:00.001-05:002015-06-26T17:40:43.629-05:00The Grinder - September 2012<div dir="ltr" style="text-align: left;" trbidi="on">
The most recent of my collection of miscellaneous articles, which were found in my refrigerator on return from vacation.<br />
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--- --- --- <span style="font-size: large;">The Grinder</span> --- September 21, 2012 --- --- ---<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuL2DtGyycj3A-lKfB3MH63dSg8Y5vKBSf0EQA9gqG-qZdPzvnj22i9wOCRb_288V2pw5h2NtbisHDdqRMrg1Ewd6Veb50IQe8CDQwsx_4AvqIHwfs3pyjJlqI-l1TYHOmE5w6KJXoNPk/s1600/clan_box_cover_small_2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuL2DtGyycj3A-lKfB3MH63dSg8Y5vKBSf0EQA9gqG-qZdPzvnj22i9wOCRb_288V2pw5h2NtbisHDdqRMrg1Ewd6Veb50IQe8CDQwsx_4AvqIHwfs3pyjJlqI-l1TYHOmE5w6KJXoNPk/s200/clan_box_cover_small_2.jpg" width="160" /></a><br />
A little bit of Battletech history from a Mechwarrior Online interview with Jordan Weisman (source <a href="http://mwomercs.com/news/2012/09/443-jordan-weisman-interview-part-1" target="_blank">1</a>, <a href="http://mwtactics.com/forums/index.php?/topic/1050-jordan-weisman-interview-%E2%80%93-part-2/" target="_blank">2</a>):<br />
<blockquote class="tr_bq">
<b><i>MWO</i>: What was your inspiration to create BattleTech?</b><br />
<i>Jordan Weisman:</i> I had seen images and model kits from the Japanese shows Macross, Southern Cross, and Crusher Joe. I loved the visuals but wanted to create a story for them in which the Mechs where only machines, but machines that their pilots imbued with personality like we do with our warplanes, tanks, and even cars. I wanted to adapt these wonderful machines to setting that was born from Western tradition, in this case <i>a retelling the Roman Successor States</i>. And most of all, I wanted to create a game which merged the reality of tank warfare with the sci-fi/fantasy of giant suits of armor.</blockquote>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN_cMXa8Ge28Eld4XH-4g5zHf8vTiEu7O-z_8p7rlqachyphenhyphen1TrbCRzkX0M_-UIU5FZjxo_CR161mBODBgXLwbPT-2X1rqogGYR7WSfBCFdPIGq7U6-zoauhehiGOPDKAApBTzYkvIAj_CY/s1600/fClassic_BattleTech_-_A_Game_of_Armored_Combat_King_of_pain_Cover%2540150.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN_cMXa8Ge28Eld4XH-4g5zHf8vTiEu7O-z_8p7rlqachyphenhyphen1TrbCRzkX0M_-UIU5FZjxo_CR161mBODBgXLwbPT-2X1rqogGYR7WSfBCFdPIGq7U6-zoauhehiGOPDKAApBTzYkvIAj_CY/s200/fClassic_BattleTech_-_A_Game_of_Armored_Combat_King_of_pain_Cover%2540150.jpg" width="200" /></a></div>
Emphasis added: I never knew about the historical reference to the fall of Rome. Parts of the Battletech universe story line makes more sense to me now <span style="font-size: x-small;">(not <i>much</i> more sense, but hey, it's Battletech)</span>.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGmSwNcWkT9vz1xUi4BXIWjtXGG43mIkbSdcZ2_ildOBMtA0AQ87grF5bYdAoOdh71nFi-C4A9W7LglIFY6ix44U-T6_qGRya0aq8eRaSrakkU1_X4Twkm2G5xlY8Jo0ryyaHAl14RYI4/s1600/how+to+paint+shades+of+pink+armour.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="156" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGmSwNcWkT9vz1xUi4BXIWjtXGG43mIkbSdcZ2_ildOBMtA0AQ87grF5bYdAoOdh71nFi-C4A9W7LglIFY6ix44U-T6_qGRya0aq8eRaSrakkU1_X4Twkm2G5xlY8Jo0ryyaHAl14RYI4/s200/how+to+paint+shades+of+pink+armour.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">image: <a href="http://fromthewarp.blogspot.com/2012/09/the-flawless-host-and-how-to-paint-pink.html" target="_blank">From The Warp</a></td></tr>
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<a href="http://fromthewarp.blogspot.com/2012/09/the-flawless-host-and-how-to-paint-pink.html" target="_blank"><b>Painting Pink</b> - From the Warp</a> -- A nice little tutorial on an often misunderstood color. --><br />
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<span style="font-size: x-small;">(Some of you may recall my own <a href="http://giantbattlingrobots.blogspot.com/2010/02/pink-explosion.html" target="_blank">misadventure with this lovely hue.</a>)</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJLiJX_HrKlWnLZUdFoVMI3Tp9GpIKdHYgtk6XJ3Mi2cBIrj3EHhyphenhyphenSf2Kwn3fbfoCVZao-3ewj0oQEoJbDKVLwFnTORl3LaP9ZhO-E9FqqgN-ibhII8NLP-03fFOmRn4hkq1tPXDVELvQ/s1600/node-design2.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="80" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJLiJX_HrKlWnLZUdFoVMI3Tp9GpIKdHYgtk6XJ3Mi2cBIrj3EHhyphenhyphenSf2Kwn3fbfoCVZao-3ewj0oQEoJbDKVLwFnTORl3LaP9ZhO-E9FqqgN-ibhII8NLP-03fFOmRn4hkq1tPXDVELvQ/s320/node-design2.jpg" width="320" /></a></div>
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<div style="text-align: center;">
<a href="http://thealexandrian.net/wordpress/7949/roleplaying-games/node-based-scenario-design-part-1-the-plotted-approach" target="_blank">Node-Based Scenario Design</a> -</div>
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<a href="http://thealexandrian.net/" target="_blank">The Alexandrian</a> </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO6Q3f0AwxCfuSueeR0R33g85N2ziaKQ8TOOP4RRtQhfLZgUe50dYnILzhKOQF70JQ0aGFiqM6JMZ2yifOaIXFQkA9XXmA_LGi9L6aHcOIca0VCkz72PRA2bWH6Ljyh4yA9rmagnq8Ccg/s1600/playing_world.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO6Q3f0AwxCfuSueeR0R33g85N2ziaKQ8TOOP4RRtQhfLZgUe50dYnILzhKOQF70JQ0aGFiqM6JMZ2yifOaIXFQkA9XXmA_LGi9L6aHcOIca0VCkz72PRA2bWH6Ljyh4yA9rmagnq8Ccg/s200/playing_world.jpg" width="138" /></a>From <a href="http://www.wired.com/geekdad/2012/09/new-d-d-history-book/" target="_blank">WIRED</a>: An interview with <b>Jon Peterson</b>, author of <a href="http://www.wired.com/geekdad/2012/09/new-d-d-history-book/" target="_blank">Playing at the World</a>. I <i>want</i>.<br />
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<a href="http://playingattheworld.blogspot.com/" target="_blank">Web site for the book</a>, and the <a href="http://www.amazon.com/Playing-at-World-Jon-Peterson/dp/0615642047" target="_blank">Amazon page</a>.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-FKH-jLQkdzeDAQhVkPV8wLZHpKg0yxvyBJ13T2PvBxbwZSP61hTdHhZncO_ug-aFvoCW2VSQle356MygkjldJwck3otYyKVYmAQxChkQMgkyfyDcQdKWAuDoat3ZGud9fSCkH_Evp-w/s1600/Sudoku+richter+scale.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-FKH-jLQkdzeDAQhVkPV8wLZHpKg0yxvyBJ13T2PvBxbwZSP61hTdHhZncO_ug-aFvoCW2VSQle356MygkjldJwck3otYyKVYmAQxChkQMgkyfyDcQdKWAuDoat3ZGud9fSCkH_Evp-w/s320/Sudoku+richter+scale.png" width="320" /></a>From <a href="http://www.technologyreview.com/" target="_blank">Technology Review</a>:<br />
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<a href="http://www.technologyreview.com/view/428729/mathematics-of-sudoku-leads-to-richter-scale-of/" target="_blank">Mathematics of Sudoku Leads To </a><a href="http://www.technologyreview.com/view/428729/mathematics-of-sudoku-leads-to-richter-scale-of/" target="_blank"></a><a href="http://www.technologyreview.com/view/428729/mathematics-of-sudoku-leads-to-richter-scale-of/" target="_blank">"Richter Scale" </a><a href="http://www.technologyreview.com/view/428729/mathematics-of-sudoku-leads-to-richter-scale-of/" target="_blank">of Puzzle Hardness</a></div>
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There might be some studying in my future, if I want figure this one out.<br />
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And now it's time to go clean out the 'Fridge, and maybe shave.<br />
~
<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}">
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-60541113449227560242012-03-18T08:29:00.000-05:002012-03-18T08:29:00.040-05:00History of Wargaming Videos<div dir="ltr" style="text-align: left;" trbidi="on">
I have previously mentioned <b><a href="http://www.wargaming.co/index.htm" target="_blank">John Curry's History of Wargaming Project</a></b>, mostly in reference to <a href="http://giantbattlingrobots.blogspot.com/2011/04/fletcher-pratts-naval-wargame.html" target="_blank">Fletcher Pratt's Naval Wargame</a> (FPNW). I just discovered a series of <a href="http://www.youtube.com/user/john9uk" target="_blank">YouTube videos from John Curry</a>, and I am working my way through them. This will be a brief review, and maybe serve as a launch point for your own exploration.<br />
--- More after the fold. ---<br />
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<a name='more'></a><br />
History of Wargaming Project, part 1<br />
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/HmpUwvQ70v8" width="420"></iframe>
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John Curry discusses the beginning of the History of Wargaming project, and tells the story of how he recovered the materials for <a href="http://giantbattlingrobots.blogspot.com/2011/04/fletcher-pratts-naval-wargame.html" target="_blank">Fletcher Pratt's Naval Wargame</a>. Also a bit about <b>Jim Dunnigan</b> (<a href="http://www.strategypage.com/jfdbooks/default.asp" target="_blank">1</a>,<a href="http://en.wikipedia.org/wiki/Jim_Dunnigan" target="_blank">2</a>), and <a href="http://boardgamegeek.com/boardgame/8833/firefight" target="_blank"><b>SPI's</b> Firefight</a>. His style is a bit rambling, but he seems to have done good research. Lot of interesting stories here.<br />
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History of Wargaming Project, part 2<br />
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/yGzdVw2lRIo" width="420"></iframe>
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John Curry discussed wargaming history, and wargaming present.<br />
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Fletcher Pratt's Naval Wargame, part 1/5 <br />
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/1K_TMVO3OIM" width="420"></iframe>
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John Curry giving a presentation on FPNW. At 2:20s there is mention of Jim Dunnigan, which is a connection between FPNW and modern games that Ihave been looking for.<br />
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Fletcher Pratt's Naval Wargame, part 2/5<br />
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/CkZJsz259t4" width="420"></iframe>
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The story of the hunt for FPNW, the people involved, lost rules rediscovered,<br />
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Fletcher Pratt's Naval Wargame, part 3/5<br />
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/_SOBV7BtiPg" width="420"></iframe>
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Decline of interest following World War II. FPNW for simulation and training at US Naval War College..<br />
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Fletcher Pratt's Naval Wargame, part 4/5<br />
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/hOLU57A0zYU" width="420"></iframe><br />
Strategic aspects. Formula for ship value. The deterministic model.<br />
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Fletcher Pratt's Naval Wargame, part 5/5<br />
<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/RsDN0Rjirh4" width="420"></iframe><br />
The multiplayer game. Fred Jane's and Fletcher Pratt's games as used for training. Question and answer.<br />
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Wargaming and gaming in general are just beginning to receive attention as a topic of serious study. For most of us it's just a hobby - a way to pass some time. It's easy to think that our favorite games are new and innovative, but there really is a lot that has gone before. I'm glad there are people making the effort to preserve this history.<br />
<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-55900966632440978832012-03-16T22:04:00.000-05:002012-03-16T22:12:56.658-05:00The Grinder - March 2012<div dir="ltr" style="text-align: left;" trbidi="on">
Haven't done this for a while, so there is a lot of grist for the mill. <br />
Also, <a href="https://plus.google.com/u/0/b/116786504371944266405/" target="_blank"><b>GBR</b> has a Google+ page</a>.<br />
