26 January 2011

The Grinder

Fresh ground links*, salt, chili pepper, onion powder, tomato powder, oats, soy lectithin, sugar, soybean oil, garlic powder, yeast extract, citric acid and cocoa powder.

* If the total link content is less than 40%, can I still call them links?

First a bit of administrivia: Though I have previously refused any sort of ads or commercial links, I recently received and accepted a polite offer to link to an online Games Software Development degree program from Westwood college (that's it over in the sidebar). This makes my ORIGINS trip this year a bit more affordable, especially when tuition costs are up.

Now back to our the grind ...

Spiked Math brings us a Magic the Gathering card for the Banach-Tarski paradox.

[IO9] Giant Teen Robot Angst ... no ... Teen Robot Giant Angst? ... still no ... Giant Robot Teen Angst. That's it! (Evangelon)

[more IO9] Chevy Chase to play D&D. Hilarity ensues.

A Gentleman's Duel (Bugs Bunny homage at 5:00)

[Found on SFSFW (Society of Fantasy and Science Fiction Wargamers)]

[22 Words, via John Cook's shared items] Racist Robot Joke

Found on Web 2.0 RC1
Speaking of sharing, any Reader or Buzz users out there?

[Pat's Blog] Q: Which type of polyhedral die most closely resembles sphere? Think about it carefully, then go see it you were right.

[Cinerati] This looks like fun: Adventure Gamebooks as RPGs Part 1 -- Fighting Fantasy's Warlock of Firetop Mountain

Image: Geeks are Sexy
[Geeks Are Sexy] Sexy D&D Pics.

Hint: It's not the D20.

[IO9] 55 Science Fiction/Fantasy Movies to Watch Out for in 2011, but I probably won't see most of them.

[Schlock Mercenary] Howard does a Happy Dance! Don't read Schlock? Try this.

Image: Ottawa Gamer
The Ottawa Gamer launchers his Avalon Cruiser.

All ground up. Keep rolling those dice!

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23 January 2011

After Action Report

I hosted a Saturday Battletech session at my home. It was a very cold morning (-11 F) and there had been a light snow - a good day to stay inside to play a game (and absolutely perfect for chilling the beer and soda!). The scenario was a rather generic "Assault" on a defended area, but I set myself some very specific guidelines for unit selection and pilot/gunnery skills.  One guideline was that all units should be selected from miniatures I actually have (which I almost accomplished), and that the battle should start off light mechs on both sides. Someone also requested I add some armor/tanks into the mix, which complicated my plans a bit. Another guideline was that the skill levels of mech pilots should be very mixed. I actually created a quite elaborate system for generating skills, and I might write that up some other day, but for now it's enough to know that about half of each force had an gunnery skill of about 4, with a range from 2 to 5. I created over 20 lances (groups of 4 units), which was MUCH more than could possibly be needed, but I wasn't sure how many people could make it or how late we might play. Pilots (and vehicle crews) were randomly generated, but within each lance I assigned pilots where I thought they were the best fit.

Each side started with 1 lance of vehicles and 2 of mechs. The mechs were all small and medium (because I stacked them that way), but vehicle selection was random, and by chance both sides started with some BIG tanks - 2 Demolisher's for the defenders, and 2 Alacorn's (heavy gauss version) for the attacker. The attackers started with an advantage of two extra medium mechs, and the only objective was to try to make the defenders "call for reinforcements" before 7 turns or so, with the idea the battle could continue indefinitely with each side alternately calling for reinforcements.

The defenders "home edge" was the lower/right corner of the photo above, and could set up on either of these two maps. Attackers entered on the far side. I was playing on the defenders side, but I stayed out of the initial setup decisions to make it more fair. Consequently, the defenders set up "forward" and took the fight immediately to the defenders on turn one (pictured above).

Here's another turn 1 photo, and it must be after combat because I see a "prone" marker in the mix. I'm not going to give all the gory detail, just a few that time and memory allow. With so many fast mechs, mediocre gunners, and big guns (on the tanks) there was a lot of wild maneuver going on. This is sort of what I was hoping would happen when I set up the scenario, and if anything it was even better than I expected.

Here's a turn 3 photo (I forgot to take any photos on turn 2). The attacker Alacorns are perched on a hill in heavy woods (lower left). They kept this position from turn 1 and made life very unpleasant (and much shorter) for several of the defenders. The defending Demolisher tanks are near the "frac tower" (upper mid) facing an uppity pair of UC/20 Saladin hovertanks.

Turn 4: The attackers have two units, a Cicada and the surviving Saladin, on the town map (lower) and are menacing a nearsighted LRM Carrier and an outmatched Flea-17. On the right an attacker Javelin is about to have a showdown with a Demolisher tank (guess who has a bigger gun?)