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<b><span style="font-size: large;">--- The Grinder, March 16, 2012 ---</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVBtreMpraG9jssYC5mZgr1hAHIV6S9iyEoWtS-ksAwMzZkwEpNOgKZ3JSlY525kcYwI55erRn35G4n7y4qYbtabn6JChUru-rvjr6HOy9f0XERqJWMZ7kLIMzlCDU9b9yGGoM_XRPus0/s1600/tumblr_proof_dice_sculpture.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVBtreMpraG9jssYC5mZgr1hAHIV6S9iyEoWtS-ksAwMzZkwEpNOgKZ3JSlY525kcYwI55erRn35G4n7y4qYbtabn6JChUru-rvjr6HOy9f0XERqJWMZ7kLIMzlCDU9b9yGGoM_XRPus0/s200/tumblr_proof_dice_sculpture.jpg" width="132" /></a>Dice Sculptures, via <a href="http://proofmathisbeautiful.tumblr.com/post/12226136932/ianbrooks-dice-sculptures-by-tony-cragg" target="_blank">P<b>roof Math is Beautiful</b></a><br />
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Three recently released books from <b>John Curry's</b><br />
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<b><a href="http://www.wargaming.co/index.htm" target="_blank">History of Wargaming Project</a></b>:</div>
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1. <a href="http://www.wargaming.co/books/featherstonetankvol4/homepage.htm" target="_blank">Donald Featherstone's Tank Battles in Miniature Vol 4</a><br />
2. <a href="http://www.wargaming.co/books/ewvol1/homepage.htm" target="_blank">The Wargame Pioneers</a><br />
3. <a href="http://www.wargaming.co/books/innovations/homepage.htm" target="_blank">Innovations in Wargaming</a><br />And a <a href="http://www.youtube.com/watch?v=HmpUwvQ70v8" target="_blank">video</a>, the first of a series = a future post topic.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsrNMcMHTl1AvsoIPHM_iKDsPkYn7pwcTJp6cX3sEyin6vjBStPZeQG8xrc4n_WkDeD3uYSmpyr4qZSQ4BHOX2VQ8DN0c218MiypGxFA58B53iFJ06bilYfVEGoBtR4ttFKGAvxe2_-3M/s1600/tetris_fail-12823.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsrNMcMHTl1AvsoIPHM_iKDsPkYn7pwcTJp6cX3sEyin6vjBStPZeQG8xrc4n_WkDeD3uYSmpyr4qZSQ4BHOX2VQ8DN0c218MiypGxFA58B53iFJ06bilYfVEGoBtR4ttFKGAvxe2_-3M/s200/tetris_fail-12823.jpg" width="160" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-size: xx-small;">www.graphicshunt.com</span></td></tr>
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Why you think you are good at something (when you really aren't).<br />
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<blockquote class="tr_bq">
From <b>The Psychology of Video Games</b>:<br />
<a href="http://www.psychologyofgames.com/2012/03/the-dunning-kruger-effect-and-multiplayer-games/" target="_blank">The Dunning-Kruger Effect and Multiplayer Games</a></blockquote>
More on <a href="http://feedproxy.google.com/~r/ImprobableResearch/~3/JSVTTtM74LI/" target="_blank">Dunning-Kruger at Improbable Research</a>.<br />
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**** <a href="http://en.wikipedia.org/wiki/World's_funniest_joke" target="_blank">The World's Funniest Joke</a> ****<br />
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Eighteen (<b>!!!</b>) years in the making. This is love of miniatures!<br />
<b>Toy Soldiers Forever</b>: <a href="http://toysoldiersforever.blogspot.com/2012/02/old-third-all-present-or-accounted-for.html" target="_blank">The "Old Third": All Present or Accounted For</a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2M1QZLS3ADlxIvX1fkMeW_ar8eJffCySza4kOlXQXt1JuzjVL15jnKAzU6ZI4nSiuE8HRxdyTTp3AsSbZ8mmZWnm0buLJdgVYTyLuOWInMbeHX1TIM2lvmM0zpL9PYKm-WJRo0LvxVdE/s1600/kefko.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2M1QZLS3ADlxIvX1fkMeW_ar8eJffCySza4kOlXQXt1JuzjVL15jnKAzU6ZI4nSiuE8HRxdyTTp3AsSbZ8mmZWnm0buLJdgVYTyLuOWInMbeHX1TIM2lvmM0zpL9PYKm-WJRo0LvxVdE/s1600/kefko.gif" /></a></div>
Via <b><a href="http://grognews.blogspot.com/2012/03/make-your-own-counters-online.html" target="_blank">GrogNews</a></b>:<br />
<a href="http://zho.berka.com/rules/war/tank_counter.html" target="_blank">Make your own game counters online</a><br />
and<br />
<a href="http://grognews.blogspot.com/2012/03/battle-lab-warfighter-101-designers.html" target="_blank">Warfighter 101 Designer's Notes</a> (a great read)<br />
and<br />
<a href="http://grognews.blogspot.com/2012/02/random-friday-wargaming-cod-wars.html" target="_blank"><i>something fishy</i></a>.<br />
<br />
<br />
Maybe this should just be the <b>GrogNews</b> edition of the <b>Grinder</b><br />
Via <b><a href="http://grognews.blogspot.com/" target="_blank">GrogNews</a></b>: <a href="http://grognews.blogspot.com/2012/01/following-up-on-last-weeks-gametalk.html" target="_blank">Games and Simulations, with Dr. James Sterrett</a><br />
<br />
<b>Gamasutra</b>: <a href="http://www.gamasutra.com/view/feature/6549/how_tough_is_your_game_creating_.php" target="_blank">How tough is your game? Creating Difficulty Graphs</a><br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><span style="text-align: left;">The relationship between cubes and hexagons, animated.</span> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgB3_KnHnO_Gsr_lOr6aAPetsDG2emHTlpIgUKiImjAV7E5CWXG9DXGcoDQgy8cbj5-SAkwFrxRyBqKfxbvtu3Rv9KNnUPlohrnaj9pJtBdGKHVaHxhNR93y9ZQ3exe6akHhmeea4mzvmM/s1600/tumblr_lvbsbjxqd61qfg7o3o1_400.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgB3_KnHnO_Gsr_lOr6aAPetsDG2emHTlpIgUKiImjAV7E5CWXG9DXGcoDQgy8cbj5-SAkwFrxRyBqKfxbvtu3Rv9KNnUPlohrnaj9pJtBdGKHVaHxhNR93y9ZQ3exe6akHhmeea4mzvmM/s320/tumblr_lvbsbjxqd61qfg7o3o1_400.gif" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">from <a href="http://proofmathisbeautiful.tumblr.com/post/13785284615" target="_blank"><b>Proof</b></a> (Math is Beautiful)</td></tr>
</tbody></table>
These posts are fun, I should do them more often. ;-)<br />
<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>
</div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-19230447103645644392012-03-11T21:27:00.005-05:002012-03-11T21:27:52.682-05:00Hot Topic: Battlemechs Dropped from Orbit<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMON7_0HTbKvf8XZu2Ts20yic9hV8gIc14puR4x2yTGtErlW36TB1760XIPCBjl8iBvOqaefzOhCKs324MdovVMAaGeXzMS2NB7pYkG8GKghpA6ztkciyg-EfPeaCtShV8kZXOzmOLo4k/s1600/gundam7.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="133" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMON7_0HTbKvf8XZu2Ts20yic9hV8gIc14puR4x2yTGtErlW36TB1760XIPCBjl8iBvOqaefzOhCKs324MdovVMAaGeXzMS2NB7pYkG8GKghpA6ztkciyg-EfPeaCtShV8kZXOzmOLo4k/s200/gundam7.png" width="200" /></a>This happens in the cartoons, and in the occasional Battletech scenario, where a battlesuit/battlemech drops from orbit; these folks say it will get <i>a little bit warm</i> on the way down.<br />
<br />
<blockquote class="tr_bq">
<b>Journal of Physics Special Topics<br /><a href="https://physics.le.ac.uk/journals/index.php/pst/article/view/443/304" target="_blank">P2_7 Mobile Suit Gundam: Falling From Space</a></b><br />
R. Hall, A. West, M. McHugh, J. Blake,<br />
Department of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH.<br />
November 30, 2011<br />
<i>Abstract<br />This paper explores the upper limits of the active cooling system on board a Mobile Suit from the Gundam series as it goes through atmospheric re-entry. A Mobile Suit falling through the Earth’s atmosphere experiences drag forces of nearly 10,000 kN. The increase in temperature due to the resistive drag forces felt upon re-entry would require an active cooling system with an output of 112MW which is over 37 times greater than known power outputs on board Mobile Suits.</i></blockquote>
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhioYvUGjE4hzx8eqel0cDXVi8YacrUL987bdl6L9cf38qRGa849Q1Ee0-TYASYAwLCge_y9FRzVwgWqfeiHsycpjW1LLXPtoqEYbhZ10Nm9o_xmWxGe1DOKnROXPmxLmP1IfIpjh9f0Zc/s1600/ms_gundam_a.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhioYvUGjE4hzx8eqel0cDXVi8YacrUL987bdl6L9cf38qRGa849Q1Ee0-TYASYAwLCge_y9FRzVwgWqfeiHsycpjW1LLXPtoqEYbhZ10Nm9o_xmWxGe1DOKnROXPmxLmP1IfIpjh9f0Zc/s200/ms_gundam_a.gif" width="165" /></a></div>
That's going to go over 30 on the heat scale. I also see they don't take into account any heat generated by deceleration, which means either more heat, or a very sudden stop. ;-)<br />
<br />
The full article is a short exploration into some fun physics - <a href="https://physics.le.ac.uk/journals/index.php/pst/article/view/443/304" target="_blank">find it here</a>.<br />
<br />
<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com3tag:blogger.com,1999:blog-3055805266991720601.post-65898300214592622542012-03-09T07:37:00.000-06:002012-03-09T14:07:06.940-06:00Battletech Cake<div dir="ltr" style="text-align: left;" trbidi="on">
A nice surprise treat at the Wednesday Battletech night:<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM-5zQaPGJtCIq0s410iAOEA00lZuFprvGCKItiqssexsLwFUBokjF2JPDrRZJIda_h6aT8abnQnoRhOcHiJZN2mC_u3YJQDf-yU42Kty08MiVnQ4wLr89c1TLCZM0SKr1sWy40JZP5aY/s1600/IMG_0040.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="249" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM-5zQaPGJtCIq0s410iAOEA00lZuFprvGCKItiqssexsLwFUBokjF2JPDrRZJIda_h6aT8abnQnoRhOcHiJZN2mC_u3YJQDf-yU42Kty08MiVnQ4wLr89c1TLCZM0SKr1sWy40JZP5aY/s320/IMG_0040.JPG" width="320" /></a></div>
<br />
A creation of the talented Mrs. <b>D</b>. All the guys were really impressed.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDm75NeSDSbxWhXMpJTlP-Vx_hzB-e0szUmErNreA1-rxv3mSBn4qfp_Uf7Yo3rTuY0YnAo5_T3-x72Uy_1h3ERq5PELMDEjYjmAyfymS-sEfiP2IAXryGLF7mF30EpMEcSEY4bHUZyqk/s1600/IMG_0043.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="177" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDm75NeSDSbxWhXMpJTlP-Vx_hzB-e0szUmErNreA1-rxv3mSBn4qfp_Uf7Yo3rTuY0YnAo5_T3-x72Uy_1h3ERq5PELMDEjYjmAyfymS-sEfiP2IAXryGLF7mF30EpMEcSEY4bHUZyqk/s320/IMG_0043.JPG" width="320" /></a></div>
If I has known in advance, I would have carefully cleaned up a few miniatures and posed them on top. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOhEEMJbDQAZrdOjLDIZbF1ADZxCJyaRuRuOlIzOkNvywVMFrunxlwi-DmJUAJG8ucyk9wL1Qfbfx2fA1zCWl6bGn5FeYJLcQdODJbksGRT-Fkk-X8NwO-XcL9n1LYbhyphenhyphend4ShYfbBUzVg/s1600/IMG_0042.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOhEEMJbDQAZrdOjLDIZbF1ADZxCJyaRuRuOlIzOkNvywVMFrunxlwi-DmJUAJG8ucyk9wL1Qfbfx2fA1zCWl6bGn5FeYJLcQdODJbksGRT-Fkk-X8NwO-XcL9n1LYbhyphenhyphend4ShYfbBUzVg/s320/IMG_0042.JPG" width="277" /></a></div>
<br />
You may be asking yourself the same question I asked myself, <i>"Does the cake taste as good as it looks?"</i><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvHdt9aL8apoSrjVmZ9qh-exS7XFAml2ECvG4biX8DU1I8DrbHdcQ1f2JeqiBa-jDOwD7PHkQr-peg-nXxgvjhjESrzLY81mGhwBJNP74alWoBhzi6Y2EIzCu6od5SHOwh_yVJ47kH91g/s1600/IMG_0044.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvHdt9aL8apoSrjVmZ9qh-exS7XFAml2ECvG4biX8DU1I8DrbHdcQ1f2JeqiBa-jDOwD7PHkQr-peg-nXxgvjhjESrzLY81mGhwBJNP74alWoBhzi6Y2EIzCu6od5SHOwh_yVJ47kH91g/s320/IMG_0044.JPG" width="255" /></a></div>
<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601"><br /></a><br />
To which the answer is <b>"YES."</b><br />
<b><br /></b><br />
<b>UPDATE: </b><br />
<blockquote class="tr_bq">
<b>Nate D.</b> informs me<b>: </b><b><span class="Apple-style-span" style="border-collapse: collapse; color: #222222; font-family: arial, sans-serif; font-size: 13px; font-weight: normal;">Thank you for posting those. She was glad to hear that it wasn't just me who thought it was great. It's somewhere between semi-pro & a hobby for her, but if anyone needs a cake for any reason her email is [***]. She does have a portfolio of previous cake designs if anyone's looking for inspiration.</span></b></blockquote>
<b><span class="Apple-style-span" style="border-collapse: collapse; color: #222222; font-family: arial, sans-serif; font-size: 13px; font-weight: normal;">*** I chose not to publicly post the email. Contact me if you want to be put in touch.</span></b><br />
<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com7tag:blogger.com,1999:blog-3055805266991720601.post-37941195002230645092012-03-06T18:08:00.004-06:002012-03-06T18:09:54.357-06:00Special Request: Battletech in the Annapolis MD area<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioyRDFjckcSyPxJB0leKUAh7IvgajOeYGS3XwKfBZgwEDXu-1DfNhyphenhyphenduMNqg1wFVDWmKNBL4xH1hNiNmOu0FfCkRN_YoPL3OdEwtA-bQen4-ZKh-od_mZTaqmR-kjl4ycDHEsE3yvdBy8/s1600/150px-Battletech_20Year_Transparent.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioyRDFjckcSyPxJB0leKUAh7IvgajOeYGS3XwKfBZgwEDXu-1DfNhyphenhyphenduMNqg1wFVDWmKNBL4xH1hNiNmOu0FfCkRN_YoPL3OdEwtA-bQen4-ZKh-od_mZTaqmR-kjl4ycDHEsE3yvdBy8/s1600/150px-Battletech_20Year_Transparent.gif" /></a><b>John F.</b> sends me a request:<br />
<blockquote class="tr_bq">
<span class="Apple-style-span" style="font-family: arial; font-size: large;">I'm looking to play more Battletech and Battleforce but haven't been able to find too many players in the <a href="http://maps.google.com/maps?hl=en&pwst=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&biw=1063&bih=608&q=annapolis+MD&um=1&ie=UTF-8&hq=&hnear=0x89b7f66570672fd5:0x43f854fdd3a8274b,Annapolis,+MD&gl=us&ei=1qNWT6nUDsGWgweupoSzCg&sa=X&oi=geocode_result&ct=title&resnum=2&ved=0CEEQ8gEwAQ">Annapolis area</a>. Any chance you could point me to some locals on the East of I-95 side that are looking for another gamer?</span></blockquote>
<span class="Apple-style-span" style="font-family: arial; font-size: x-small;">Can anyone help him out? Post here or email me and I will put you in touch.</span><br />
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<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>
</div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com1tag:blogger.com,1999:blog-3055805266991720601.post-2985661747962298092012-02-18T23:03:00.001-06:002012-02-18T23:20:09.885-06:00Sword and Dragon: After the Dust UP<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCJLz9bmPRDhMxvTZtTxtqLLaEjGG8vtrFjZU5UZV92qRZFA9U-5AGiaMCEUJoD4HfzcagUmmDY3V_c632l9p2mGMjL7nlH2LUwddMNT5rIS1XtmBFvXnIHp6uvt5Ixz7qKV9TNPxz3fQ/s1600/Sword%252BDragon-cover_150.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCJLz9bmPRDhMxvTZtTxtqLLaEjGG8vtrFjZU5UZV92qRZFA9U-5AGiaMCEUJoD4HfzcagUmmDY3V_c632l9p2mGMjL7nlH2LUwddMNT5rIS1XtmBFvXnIHp6uvt5Ixz7qKV9TNPxz3fQ/s320/Sword%252BDragon-cover_150.jpg" width="246" /></a></div>
Today a follow up on our local Battletech sessions. We had been playing through the Sword and Dragon Starterbook scenarios, and this past Wednesday we finally finished the last scenario: <i>Dust Up</i>. I <a href="http://giantbattlingrobots.blogspot.com/2010/12/battletech-sword-and-dragon-sessions.html">wrote about these sessions</a> over a year ago, and despite the problems we managed to soldier through to the final mission. Our group is very persistent about playing scenario packs through to the end.<br />
<br />
No, we haven't been playing these the whole time, we took several breaks, the most recent from mid-November to the start of this final mission, which played out these past three weeks. In the interim we played a few <i>Grinders</i> and some scenarios out of <a href="http://www.amazon.com/Tales-Black-Widow-Company-Battletech/dp/0931787653">Tales of the Black Widow Company</a>. I know I was <a href="http://giantbattlingrobots.blogspot.com/2010/12/battletech-sword-and-dragon-sessions.html">critical</a> of the Sword and Dragon scenarios, but it anything some of these TBWC scenarios are worse. But I digress.<br />
<br />
In the course of the Sword and Dragon scenarios we made a few discoveries that are worth sharing (I hope).<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPxqYG7mm2LNgn76QlbdEfYAdWUivkoICLGp9hlcC6pFHXoODU9mW-PcSw1DEBjkNCHuqJe-BKanUQRkwK-DuNYVNHadTckStIi9TgV2T4z_jY_KEbGHMLnPqEE-4q3AEg7y9b0RwSopY/s1600/Total_Warfare_Panorama%2540640x480.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPxqYG7mm2LNgn76QlbdEfYAdWUivkoICLGp9hlcC6pFHXoODU9mW-PcSw1DEBjkNCHuqJe-BKanUQRkwK-DuNYVNHadTckStIi9TgV2T4z_jY_KEbGHMLnPqEE-4q3AEg7y9b0RwSopY/s200/Total_Warfare_Panorama%2540640x480.jpg" width="200" /></a>Who won the final battle? Technically McKinnon's Raiders, but it was never a fair fight, and the Sabres make a good show of it. The bias towards the Davion forces, primarily in pilot skills and abilities was apparent from the beginning and carried through to the final mission. This helped the Raiders come out a little ahead on WP after every mission, leading to bigger and better mechs much sooner than the Sabres, and magnifying the advantage.<br />
<br />
Some of the more powerful pilot abilities that make the characters so special might be fun once, or even occasionally, but used all the time are just silly. We got the feeling the S&D book was written by people who only play Battletech a few times a year, rather than by anyone who actually plays on a regular basis. Battletech should always be about the mechs, with only a very few pilots that really stand out. A single company where half the pilots have outrageously useful special abilities was a bad idea.<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN_cMXa8Ge28Eld4XH-4g5zHf8vTiEu7O-z_8p7rlqachyphenhyphen1TrbCRzkX0M_-UIU5FZjxo_CR161mBODBgXLwbPT-2X1rqogGYR7WSfBCFdPIGq7U6-zoauhehiGOPDKAApBTzYkvIAj_CY/s1600/fClassic_BattleTech_-_A_Game_of_Armored_Combat_King_of_pain_Cover%2540150.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN_cMXa8Ge28Eld4XH-4g5zHf8vTiEu7O-z_8p7rlqachyphenhyphen1TrbCRzkX0M_-UIU5FZjxo_CR161mBODBgXLwbPT-2X1rqogGYR7WSfBCFdPIGq7U6-zoauhehiGOPDKAApBTzYkvIAj_CY/s200/fClassic_BattleTech_-_A_Game_of_Armored_Combat_King_of_pain_Cover%2540150.jpg" width="200" /></a>Those quirky mechs in the books, the ones that malfunction in such interesting ways, were the first things we sold off. If your want to write a scenario book with quirky mechs, some of those quirks must be worth keeping around. The most obvious way to do this would be to tie some of the pilot abilities to only work in combination with their quirky mechs. This would have helped with some of the game balance issues too.<br />
<br />
When the player forces (McKinnon's Raiders or Sorenson's Sabres) are up against a randomly determined OpFor, it's usually a very one sided battle. Often the best the OpFor player can do is try to get some damage on every player mech, forcing them to spend more Warchest Points for repairs, and slowing their progress in future missions. This sort of game might be OK to introduce new players to the game in a scenario they can win, but new players on the OpFor side are going to get bored and quit. In our group of veteran players, it was sometimes a challenge to see how you could do in a losing effort. Other times we played crazy-aggressive, charging forward into fire in an effort to end the scenario quickly.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgym80RtNcoqsy8xjhyOklCiuPZC-AVNNwlI_tTDUu9yDM8zx8sTnE6YtLz-LZAHuLXF0dPrYvM2KuFZtJjA5oZwwfJhiJ9ceTgnO2qoVMF0KT7kXsek9Hh0sv8gQw7oBTtgYyvOCqwcCY/s1600/BattleTech_Record_Sheets_3060_cover%2540150.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgym80RtNcoqsy8xjhyOklCiuPZC-AVNNwlI_tTDUu9yDM8zx8sTnE6YtLz-LZAHuLXF0dPrYvM2KuFZtJjA5oZwwfJhiJ9ceTgnO2qoVMF0KT7kXsek9Hh0sv8gQw7oBTtgYyvOCqwcCY/s1600/BattleTech_Record_Sheets_3060_cover%2540150.jpg" /></a>That's not to say the players <i>always</i> win. In several battles the OpFor was able to pull out a victory by luck or choosing the scenario setup to be especially difficult for the player force. In one particularly memorable defeat, our augmented recon lance (6 mechs) got their asses handed to them after the OpFor rolled 4 assault mechs, 2 heavies, and with veteran skills. If the post game discussion we determined that even our heaviest mechs might not have won.<br />
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In between scenarios we always had enough WP for repairs, and generally enough left over for a little new equipment or mechs. What both teams had trouble with was pilot hits. Pilots heal one hit if they sit out for a scenario, but after playing 3-4 missions we started to accumulated many injuries, and running out of healthy pilots. Our solution was to hire extra pilots and outfit a replacement lance with salvaged mechs, giving the regular pilots more time off. Even this wasn't enough, and after out summer break to play the "historical" scenarios from the new map pack, our GM declared all pilots to be fully healed.<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDL1VIei3LV-cKU0FVHZjyZ88zhrTuv1EeVvhZl2d1xPawX3yl9IKh3aTp8KxhSdji3UJRyS5o78kVUp1ZIst7BXlgV0obDFsxv1YCm1FqIwlglKlG-nxomHNloi5UNAFZYPlDgqhelHU/s1600/Classic_BattleTech_Technical_Readout_Project_Phoenix_Cover%2540150.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDL1VIei3LV-cKU0FVHZjyZ88zhrTuv1EeVvhZl2d1xPawX3yl9IKh3aTp8KxhSdji3UJRyS5o78kVUp1ZIst7BXlgV0obDFsxv1YCm1FqIwlglKlG-nxomHNloi5UNAFZYPlDgqhelHU/s1600/Classic_BattleTech_Technical_Readout_Project_Phoenix_Cover%2540150.jpg" /></a><br />
That wasn't the only problem with pilot hits, over time there were casualties. The characters/pilots Daniel Sorenson AND Ian McKinnon (both Company commanders) died; taking kicks to the head after their mechs had fallen. After McKinnon's death, for obscure reasons, the Raider's were renamed "Lenny's Lemmings".<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik7adPW_OHOpqQRaWpVa8LQascrb2qW1faIdhRpFndBZr5ooMGDWGgwwNekUV1njl0IZuecvVS9Mm-EhALchKmSzTU0Ufzy79Ql-T-HjcjELuTTVlSrD4ZJ4BXmy0soWGWjc6SYa9q79o/s1600/CityTech_Cover%2540150.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik7adPW_OHOpqQRaWpVa8LQascrb2qW1faIdhRpFndBZr5ooMGDWGgwwNekUV1njl0IZuecvVS9Mm-EhALchKmSzTU0Ufzy79Ql-T-HjcjELuTTVlSrD4ZJ4BXmy0soWGWjc6SYa9q79o/s1600/CityTech_Cover%2540150.jpg" /></a>Despite the problems I keep rumbling on <span style="font-size: x-small;">(and on and on ...)</span> about, one good thing that has come of this. We have nearly twice the number of regular players attending the weekly games now as we had a year ago. I think the focus on (mostly) old school Battletech has brought a lot of players back, and it's certainly nice to see the <i>Singapore Longshoremen</i> back up to full unit strength.<br />
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Later this month we begin playing the <a href="http://www.amazon.com/Starterbook-Wolf-Blake-Catalyst-Game/dp/1934857076">Wolf and Blake Starterbook</a>, and we are already making plans to correct many of the problems we had with Sword and Dragon. Look for some posts on this topic in the coming months.<br />
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</div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com5tag:blogger.com,1999:blog-3055805266991720601.post-63040507966591363772012-02-09T23:22:00.000-06:002015-06-26T17:47:20.309-05:00Conditional Dice Rolls with Partial information<div dir="ltr" style="text-align: left;" trbidi="on">
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Last time I wrote about <a href="http://giantbattlingrobots.blogspot.com/2012/02/conditional-dice-rolls.html">Conditional Dice Rolls</a>, or using conditional probability to correct the results of an earlier roll that was made incorrectly. The rest of this will make more sense if you read that first. <br />
To do this you need to know 2 things --- You need to know what the probability of success for your first roll, and what that probability should have been. But wait, there is one more thing, an important assumption I rather glossed over last time --- You need to have completely forgotten <i>everything</i> about the first roll <i>except</i> that you succeeded or failed.<br />
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And that's harder than you might think. ---> More after the fold ---><br />
<a name='more'></a><br />
This post is perhaps more philosophical than mathematical, because it has more to do with things that you can honestly remember, rather than a clear-cut way to fix a problem. Many players are remarkably good at remembering their dice rolls. Battletech players tend to note when they roll 2's and 12's, which is not surprising since those numbers sometimes lead to a little extra mayhem. But some events are more memorable than others. Consider the following:<br />
<blockquote class="tr_bq">
Example 4: Dan rolled and hit with two medium lasers needing 7+ on 2d6. Later he realizes the base of the Jenner miniature he was shooting at obscured a light woods (a +1 modifier), and he should have rolled with 8+ to-hit. Dan then approaches Scott to correct his mistake. Scott notes, "I remember that one of the dice was a six."</blockquote>
Now we have broken the last assumption, because Scott remembered some information about what was rolled. That's OK though, because we can use this partial information as part of the correction.<br />
<blockquote class="tr_bq">
Example 4 continued: Dan sets down one die showing a 6, and rolls the other one. If he rolls a 2 or more the result will remain a hit (8+), but will change to a miss if he rolls a 1 (6+1=7).</blockquote>
Here the recollection that one of the dice was a 6 mean the conditional re-roll is very likely to succeed (remain a success). If Scott recalled one die was a 2, then the conditional result would stay a success only if the other on a 6 (5 or less changes to a miss). In general, if you remember any bit of information about what the original die roll was, then you can make use of it.<br />
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Now here is where things get a little fuzzy for me. If as in the example, one of the dice showed a 6, it seems unlikely that the other dice was also a 6. If I had rolled "12" then I would probably have remembered that. This is true even without Scott's recall of a 6, because if I had rolled a 12 in the first place, I am more likely to remember it. Therefore, I probably did not roll a 12, and maybe I should exclude a 12 result from my re-roll and take this into account. But now we are on a slippery slope, because if I'm pretty sure I didn't roll a 12, then maybe I didn't roll as high as 11 either, or 10 ...<br />
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In other words maybe the conditional re-roll I described in my last post isn't quite fair either, because it pretends that you really don't remember anything at all. I may still be getting away with a slightly higher probability of hitting than I should.<br />
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This is more of a philosophical problem, but I have a good answer for it in the form of a basic gaming table rule. When it comes to games and mistakes made during play, it's just good sportsmanship it admit the mistake and attempt to make it right with the other player. Further, the person who goofed should expect to pay a bit of a penalty for it. In this case, the conditional dice roll should attempt to partly correct the mistake, but stop short in favor of the other player.<br />
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Here is my suggestion. Always assume the original roll was no higher than what was needed, and ignore and numbers above that in the conditional re-roll.<br />
<blockquote class="tr_bq">
Example 5: Dan rolled and hit with two medium lasers needing 7+ on 2d6. Later he realizes the base of the Jenner miniature he was shooting at obscured a light woods (a +1 modifier), and he should have rolled with 8+ to-hit. Dan then approaches Scott to correct his mistake. He rolls for the first laser until he gets a 7 or an 8 (not a 9, 10, 11, or 12!), and it eventually comes up 8, and this remains a hit. The rolls for the second laser, re-rolling several results less than 7, and finally gets a 7. This result is changed to a miss, and Scott erases the appropriate damage from the record sheet.</blockquote>
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This is a little awkward to do with dice, so knowing a little probability will help. We are down to two outcomes, 7 or 8, with probabilities 6/36 and 5/36 on 2d6. We only want those two rolls though, so this reduces to 6/11 and 5/11 if we only consider those two possibilities*. My original probability of hitting on 7+ was too high by 5/36, and given that I rolled at least a 7 but no higher than 8, then the conditional re-roll should have 5/11 chance of remaining a hit, and 6/11 chance of changing to a miss. This is a ~54.5% chance I will now miss, but compare this to my example 2 in the last post, where the chance of missing was 6/21 or ~28.6%. This is almost always an over-correction, but this is more fair to Scott (the injured party), because it gives him the benefit of the doubt for all other partial information - what may or may not be remembered about the original roll.<br />
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* [Math note: the two possibilities we are interested in are rolls of 5 or 6, with a total probability of 5/36+6/36 = 11/36. To make the probabilities of the two rolls we are interested in sum to 1.0, we multiply by 36/11, so 5/35 * 36/11 = 5/11, 6/36 * 36/11 = 6/11.]<br />
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So we pull out our handy 11-sided die and roll ... 6 or less is a hit and 7 or more is a hit ... and what do you mean you don't have any 11-sided dice?<br />
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If you have followed me this far, I'm pretty sure you can figure out the 11- sided die problem. ;-)<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvYTuX17YjY3pFMLwg_HRkTDvI7jbNyBBBtsxVB7m1SjRrYz5Lf0afmu42ezc4V3HSgXW5c-PujskJaTY_yS2H0-ICvSFCvl3jUdulIN4rQU_KRiTsAJbRh17s958jRmzQvZbmpULQ1io/s1600/Handy_D36_chart.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="264" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvYTuX17YjY3pFMLwg_HRkTDvI7jbNyBBBtsxVB7m1SjRrYz5Lf0afmu42ezc4V3HSgXW5c-PujskJaTY_yS2H0-ICvSFCvl3jUdulIN4rQU_KRiTsAJbRh17s958jRmzQvZbmpULQ1io/s320/Handy_D36_chart.png" width="320" /></a></div>
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In the process of writing this post I thought I was going to need a 36-sided die, so I went and made a table for it. That didn't work out, but here is the table anyway. --><br />
<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>
Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-78557337132110528372012-02-05T14:04:00.002-06:002015-06-26T17:45:45.519-05:00Conditional Dice Rolls<div dir="ltr" style="text-align: left;" trbidi="on">
It happened to me again at the Wednesday Battletech game, one of those honest mistakes that can happen in a complicated situation. My Griffin fired two medium lasers at a Jenner needing 7's or better, and both hit. A short time later I realized my mistake, I had miscounted and the roll should have been 8 or better. I could not remember what the original rolls had been.<br />
There is a way to fix this, to repair my mistake, to determine if my shots really should have missed, and that is fair to both players. It's a good trick, and you don't even have to do any math to use it.<br />
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But you might have to roll a lot of dice. ---> More after the fold ---> <br />
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<a name='more'></a>The trick is to use conditional probability, an application of <a href="http://en.wikipedia.org/wiki/Bayes'_theorem">Bayes Law</a> to correct the mistake. We are not going to do the calculations though, the dice will take care of that for us. To make this work, you need to know two things: The first condition in which you were first rolling the dice (the error), and what the correct and second condition should have been. It works like this: Recreate the first event (the wrong one) by rolling the dice until you get the same result (<span style="font-size: x-small;">success, or failure</span>) as the first time. Next apply the second (correct) condition to the same roll, possibly changing the first outcome. The procedure changes the result from the original roll with the probability needed to correct the original error.<br />
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Here is a really simple example using a success-roll on a single six-sided die to show how this is done. You might spot some ways to make it even simpler.<br />
<blockquote class="tr_bq">
Example 1: You roll 1d6 needing 4, 5, or 6 to succeed, and you do succeed. Later you realize that was a mistake, and it should have been just 5 or 6 to succeed. You do not remember what the actual roll was, only that it was successful (therefore a 4, 5, or 6). To correct the mistake roll the die again, re-rolling any results of 1,2,or three. You should now have a die with a 4, 5, or 6 showing. If the die shows a 5 or 6, keep the original result, if it is a 4, change the result to a failure.</blockquote>
Now a little math: The first roll had a 50% probability of success (3 out of 6), but should have been ~33% (2/6 or 1/3). After re-rolling the die until you get 4, 5,or 6, the probability of 5 or 6 is ~67% (2/3), and ~33% (1/3) of a 4. The probability that this second roll is a success (2/3) given that you know the first roll succeeded (50%) is 0.5 times 0.67, or ~33%, which gives you the correct probability of success (1/3) as if you had done it right in the first place.<br />
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That may have been a little overly-complicated. If you followed the math you know this could have been done with only one additional die roll, which would be much simpler. I did it this way because the same procedure works no matter what sort of dice you are using. Try this on my original example.<br />
<blockquote class="tr_bq">
Example 2 <span style="font-size: x-small;">(my opening example)</span>: Dan rolled and hit with two medium lasers needing 7+ on 2d6. Later he realizes the base of the Jenner miniature he was shooting at obscured a light woods (a +1 modifier), and he should have rolled with 8+ to-hit. Dan then approaches Scott to correct his mistake. He rolls for the first laser getting a 10 on the first try, and this remains a hit. The rolls for the second laser, re-rolling several results less than 7, and finally gets a 7. This result is changed to a miss, and Scott erases the appropriate damage from the record sheet.</blockquote>
Now the math: The probability of rolling 7+ on 2d6 is 21/36, for 8+ is 15/36, and of rolling exactly 7 is 6/36. Given that my first roll(s) were at least 7 (I know that, because they hit) the conditional probability distribution of my second roll becomes 1/21 chance of a 12, 2/21 chance of 11, 3/21 chance of 10, 4/21 chance of 9, 5/21 chance of 8, and 6/21 chance of 7 and the conditional probability of 8+ is now (adding things up) 15/21. The probability of my first roll (21/36) times the probability of the conditional roll (15/21) is<br />
(21/36) * (15/21) = 15/36 --> The probability I should have used in the first place (Hooray!).<br />
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Conditional probability is confusing to a lot of people, usually because they do not consider all the event-probabilities that lead to the final outcome. If you use most obvious way to correct a mistake - <b>a simple re-roll</b> where you ignore the first result and roll again correctly - the player faces a sort of double jeopardy, and has to succeed on two different rolls. The chance of rolling both 7+ and 8+ is (21/36) times (15/36) = (315/1296) or ~24.3%, considerably less that the (15/36) = ~41.7% probability that results if you ignore the result of the first roll.<br />
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Conditional dice rolls also work to correct mistakes in failed rolls, and here the unfairness of the <b>simple re-roll</b> is more evident.<br />
<blockquote class="tr_bq">
Example 3a: Dan rolls to hit at 8+ on 2d6 and misses. Later he realizes the roll should have been at 7+, and talks Scott into giving him a new roll, throwing out the first result (the miss) and replacing it with the result of the second roll. Dan now has a 21/26 chance of hitting with the second roll, but this ignores that Dan already had one chance of hitting which failed. Dan is essentially getting a free re-roll, which is unfair to Scott.</blockquote>
Now let's redo Example 3 with conditional probability, and this time just a little math.<br />
<blockquote class="tr_bq">
Example 3b: Dan rolls to hit at 8+ on 2d6 and misses. Later he realizes the roll should have been at 7+, and Scott agrees to a conditional re-roll. Dan and Scott figure out the difference between the two rolls is just the probability of rolling exactly 7 on 2d6, which is 6/36 or 1/6. Scott agrees that Dan should roll 1d6, and if the results is a 6, to change the miss into a hit.</blockquote>
One assumption I am using for all these examples is that there is <i>no memory</i> at all of what the first roll might have been. What if you don't recall exactly what the roll was, but maybe you know it was "more than 5", or "one die was a 6"? You can take this sort of partial information into account too, and probably should. I'll save that for <a href="http://giantbattlingrobots.blogspot.com/2012/02/conditional-dice-rolls-with-partial.html">part 2</a>, where I contemplate <a href="http://giantbattlingrobots.blogspot.com/2012/02/conditional-dice-rolls-with-partial.html">Conditional Dice Rolls with Partial Information</a>.<br />
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[EDIT] - As noted in the comments, there is an additional assumption that there is nothing else that happens in between that cannot be undone. If players make decision based on the outcome, if becomes especially difficult to go back and fix it.<br />
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com2tag:blogger.com,1999:blog-3055805266991720601.post-29754788908051728112012-01-29T22:07:00.001-06:002015-06-26T17:38:02.515-05:00My Wikipedia Problem<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Some </b>months back I started getting a lot of traffic from the <a href="http://en.wikipedia.org/wiki/Lanchester's_laws">Wikipedia page on Lanchester's Laws</a>. It seems that someone had noticed my efforts on the subject and linked to me as a reference. It wasn't much really, just a reference in support of a single sentence - Here it is, and [5] links to <a href="http://giantbattlingrobots.blogspot.com/2010/06/lanchesters-laws-and-attrition-modeling.html">my first post on Lanchester's Laws</a>:</span><br />
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<span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19px; text-align: -webkit-auto;">In modern warfare, to take into account that to some extent both linear and the square apply often an exponent of 1.5 is used.</span><sup class="reference" id="cite_ref-3" style="background-color: white; font-family: sans-serif; line-height: 1em; text-align: -webkit-auto;"><a href="http://en.wikipedia.org/wiki/Lanchester's_laws#cite_note-3" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none; white-space: nowrap;">[4]</a></sup><sup class="reference" id="cite_ref-4" style="background-color: white; font-family: sans-serif; line-height: 1em; text-align: -webkit-auto;"><a href="http://en.wikipedia.org/wiki/Lanchester's_laws#cite_note-4" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: none; white-space: nowrap;">[5]</a></sup><sup class="reference" id="cite_ref-5" style="background-color: white; font-family: sans-serif; line-height: 1em; text-align: -webkit-auto;"><a href="http://en.wikipedia.org/wiki/Lanchester's_laws#cite_note-5" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: none; background-origin: initial; color: #0b0080; white-space: nowrap;">[6]</a></sup></blockquote>
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<span style="font-size: x-small;">Citation: Lanchester's laws. (2011, December 12). In <i>Wikipedia, The Free Encyclopedia</i>. Retrieved 03:02, January 30, 2012, from<a class="external free" href="http://en.wikipedia.org/w/index.php?title=Lanchester%27s_laws&oldid=465382667" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: url(data:image/png; background-origin: initial; background-position: 0% 0%; background-repeat: no-repeat no-repeat; color: #663366; padding-bottom: 0px !important; padding-left: 0px !important; padding-right: 13px; padding-top: 0px !important; text-decoration: none;">http://en.wikipedia.org/w/index.php?title=Lanchester%27s_laws&oldid=465382667</a></span></blockquote>
<span style="font-family: 'Trebuchet MS', sans-serif;">I've put a lot of study into Lanchester's Laws, so I was happy that someone thought I was worth a reference, but <i>I have a problem with that sentence</i>. <i><b>It's wrong</b>.</i></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><i><br /></i></span>
<span style="font-family: 'Trebuchet MS', sans-serif;">To be fair, perhaps I ought to say it is incomplete statement on a complex topic, and the complete explanation would be much, much longer. It is true that an exponent between 1 and 2 is often used to approximate situations where both Linear and Square laws are in effect, but this exponent represents (in a very abstract sort of way) that a portion of each force are subject to the Linear law (exponent of 1), while the remainder is subject to the Square law (exponent of 2). There is no mathematical rule that makes any other values for the exponent correct, it just sort of works to describe how battles actually play out in an average sort of way. The article makes no previous mention of exponents at all, so it's hard to see how anyone could come away with a proper understanding of the statement. To my mind that makes it wrong.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;">Fixing it though, is another matter. I've thought about fixing it myself, and even contacted a Wiki editor about it, but I haven't had time or energy to take on the task. I still hope to get back to writing regularly again, but I have a stack of other topics to address, and I am not sure I really want to spend my time fixing someone else's problem. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><i>Tangent: </i>If you are new to the subject of Lanchester's Laws, the Linear law (exponent 1) describes combat attrition in a one-on-one combat setting, such as might occur with archaic weapons or between aircraft in air-to-air dogfights. The Square law (exponent 2) applies when multiple combatants can attack the same target, and vice-versa, such as a naval gunnery battle. Those are ideas though, and in practice there is almost always some complex mixture of these situation.</span><br />
<a href="http://www.blogger.com/blogger.g?blogID=3055805266991720601"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>
Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-26621294839861243152011-08-20T10:48:00.003-05:002015-06-26T17:44:26.098-05:00The Grinder<div dir="ltr" style="text-align: left;" trbidi="on">
Assorted bits of internet, selected from a stratified sample, sorted in ascending sequence, collated, assembled in logical order, then just sort of thrown in a pot and given a good hard shake. Completely by accident, I seem to have a fine selection of game design articles for this edition. How did that happen?<br />
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<b>--- The Grinder - August 2011 ---</b><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxgAoaBUyOUWzfONwJQwDcUMIrNXAPJNUb0PW5EUTyt1fC4lPr4LljZvUjVp9FjcjJMq-_1jqA7VSJIaofHCc8v0yhVruEelgxT2miVUiRdh82imruaiuDdPDI6DkuEhVxLS-yi4TsPiU/s1600/achillesajaxdice002-1.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxgAoaBUyOUWzfONwJQwDcUMIrNXAPJNUb0PW5EUTyt1fC4lPr4LljZvUjVp9FjcjJMq-_1jqA7VSJIaofHCc8v0yhVruEelgxT2miVUiRdh82imruaiuDdPDI6DkuEhVxLS-yi4TsPiU/s320/achillesajaxdice002-1.jpg" width="320" /></a></div>
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<b><a href="http://paxsims.wordpress.com/">PAXsims</a></b> - The latest Game Design blog I am following. Some good stuff here I need to check out.<br />
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<a href="http://io9.com/5830388/awesome-robot-action-for-your-desktop-wallpaper">IO9: Robot Art Wallpapers</a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNNT5e2q7z-qqc84TqhXra-FO0HMthyJjdTyJ_dkV6cB3zSH_xg__6rQbtSLdaY5stG8r930F-6jYF1uOtJTToMpZuDiuth3JAh6XGJDhwiKbMp5VigrMsLopsBetYzZaNOaskuMqVRSQ/s1600/wake_up_baby.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="125" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNNT5e2q7z-qqc84TqhXra-FO0HMthyJjdTyJ_dkV6cB3zSH_xg__6rQbtSLdaY5stG8r930F-6jYF1uOtJTToMpZuDiuth3JAh6XGJDhwiKbMp5VigrMsLopsBetYzZaNOaskuMqVRSQ/s200/wake_up_baby.jpg" width="200" /></a><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE9af_LnlzhsYUr-PjrPxKHxMmsNTp3vQfNl2PPRhg7f8AqcYKfmXbSAAe3qX8CcZGpU5ATjOSYhKQjpVaAvqyQ424NzUfFtR0l46CDNpqwN5CtqtxNrhNPUf9hcOXd6KWyqQAxpivhlQ/s1600/medium_mechwarrior_mercs_wallpaper_6_by_mecha_master.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="156" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE9af_LnlzhsYUr-PjrPxKHxMmsNTp3vQfNl2PPRhg7f8AqcYKfmXbSAAe3qX8CcZGpU5ATjOSYhKQjpVaAvqyQ424NzUfFtR0l46CDNpqwN5CtqtxNrhNPUf9hcOXd6KWyqQAxpivhlQ/s200/medium_mechwarrior_mercs_wallpaper_6_by_mecha_master.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A Fafnir crashes the party</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE9af_LnlzhsYUr-PjrPxKHxMmsNTp3vQfNl2PPRhg7f8AqcYKfmXbSAAe3qX8CcZGpU5ATjOSYhKQjpVaAvqyQ424NzUfFtR0l46CDNpqwN5CtqtxNrhNPUf9hcOXd6KWyqQAxpivhlQ/s1600/medium_mechwarrior_mercs_wallpaper_6_by_mecha_master.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br />
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<blockquote>
<a href="http://wgnb.blogspot.com/2011/08/moment.html"><b>Wargamer's Notebook</b>: <b>The Moment</b></a> -- "I wish this was something I experienced more often. The point during a wargame after several plays or turns when things magically click. The moment when the scaffolding of the the rules and latticework of the bits fall away and the narrative zooms into the foreground and you - as the player - are completely absorbed by the game. Events occur that could not have been imagined, but that are totally plausible. Victory hangs in the balance. And you are not moving counters or playing cards, but making choices that give you hope of victory."</blockquote>
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<a href="http://www.pbfcomics.com/?cid=PBF034-Space_Disaster.jpg">Space Disaster!</a><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMvxO-7qrVEN93UMefUSSlJMETOSOc_1TPB8Ybs0MnOlI5m73-8TpohzY0AIlmlBhykM2rIhrfVTEwJaDgn91NUBej1LZ4HgPM8SnK0qtZUqAxUZU5ZnRxrMg6rl1t49_IOcYgBNonJ34/s1600/PBF034-Space_Disaster.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="132" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMvxO-7qrVEN93UMefUSSlJMETOSOc_1TPB8Ybs0MnOlI5m73-8TpohzY0AIlmlBhykM2rIhrfVTEwJaDgn91NUBej1LZ4HgPM8SnK0qtZUqAxUZU5ZnRxrMg6rl1t49_IOcYgBNonJ34/s400/PBF034-Space_Disaster.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://www.pbfcomics.com/?cid=PBF034-Space_Disaster.jpg">original</a></td></tr>
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<a href="http://www.pbfcomics.com/?cid=PBF034-Space_Disaster.jpg">Genius Sir!</a><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-DTaoprCY6dz1hattihV8Zgjy0XcKLtcQsOyfk3ck4WUQF24i3rC_H-5Y12EhVlKqFaxocFsJ4fgCo9KEy1HYytcsY3COC3oIU8cD5gC8c1BMsBSXhrA8W7lKBmO0ifevJz6dgXst1Ok/s1600/PBF108-Genius_Sir.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="132" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-DTaoprCY6dz1hattihV8Zgjy0XcKLtcQsOyfk3ck4WUQF24i3rC_H-5Y12EhVlKqFaxocFsJ4fgCo9KEy1HYytcsY3COC3oIU8cD5gC8c1BMsBSXhrA8W7lKBmO0ifevJz6dgXst1Ok/s400/PBF108-Genius_Sir.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://www.pbfcomics.com/?cid=PBF034-Space_Disaster.jpg">original</a></td></tr>
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More irreverent humor to be found at <b><a href="http://www.pbfcomics.com/">Perry Bible Fellowship</a>.</b><br />
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<b><a href="http://supergalacticdreadnought.blogspot.com/">Desert Scibes</a></b> brings us a bit bit of gaming history at <b><a href="http://supergalacticdreadnought.blogspot.com/2011/08/making-of-starfleet-wars.html">Supergalactic Dreadnaught</a>:</b><br />
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<b><span class="Apple-style-span" style="font-size: large;"><a href="http://supergalacticdreadnought.blogspot.com/2011/08/making-of-starfleet-wars.html">The Making of Starfleet Wars</a></span></b></div>
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<span class="Apple-style-span" style="font-size: x-small;">NOTE: Scott R. Spicer (credited as "S.R. Spicer, Lt., TFSF"), along with his father, Ron Spicer (R.E. Spicer, Lt. Commander, TFSF), developed the <a href="http://supergalacticdreadnought.blogspot.com/2010/08/about-starfleet-wars.html">Starfleet Wars</a>miniatures line for <a href="http://www.alnavco.com/c_history.htm">Superior Models</a>. As you probably know if you've read this blog before, the SfW universe contains <a href="http://supergalacticdreadnought.blogspot.com/2010/12/five-powers.html">five starfaring factions</a>, each with a distinctive design style. Curious about the origin of this game and its minis, I emailed Scott Spicer about his work on these spaceship models. He was gracious enough to reply to my inquiry, and his response follows in its entirety ...</span></blockquote>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7Q-S8RdfwQ09fwyfov_6vBkZRWAgjnCqOXWwPRZE4rhuA9fztbqKnsiIkeReh5KfpJnnarOh8QthstlcTGkG9cyKPHF5Ro4ex_qaLwnS5IOa0xezoOgiJ-57RLGGB0ddv7Ltq3ikceaU/s1600/make-008.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7Q-S8RdfwQ09fwyfov_6vBkZRWAgjnCqOXWwPRZE4rhuA9fztbqKnsiIkeReh5KfpJnnarOh8QthstlcTGkG9cyKPHF5Ro4ex_qaLwnS5IOa0xezoOgiJ-57RLGGB0ddv7Ltq3ikceaU/s200/make-008.jpg" width="200" /></a><a href="http://www.dicecreator.com/2010/05/20/open-source-dice-making/">Make your own custom dice</a> (with a bit of work).<br />
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<a href="http://www.smbc-comics.com/comics/20110728.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://www.smbc-comics.com/comics/20110728.gif" height="400" width="191" /></a><br />
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From SMBC: (If only it were this easy!) </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7Q-S8RdfwQ09fwyfov_6vBkZRWAgjnCqOXWwPRZE4rhuA9fztbqKnsiIkeReh5KfpJnnarOh8QthstlcTGkG9cyKPHF5Ro4ex_qaLwnS5IOa0xezoOgiJ-57RLGGB0ddv7Ltq3ikceaU/s1600/make-008.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br />
</a><b><a href="http://www.gamasutra.com/view/feature/5986/game_design_essentials_20_.php">Gamasutra: Game Design Essentials: 20 Real-World Games</a></b><br />
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Chess, Go, and Life. Which one is the <b><a href="http://www.patternsinthevoid.net/blog/2011/07/best-game-ever/">Best. Game. Ever.</a> </b>A nice bit of gamey mathiness from <a href="http://www.patternsinthevoid.net/blog/">Patterns in the Void</a>.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9vk_dsFYPA7M9eW48HUDWbZCNmZrLRUeF9z2YE-cnCuC7c__k61GXQvU2IXai1bd3Zw8o-HoFeDsjYF41I1uEWN5r4VMs7P0zQOGBlsuc8XYaVKZl5QVrhTyUKnuoJt8mCLxRkxE5bX8/s1600/37_rvdcascolab07.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9vk_dsFYPA7M9eW48HUDWbZCNmZrLRUeF9z2YE-cnCuC7c__k61GXQvU2IXai1bd3Zw8o-HoFeDsjYF41I1uEWN5r4VMs7P0zQOGBlsuc8XYaVKZl5QVrhTyUKnuoJt8mCLxRkxE5bX8/s400/37_rvdcascolab07.jpg" width="281" /></a></div>
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Finally, <a href="http://www.planetaryfolklore.com/2011/05/cascolab.html">this is just cool.</a><br />
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<a href="http://www.blogger.com/post-edit.g?blogID=3055805266991720601&postID=2662129483986124315"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com2tag:blogger.com,1999:blog-3055805266991720601.post-9739873744704410642011-07-25T22:40:00.000-05:002011-07-25T22:40:08.748-05:00Taking a RISK - the distribution of armies lostI came across the following question at boardgames.stackexchange.com:<br />
<blockquote><b><a href="http://boardgames.stackexchange.com/q/3514">How can I estimate my chances to win a Risk battle?</a></b></blockquote><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPHZSUjM4xm051pSYekZS9goBh6W6RUG_a3qMlqrsgHGBWmyXAVZtoPiSEz0FzLSTXAStX9b33xPx1Smv5c6NUgodb-qX9pbfQrluMseZjBPf_eVRkdYt3dpJ_5b4aEgFyHkW2yoIpD4c/s1600/risk_box_classic.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPHZSUjM4xm051pSYekZS9goBh6W6RUG_a3qMlqrsgHGBWmyXAVZtoPiSEz0FzLSTXAStX9b33xPx1Smv5c6NUgodb-qX9pbfQrluMseZjBPf_eVRkdYt3dpJ_5b4aEgFyHkW2yoIpD4c/s320/risk_box_classic.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://gamesmuseum.uwaterloo.ca/VirtualExhibits/Whitehill/risk/index.html">Elliot Avedon Virtual Museum of Games</a>, Courtesy <a href="http://www.civilization.ca/cmc/home">Canadian Museum of Civilization</a>.</td></tr>
</tbody></table>Now there is already plenty of material on the web about probability in the popular boardgame <b><a href="http://www.hasbro.com/risk/">RISK</a>*</b>, but maybe I can add just a little bit more.<br />
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Most people already know that, given the choice, the Attacker should always 3 dice and the Defender should always roll 2, since this always gives the best results (<span class="Apple-style-span" style="font-size: x-small;">a Nash equilibrium</span>). Since it's always the Attackers choice to roll an attack or not, the relevant question seem to be <i>"How many armies [<b>X</b>] will the Attacker lose if they make [<b>N</b>] attack rolls?"</i><br />
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<tr><td style="text-align: center;"><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBNn8gi1NMXzNgNsKDgwE2HmdOAJAV0IKeR67wmnC8OxZU860vJ5yo9HBP63vshhUzmASc_w749S5cY8_Xvi6q6tcXPW-HzPqUTjuXtIAMJdMulb1aNKgCoMGEPvJpgOuGUfoOMIrK8O0/s1600/risk_game_board.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBNn8gi1NMXzNgNsKDgwE2HmdOAJAV0IKeR67wmnC8OxZU860vJ5yo9HBP63vshhUzmASc_w749S5cY8_Xvi6q6tcXPW-HzPqUTjuXtIAMJdMulb1aNKgCoMGEPvJpgOuGUfoOMIrK8O0/s320/risk_game_board.jpg" style="cursor: move;" width="320" /></a></div></div></td></tr>
<tr><td class="tr-caption" style="font-size: 13px; padding-top: 4px; text-align: center;"><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><a href="http://gamesmuseum.uwaterloo.ca/VirtualExhibits/Whitehill/risk/index.html">Elliot Avedon Virtual Museum of Games</a>, Courtesy <a href="http://www.civilization.ca/cmc/home">Canadian Museum of Civilization</a>.</div></div><div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><br />
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Using some probabilities from a <a href="http://www.kent.ac.uk/IMS/personal/odl/riskfaq.htm#Prob">RISK FAQ</a> for the probabilities of losses, I calculated the average attacker losses (about 0.921 per roll) and standard deviation (~0.81). It's not possible to lose 0.9 armies in RISK! as the attacker losses vary between 0, 1, and 2 per roll. However, as the results of many attack rolls are added up, the losses will begin to resemble the <i>normal distribution</i>. We can plug the average and standard deviation into a <a href="http://en.wikipedia.org/wiki/Normal_distribution">normal approximation</a> formula, and get back a probability for losses in a fairly simple calculation. For a given number of attack rolls "<b>A</b>" and number of attacking armies lost "<b>K</b>",<br />
<blockquote><span class="Apple-style-span" style="font-size: large;">Z = (K - 0.921*A) / (0.811*sqrt(K))</span></blockquote>where <b>Z</b> is a standard normal variable (mean 0, standard deviation 1), and the probability of <b>K</b>-or-fewer losses in <b>A</b> attack rolls can be evaluated with the <a href="http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function">standard normal probability CDF function</a>, otherwise known as the NORMSDIST(<b>Z</b>) function in Excel. That's pretty much it, except maybe for some graphs to show off the results.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhemGKchdyF2cnKC_c0tPu1_PemI-5A8b3ocmxSx6S-eeVL7tdCkMgCGLd43tj-ct3wD_KjPOTVGc-IxhfhI-wkGF87aKTDDLakBhg2mzsw2hSJGC0VsvOStRBT8MFzU8913j8TkYtNmko/s1600/Risk_losses_25.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="265" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhemGKchdyF2cnKC_c0tPu1_PemI-5A8b3ocmxSx6S-eeVL7tdCkMgCGLd43tj-ct3wD_KjPOTVGc-IxhfhI-wkGF87aKTDDLakBhg2mzsw2hSJGC0VsvOStRBT8MFzU8913j8TkYtNmko/s400/Risk_losses_25.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Cumulative probability of <b>K</b> attacking armies lost in 25 attack rolls</td></tr>
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</div><div>The <span class="Apple-style-span" style="background-color: cyan;">blue line</span> shows the cumulative probability of K losses in A attack rolls (vertical <span class="Apple-style-span" style="background-color: #ea9999;">red line</span>). The <span class="Apple-style-span" style="background-color: #ffd966;">yellow</span> triangles show an approximate 50% confidence interval, meaning that your actual losses should be within this range 50% of the time. The <span class="Apple-style-span" style="background-color: #ea9999;">red</span> diamonds show a 90% interval for the same. These intervals are actually slightly wider than the stated 50%/90%; because I rounded <i>outwards</i> to the nearest whole number of armies, and there is no other good way to do it.</div><div><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFLBzwfAIT4pWZeVt3p0q0Ta0fY-QzVchwut6_Y6EHT_wGz0JkyVUBz9JDWjpIhtDrwRxv4ZOhdErlG2N5FzAqez4r6qevnm_WpkP1bONKGtRyMQvCg0b-9wCikFxd28-PEY7RAqIOsC8/s1600/Risk_losses_35.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="263" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFLBzwfAIT4pWZeVt3p0q0Ta0fY-QzVchwut6_Y6EHT_wGz0JkyVUBz9JDWjpIhtDrwRxv4ZOhdErlG2N5FzAqez4r6qevnm_WpkP1bONKGtRyMQvCg0b-9wCikFxd28-PEY7RAqIOsC8/s400/Risk_losses_35.png" style="cursor: move;" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px; padding-top: 4px; text-align: center;">Cumulative probability of <b>K</b> attacking armies lost in 35 attack rolls</td></tr>
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</div></div><div>Recall this is an <i>approximation</i>, and it depends on there being lots of independent random events (dice rolls!) for the approximation to work well. It should start to work very well somewhere between 20-30 attack rolls, and depending on how fussy you are may give usefully accurate results for as few as 10-15 rolls. For smaller battles, or deciding whether or not you should attack just one more time, you might consider more accurate methods (<a href="http://www.kent.ac.uk/IMS/personal/odl/riskfaq.htm#Prob">look here</a>, for starters).</div><div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwzGxlT9SVJTTzMr_hlv_P9pLCvk5-7Jm52W9MweJJJIxs0eoXthGT025vJm5VrE8nkuva9j7mQK5EGXXcIERu64m6aZuSZ7XVisbxJWJHlQTp3yPXLysUDgZXOqVsE-Ldx1ALh29whPY/s1600/Risk_losses_75.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="265" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwzGxlT9SVJTTzMr_hlv_P9pLCvk5-7Jm52W9MweJJJIxs0eoXthGT025vJm5VrE8nkuva9j7mQK5EGXXcIERu64m6aZuSZ7XVisbxJWJHlQTp3yPXLysUDgZXOqVsE-Ldx1ALh29whPY/s400/Risk_losses_75.png" style="cursor: move;" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px; padding-top: 4px; text-align: center;">Cumulative probability of <b>K</b> attacking armies lost in 70 attack rolls</td></tr>
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</div></div><div>You can think of this in terms of Defender losses too. Two armies are lost with every attack (between the attacker and defender), so if there are <b>A</b> attack rolls and <b>K</b> attacking armies are lost, that means the defender will be losing <b>2*A - K</b> armies. For instance, in 25 attack rolls a total of 50 armies are lost; the probability of the attacker losing 20 armies the same as the probability of the defender losing 30.</div><div><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPIbOUokf6AHwtGGiYyBBpcaOHVjl5oaqillDZdNbC0BKw4mbtzfZeqxHgYAYaBwLeudxQB9Oki0SNb_FmrH0CWcuZlp-zUDfREhCAxY0u5aJ_P3vcvHJcAA1YdtMn7S8_aj9ob8n50lE/s1600/Risk_losses_50.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="263" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPIbOUokf6AHwtGGiYyBBpcaOHVjl5oaqillDZdNbC0BKw4mbtzfZeqxHgYAYaBwLeudxQB9Oki0SNb_FmrH0CWcuZlp-zUDfREhCAxY0u5aJ_P3vcvHJcAA1YdtMn7S8_aj9ob8n50lE/s400/Risk_losses_50.png" style="cursor: move;" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px; padding-top: 4px; text-align: center;">Cumulative probability of <b>K</b> attacking armies lost in 50 attack rolls<br />
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</tbody></table></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJJfuYZ3mEgTKKSPhHWAbPqQxFAHAP98sSY-nQ3WZEHrb8qPsZhJej2Dgqx1rYfOwSZ0Reav6YiRKE348aP78EVh2Di57RQoElK-SJUBa77q2xre7IyDagtE6fEw1XNqdaxrNBRSS-m-s/s1600/tangent-button.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJJfuYZ3mEgTKKSPhHWAbPqQxFAHAP98sSY-nQ3WZEHrb8qPsZhJej2Dgqx1rYfOwSZ0Reav6YiRKE348aP78EVh2Di57RQoElK-SJUBa77q2xre7IyDagtE6fEw1XNqdaxrNBRSS-m-s/s1600/tangent-button.png" /></a></div><b>Nostalgic Tangent</b>: Calculating the probabilities of losses for the attacker and defender was one of my first mathematical efforts to figure out a game. I didn't know how to do the calculation, but I wrote a program on my Apple II+ to roll lots of electronic dice for me, and calculated the probabilities that way. Later I learned that this technique is called <a href="http://en.wikipedia.org/wiki/Monte_Carlo_method">Monte Carlo</a> simulation, and statisticians do this regularly to examine the properties of new statistical methods.<br />
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*** There WILL BE a link to the spreadsheet for these calculations, but it's getting late, so I'll have to add that in tomorrow. ***<br />
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Having written this, I realized that I haven't quite answered the question. I've given the probability for a given number of attacks/losses, but the question is <b><i>"How many armies will it cost me to win?"</i></b><br />
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There is another approximation to answer that, but it's much less well known. I guess I'll have to write a part 2. Stay tuned!<br />
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</div><div class="separator" style="clear: both; text-align: -webkit-auto;">---------------------------------------------------------------------------------</div><div class="separator" style="clear: both; text-align: left;">* RISK is a registered trademark of HASBRO, Inc., of course.</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><u>Footnote:</u> The RISK! game images used in this post are from <a href="http://gamesmuseum.uwaterloo.ca/index.htm">Elliott Avedon's Virtual Game Museum</a>, and are used with permission of the <a href="http://www.civilization.ca/cmc/home">Canadian Museum of Civilization</a>. The Virtual Game Museum has much more interesting game related information, and I may be posting about it again.<br />
<div vertical-align:text-top;=""><a href="http://www.blogger.com/post-edit.g?blogID=3055805266991720601&postID=973987374470441064" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0tag:blogger.com,1999:blog-3055805266991720601.post-61524240504722254452011-07-04T10:15:00.000-05:002016-01-28T16:19:00.343-06:00The Grinder - July 4th Edition<div dir="ltr" style="text-align: left;" trbidi="on">
A collection of red-glaring rockets and bombs bursting in air, without the rockets and bombs.<br />
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<b>The Grinder</b> for 7/4/2011:<br />
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<span class="Apple-style-span" style="background-color: magenta; color: #274e13;"> <a href="http://panther6actual.blogspot.com/" style="background-color: magenta;">Paint-It-Pink</a> </span>: <b>Ashley</b> has some Battletech math going on --> <a href="http://panther6actual.blogspot.com/2011/06/how-i-learned-to-stop-worrying-and-love.html">How I Learned to Stop Worrying and Love the Medium Laser</a>. A good discussion of how to evaluate the relative strength of weapons in Battletech, or any game.<br />
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<span class="Apple-style-span" style="font-size: large;"><i>"Can I haz tactix?"</i> </span></div>
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<img src="https://sites.google.com/site/pocketdimension42/_/rsrc/1309791822075/gbr-gallery/LOLCat_military_strategy.gif" /></div>
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Found on <a href="http://moorewr.tumblr.com/post/6428454179">Operation Odyssey Dawn</a>: If the animation doesn't work, go see it <a href="http://moorewr.tumblr.com/post/6428454179">here</a>.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguVBuW-L641tFbLcNopTnMF36h_Maw67Wjh30-K3HSikLZICT_-geEfts0NcPb9EhhYl5aqFhMcvm8WQF6YUloQUJ45vZQM69rA9PuSjE89D8Dxh6psE0G2EBNvEuvnGm2Q8BTrDSj7Zo/s1600/507de178g89223219b976%2526690.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguVBuW-L641tFbLcNopTnMF36h_Maw67Wjh30-K3HSikLZICT_-geEfts0NcPb9EhhYl5aqFhMcvm8WQF6YUloQUJ45vZQM69rA9PuSjE89D8Dxh6psE0G2EBNvEuvnGm2Q8BTrDSj7Zo/s200/507de178g89223219b976%2526690.png" width="200" /></a><br />
Linkback! --> <a href="http://blog.sina.com.cn/s/blog_507de1780100kmxu.html">程阳:Probability versus Odds</a><br />
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MathOverflow: <a href="http://mathoverflow.net/questions/13638/which-popular-games-are-the-most-mathematical">Which popular games are the most mathematical?</a><br />
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<b><a href="http://proofmathisbeautiful.tumblr.com/post/6759989752/intothecontinuum-the-120-cell-is-a-4">Proof</a></b>: The 120 cell is a 4 dimensional figure that can be <span class="Apple-style-span" style="font-size: x-small;">considered the 4 dimensional analog of the dodecahedron. It has 720 five sided faces,</span> <span class="Apple-style-span" style="font-size: xx-small;">1200 edges, and 600 vertices. This animation shows 3 dimensional cross sections of the 120 cell in a way that is similar to taking 2 dimensional cross sections of a 3 dimensional figure.</span> Translation --> <a href="http://proofmathisbeautiful.tumblr.com/post/6759989752/intothecontinuum-the-120-cell-is-a-4">Very Cool animation</a>!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7rEr9JDE5HURQUINjeVfdvwpcDHsjxUKwVZukGuLS5T9XTcob61WVKxRD9pM2Oz89QLg_CPwiOEB0UtBuwVwQFhv0QEiqSLlUC8zHsaYN2kX1BJrVRgSiMCeu-w9KFcOeY-K8VE1scUI/s1600/q-bert.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7rEr9JDE5HURQUINjeVfdvwpcDHsjxUKwVZukGuLS5T9XTcob61WVKxRD9pM2Oz89QLg_CPwiOEB0UtBuwVwQFhv0QEiqSLlUC8zHsaYN2kX1BJrVRgSiMCeu-w9KFcOeY-K8VE1scUI/s200/q-bert.jpg" width="200" /></a></div>
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The Number Warior:<b> Q*Bert</b> Teaches the Binomial Theorem (an award winner too). Sort of a long (2-part) video.</div>
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<a href="http://proof-of-false.the-user.org/27.png">Proof-of-False</a>: Do games offer a solution for <a href="http://proof-of-false.the-user.org/27">US Tax Reform</a>?</div>
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From <b><a href="http://www.madandmoonly.com/doctormatt/">doctormatt</a></b>: <a href="http://www.madandmoonly.com/doctormatt/mathematics/dice1.pdf">A Collection of Dice Problems with solutions and useful appendices</a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOrf-U8XV8r6PSfL-uPxMGRv8TTxyKclULMzH2Al55i1IRHmxDkjOOx1JaE6vTg6sVAFV6mdlGIR7OxTdINV2QMDJWJBUVFJDMDCzbxgDjIPQK0npyP0YcX74xI6EeAu8dQhrxC26XpPY/s1600/Hour+Maze+Thumbnail.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOrf-U8XV8r6PSfL-uPxMGRv8TTxyKclULMzH2Al55i1IRHmxDkjOOx1JaE6vTg6sVAFV6mdlGIR7OxTdINV2QMDJWJBUVFJDMDCzbxgDjIPQK0npyP0YcX74xI6EeAu8dQhrxC26XpPY/s1600/Hour+Maze+Thumbnail.jpg" /></a></div>
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<a href="http://mathlesstraveled.com/">The Math Less Traveled</a>: <a href="http://mathlesstraveled.com/2011/06/14/the-wonderful-world-of-mike-reilly/">The Wonderful World of Mike Reilly</a>.</div>
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Mike Reilly is a Toy/Puzzle designer and screenwriter, see what he has done at <a href="https://sites.google.com/site/reilly4puzzles/">Reilly4Puzzles</a>.</div>
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<a href="http://reinwood99.blogspot.com/">Reinwood's CBT Workbench</a> gives us an AAR for <a href="http://reinwood99.blogspot.com/2011/06/fourth-succession-war-skondia-final.html">Fourth Succession War: Skondia The Final Battle Kublacon</a>. AND it's got no math in it. Honest!</div>
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A small update to my <a href="http://giantbattlingrobots.blogspot.com/2009/01/graph-paper-race.html">Graph Paper Race</a> post (added link to a relevant article). This continues to be one of my more popular posts.<br />
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I didn't plan this, but somehow this has ended up being the most math-heavy edition of The Grinder to date. Oh well, it's all sausage now.<br />
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Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com2tag:blogger.com,1999:blog-3055805266991720601.post-4255064864283763992011-07-03T11:23:00.000-05:002011-07-03T11:23:38.460-05:00Dice Distributions RevisitedRecent thoughts about calculating the distribution of the maximum sum of several dice (ex: roll 3, sum the highest 2) made me realize I needed a better tool for calculating the distribution of sums of dice in the first place. I first wrote about this some time ago in <a href="http://giantbattlingrobots.blogspot.com/2009/02/dice-distributions.html">Dice Distributions</a>, so I knew how to do it better, I just hadn't gotten around to doing it.<br />
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<i>Tangent</i>: While researching this I can across a great set of mathematical <a href="http://www.madandmoonly.com/doctormatt/mathematics/dice1.pdf">Dice Problems</a> from <b>Doctormatt</b> (<a href="http://www.madandmoonly.com/doctormatt/mathematics/mathematics.htm">Web Page</a>, <a href="http://www.madandmoonly.com/drupal/?q=blog/4">Blog</a>).<br />
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And now back to our story -<br />
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I first set up a spreadsheet to give me <a href="http://en.wikipedia.org/wiki/Pascal's_triangle">Pascal's Triangle</a>, which looks like this:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNm1zBwO54GK1lUx1sWRYGPHq2FPohNwWLNfkXHgrCyzUM-B2o41u-zAVSGz3cqq1Z7TcYb4SlkcLNlIBIbwQK7F-racYu5gWzxhdoZD-zIgxuD7wmwHkL-S_GNXEp5Zp3f0lSH93uo_U/s1600/pascals_triangle.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNm1zBwO54GK1lUx1sWRYGPHq2FPohNwWLNfkXHgrCyzUM-B2o41u-zAVSGz3cqq1Z7TcYb4SlkcLNlIBIbwQK7F-racYu5gWzxhdoZD-zIgxuD7wmwHkL-S_GNXEp5Zp3f0lSH93uo_U/s320/pascals_triangle.png" width="312" /></a></div><br />
This gets used in lookup functions to calculate (<span class="Apple-style-span" style="font-size: x-small;">in a second worksheet</span>) what I'm calling the "Dice Triangle", The number of dice [N] rolled is indicated in the column headers, and the sum of <b>N D-</b>sided dice [X] rolled in indicated in the first column. The number of ways to roll that sum is indicated in the table. The number of sides on the die [D] can be changed by entering a different value into the <span class="Apple-style-span" style="color: blue;"><span class="Apple-style-span" style="background-color: #b6d7a8;">green shaded cell</span>.</span><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGtaQMsZoABjA2d2MR63ilkwha_KVwnDuNq_HxyDNv7knTMz_2sc-sUC8IvXoghqItr9A90Gxoln9Z0O4RQhAZHbl_0Ho-sUpxh93vWfFX4K4uX64SpkmAejCY1WEY8UVIg64GNMNBIps/s1600/dice_triangle.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="265" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGtaQMsZoABjA2d2MR63ilkwha_KVwnDuNq_HxyDNv7knTMz_2sc-sUC8IvXoghqItr9A90Gxoln9Z0O4RQhAZHbl_0Ho-sUpxh93vWfFX4K4uX64SpkmAejCY1WEY8UVIg64GNMNBIps/s320/dice_triangle.png" width="320" /></a></div><br />
The first D rows of the table come directly from Pascal's Triangle. Subsequent rows are calculated from previous rows of this table. A few more details of how this is done in my earlier post (<a href="http://giantbattlingrobots.blogspot.com/2009/02/dice-distributions.html">Dice Distributions</a>), otherwise you can ask me, or dig into the spreadsheet for yourself (sorry, in a hurry today).<br />
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Here is the spreadsheet: <a href="https://spreadsheets.google.com/spreadsheet/ccc?key=0AjfrJ01ys_yrdHp0RmdWT29BT0ltUXpNYnlfNVNnLUE&hl=en_US">Dice Distribution Calculator</a><br />
I have not made this public, so you cannot change it directly online. You can download a copy for yourself (under the File dropdown) and play with it to your hearts content.<br />
<a href="http://draft.blogger.com/post-edit.g?blogID=3055805266991720601&postID=425506486428376399" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com1tag:blogger.com,1999:blog-3055805266991720601.post-53367677727470810472011-07-01T17:54:00.012-05:002012-02-07T15:48:59.067-06:00Maximums and Minimums of Dice Rolls<div dir="ltr" style="text-align: left;" trbidi="on">
A <s>week</s> <s>month</s> a while back I received questions from <b><a href="http://cinerati.blogspot.com/">Christian</a></b> and a read post from <b><a href="http://www.scrapyardarmory.com/2011/05/14/a-time-of-war-initiative-analysis/">Saxywolf</a></b> on essentially the same question: <i>What is the probability of rolling a given value on an <b>D</b>-sided die, if you roll <b>N</b> dice and take the highest (or the lowest).</i><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTPQL1bF1w7iLgFR33XxdaA3uLq__8smlLcpASSAzN0zrP7JKDQkKsJZJG4v8XamXOrcypSVeCdKnrEt_3ycllAfpi-kylRAi_FbsxqSpYVTN4NWJ3TllCFRZjNn46x7MQl6cey5fd78k/s1600/DICE2.GIF" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTPQL1bF1w7iLgFR33XxdaA3uLq__8smlLcpASSAzN0zrP7JKDQkKsJZJG4v8XamXOrcypSVeCdKnrEt_3ycllAfpi-kylRAi_FbsxqSpYVTN4NWJ3TllCFRZjNn46x7MQl6cey5fd78k/s1600/DICE2.GIF" /></a></div>
Here's the trick:<br />
The probability of rolling a 1 on 1 d6 is 1/6. (regular 6-sided dice)<br />
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For 2d6 the probability of rolling a 1 as the maximum is 1/6 times 1/6, or 1/(6*6) = 1/36.</div>
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For <b>N</b>d6 the probability of rolling a 1 as the maximum is 1/6 times itself <b>N</b> times, or (1/6)^<b>N.</b></div>
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For D-sided dice just substitute <b>D</b> for 6 above, so that the probability of rolling a 1 as the maximum of <b>N</b> <b>D</b>-sided dice is 1/<b>D</b> times itself <b>N</b> times, or (1/<b>D</b>)^<b>N.</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS7yl1ezBjZClZk6R5zs_y9RHrVZ-dxQV77rRJZ4pYw1G9fbw2IRVRZGeGrGXUssbM2WSYYzugJeatXZtCi4scakXUkdiE2m5Q1umRXI1dyV1Fu6c22-OWvJsLYjLeJl3DBAFJzKesOAc/s1600/GBR_dice5.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS7yl1ezBjZClZk6R5zs_y9RHrVZ-dxQV77rRJZ4pYw1G9fbw2IRVRZGeGrGXUssbM2WSYYzugJeatXZtCi4scakXUkdiE2m5Q1umRXI1dyV1Fu6c22-OWvJsLYjLeJl3DBAFJzKesOAc/s200/GBR_dice5.png" width="156" /></a></div>
Now consider the problem of rolling <b><i>2-or less</i></b> as the maximum. The probability of rolling 2-or-less is 2/<b>D</b>, and the probability of rolling a 2-or-less as the maximum is 2/<b>D</b> times itself <b>N</b> times, or (2/<b>D</b>)^<b>N.</b><br />
That's 2-or-less, but we really just want the probability of rolling 2, <i>not 1 or 2</i>. BUT we already know the probability of rolling a 1 as the maximum on the same dice, so we can subtract that to get what we want:<br />
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The probability of rolling a <b>2</b> as the maximum is 2/<b>D</b> times itself <b>N</b> times, minus the probability of rolling 1 as the maximum, or (2/<b>D</b>)^<b>N - </b>(1/<b>D</b>)^<b>N</b>.<br />
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And that's it. Using the same math you can work the complete distribution of the maximum for any number of dice with any number of (equally likely) faces. Just start at <b>1</b> and work up. For minimums, just turn the problem around and find the probability of <i>X-or-less</i>.<br />
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Still too much math? Fear not for there is a spreadsheet to do the calculations for you:<br />
<a href="https://spreadsheets.google.com/spreadsheet/pub?hl=en_US&hl=en_US&key=0AjfrJ01ys_yrdG50ZlNMRlMxYWlBSHFMVnBTV0tOUVE&output=html">Link to Google Docs Spreadsheet</a><br />
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See the <b><span class="Apple-style-span" style="color: blue;">blue numbers</span></b> in the <span class="Apple-style-span" style="background-color: #93c47d;">green-shaded cells</span>? Change those to the number of side on your dice and the number you want to roll, and it will calculate the distribution for you. <strike>It might even work inside the blog?</strike>Nope, but it was worth a try. The spreadsheet is now public and can be edited at the link above (<span class="Apple-style-span" style="font-size: x-small;">also downloaded</span>). Changes made there WILL show up here when the page is reloaded, which means you are looking at whatever was most recently entered.<br />
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<iframe frameborder="0" height="300" src="https://spreadsheets.google.com/spreadsheet/pub?hl=en_US&hl=en_US&key=0AjfrJ01ys_yrdG50ZlNMRlMxYWlBSHFMVnBTV0tOUVE&output=html&widget=true" width="500"></iframe><br />
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And a chart to display the results:<br />
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<iframe frameborder="0" height="300" src="https://spreadsheets.google.com/spreadsheet/pub?hl=en_US&hl=en_US&key=0AjfrJ01ys_yrdG50ZlNMRlMxYWlBSHFMVnBTV0tOUVE&single=true&gid=3&output=html&widget=true" width="500"></iframe><br />
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This is a bit of an experiment, both linking to a shared spreadsheet, and adding the HTML code to it directly inside my blog post. One upshot of this is that when one person changes the spreadsheet, it will change it for everyone. Play nice! Let me know if it works too. [Fixed!]</div>
<a href="http://draft.blogger.com/post-create.g?blogID=3055805266991720601"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div>
</div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com2tag:blogger.com,1999:blog-3055805266991720601.post-5487550533356178832011-06-04T10:17:00.001-05:002011-06-04T22:53:49.691-05:00The Grinder[A dazzling display of delightful de ... um ... I need a D-word ... deviations ... detritus ... <i>de-links</i>?<br />
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<span class="Apple-style-span" style="font-size: large;">The Grinder - 6/4/2011 edition</span><br />
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And speaking of <i>dazzle</i>, could <a href="http://ministryoftype.co.uk/words/article/dazzle/#">Dazzle</a>-<a href="http://en.wikipedia.org/wiki/Dazzle_camouflage">camouflage</a> make a comeback? This recent research supports says <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0020233">Dazzle Camouflage Affects Speed Perception</a>. [Hat-Tip <a href="http://io9.com/5807915/army-tanks-should-be-bright-pink-with-escher-drawings-on-them">IO9</a>]<br />
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<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQIM7v6rSyaEAyQZ1b-BJAsZAq9GMhj8FP-kHcMgqbTM1ihg8ORckK9ayLXrHi99uOraRnajcOaEhmq3ppModbC3lcM0gzut5pYkef1RWmKHmleCvl4vU09KgMI7cjAAIiz-TJvM5SPkM/s1600/Albatros-DXI-sn2208-300px.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQIM7v6rSyaEAyQZ1b-BJAsZAq9GMhj8FP-kHcMgqbTM1ihg8ORckK9ayLXrHi99uOraRnajcOaEhmq3ppModbC3lcM0gzut5pYkef1RWmKHmleCvl4vU09KgMI7cjAAIiz-TJvM5SPkM/s1600/Albatros-DXI-sn2208-300px.png" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Image: <a href="http://wwiaviation.blogspot.com/">WWIaviation.blogspot.com</a></td></tr>
</tbody></table>This just in! Check out some <a href="http://wwiaviation.blogspot.com/2011/06/four-colorful-german-warbirds.html">dazzling WWI aviation paint schemes</a>.<br />
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<a href="http://spqrdave.blogspot.com/2011/04/special-guest-blogger-grand-finale.html">Terrain table pictures</a> ... Shiny!<br />
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This could be interesting ...<br />
<blockquote><a href="http://invasion3042.com/i/inews"><b>Invasion3042</b></a> is a massive multiplayer online game that is based off the game Battletech. It is a free game and is not for profit.</blockquote>Has anybody tried it?<br />
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<b><a href="http://blogs.discovermagazine.com/discoblog">Discoblog</a></b> brings us <a href="http://blogs.discovermagazine.com/discoblog/2011/05/04/throwable-robot-can-climb-aboard-ships-spy-on-pirates/">Tiny Toss-able Robots</a>.<br />
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</div><div>World Peace Games, with teacher John Hunter. Video from <b><a href="http://www.ted.com/talks/view/lang/eng//id/1127">TED</a></b>. It's a bit slow to get started, but gets interesting about 8 minutes in. <i>Never</i> cross a 9-year-old girl with tanks!<br />
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[Hat-Tip <a href="http://scienceblogs.com/gregladen/2011/04/john_hunter_on_the_world_peace.php">Greg Laden</a>]<br />
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[<a href="http://www.johndcook.com/blog/2011/05/05/platonic-solids/"><b>The Endeavour</b></a>] There are exactly five platonic solids*, and <a href="http://www.johndcook.com/blog/2011/05/05/platonic-solids/">you can prove it</a>!<br />
* Perhaps more familiar to my readers as dice - the d4, d6, d8, d12, and d20.<br />
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Another video, this one with singing and dancing! <b><span class="Apple-style-span" style="font-size: large;">Roll A D6</span></b>.<br />
<iframe allowfullscreen="" frameborder="0" height="272" src="http://www.youtube.com/embed/54VJWHL2K3I" width="425"></iframe><br />
[Hat-Tip: <a href="http://moorewr.tumblr.com/post/5202232188/roll-a-d6-by-sirconnoranderson-you-can-guess">Operation Odyssey Dawn</a>]<br />
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[<b><a href="http://io9.com/">IO9</a></b>] <a href="http://io9.com/5799753/playing-magic-the-gathering-as-an-rpg">MTG as an RPG?</a><br />
The was an MTG computer game, long ago, with very nearly this premise. With a bit of creativity it could be good for multiplayer too. Before that was a <i>great</i> game called <a href="http://en.wikipedia.org/wiki/Master_of_Magic">Master of Magic</a>. Also, there could be a <a href="http://io9.com/5801673/a-new-star-trek-animated-series-coming-to-television">new <i>Star-Trek</i> animated series</a>!<br />
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<a href="http://www.cut-the-knot.org/SimpleGames/Jam.shtml">Play JAM</a>! Can you beat the computer? Can you beat it every time?? Can you figure out the secret??? (without peaking!) Here is a hint - You have almost certainly played this game before, and many times. [Hat-Tip <a href="https://profiles.google.com/114134834346472219368/buzz">Terrace Tao</a>]<br />
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<a href="http://singingbanana.com/dice/article.htm">Non-Transitive Dice</a><br />
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<a href="http://abstrusegoose.com/369">Starcraft Humor from Abstruse Goose</a>. I didn't get it until I saw the caption.<br />
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<a href="http://www.kickstarter.com/projects/417209192/greens-cube-the-physics-boardgame">Green Cube: The Physics Boardgame</a><br />
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Enough bedazzlement for two sittings, but that's happens when I don;t post for a whole month. Writers-block sucks. Want to preview the next Grinder, <i>before</i> I post it? Check out my <a href="http://www.google.com/reader/shared/user/11383907413440419127/label/GBR">Google Reader Shared Links page for GRB</a>.<br />
<div vertical-align:text-top;=""><a href="http://draft.blogger.com/post-edit.g?blogID=3055805266991720601&postID=548755053335617883" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img align="top" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjly8cglm1Q_DZtNQtJ8fsxfo17s4EugTYUai7Sy4RHjwjxUb-Y192f3cKHtETpWwTzETzfV9FSZNGAngtzabUuSKNwndSgs1Ab0L-eZ7rLBwTiXfuoMBWYyTbFqu49kn5wlTJDRjE5dbQ/" style="height: 16px; width: 16px;" /></a></div></div>Dan Eastwoodhttp://www.blogger.com/profile/14105563883467108602noreply@blogger.com0