Another view of turn 4.

We called it quits after 5 turns. The defenders had lost 4 mechs and 2 vehicles, with 2 other mechs seriously damaged or crippled. The attackers lost 3? mechs and 1 Saladin hovertank. Had we played on the defenders would be forced to call for reinforcements immediately (well before 8 turns), so this is a clear win for the attackers. The defenders put up a good fight though, and the attackers were not too far from needing their own reinforcements.

I am quite pleased with how this turned out. The effort I put into the setup paid off with an interesting game, and the balance worked out just as had hoped. There are survivors of this battle and 14 lances of reinforcements we never got to use, so there could be a "part 2" to this battle in a month or two.

And the ice-cold beer was fantastic too. :-)
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08 January 2011

The Grinder

Carefully selected links, ground into a Truely Gritty substance (watching The Duke right now).
from Doghouse Diaries

Battlestar Galactica versus Lanchester's Squared Law ... from the The Dog House Diaries webcomic.

Blogs of War - a list of Wargaming blogs with 951 993 entries so far. You might find something you like. You might have a hard time not finding something you like.

From Pulsipher Boardgame Design, some comments on the value of playtesting: "Most players are not like us"

IO9: You might think something like this could only exist in a game ...
The manufacturer will not stand behind it.

From Vi Hart: Sick Number Games

Generating random numbers is a deep subject. Check out this free book to see how deep.

Game in the Brain: Nikolas comments on the Purpose of Realism in Games.

XKCD: Explorers

I put in my two-bits on Dice and Information (1,2,3), here's a great article about the information in a coin toss, from Tom Moertel's Blog:

That's all for this session. (I'm almost out of movie too, just the final shootout left.)
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02 January 2011

More Dice, More Information, but not as much as you think

I may have created some confusion in my previous posts on the information in dice (1,2). That's understandable, because the concept of information is complex and has multiple interpretations, most of which I would not claim to really understand either. Let's see if I can sort this out without making an even bigger mess.

Shannon Information measures the information content of a random distribution of discrete events. A coin flip (heads/tail), a To-Hit roll (hit/miss), and a Hit-Location roll (arm, leg, torso, etc.) are all examples of this. What really matter here is not the number of dice rolled or coins flipped, but the number of possible outcomes and the probability of each. So you might use 4d6 to determine the result of a to-hit roll, but there are still only two outcomes - hit or miss. In game terms, you can think this as the information you don't know yet, just before you roll the dice, or the variability of outcomes of that roll.
Shannon information is measured on a logarithmic scale (base 2), so each additional bit represents a doubling of information. In absolute terms, the difference between 10 and 11 bits of information is MUCH more than the difference between 2 and 3 bits. Be careful with this sort of comparison though, because it's a bit like comparing apples and oranges (or comparing to-hit and hit location rolls). Such comparisons may not be meaningful.

There is an extension of Shannon Information to continuous outcomes, but this also requires changing the definition somewhat. I won't go too far into this, but there is one key point I'd like to make. When dealing with the sum of multiple dice, the distribution of the sum tend to become more like a normal distribution as the number of dice increases. Calculating the entropy of the sum of 10D6 is a bit of work, but the entropy of a normal distribution is easy to calculate. Long story short, I can get a good guess at the entropy for the sum of a large number of dice by using the normal distribution as an approximation.

I had speculated about calculating the information in an entire game. This was rather silly of me, because this would mean framing the outcome of an entire game as a single probability distribution. I can't do that, but now I know how to make an educated guess. If I only considered the win/lose aspect of a game this would be easy, because that is just a complicated sort of discrete "coin-flip" outcome. The more interest way to look at this is to consider ALL the ways a game might play out, and to treat this as a sort of continuous outcome. The law of averages comes into play, some ways the game will play out are more likely than others. For instance, if at some point in the game you make multiple attacks to achieve an objective, perhaps to destroy an enemy tank, then in the final outcome of the battle it might not matter which attack was successful, so long as one of them was - they all lead to the same outcome. This might be stretching the concept too far, but I should be able to use the entropy of the normal distribution to approximate the amount of information of a very complicated random distribution - like that of an entire game.

Now I can make an educated guess about the information in a game. I'll use a Battletech example, but there is surprisingly little dependence on the game. The most common random event in Battletech is weapons fire, which includes the to-hit and hit-location rolls, which each have about about 3 bits each (as calculated here). In a two player game where each player has 4 battlemechs, and each mech makes about 5 weapons attacks per turn, there will be about 10 random events per turn for the first 5 turns or so, about 200 random events, then a decreasing number of attack for the next 5 turns, call it 150 random events. That's 350 random events in one game, but I left out anything else that might require a die roll, so I'll round it up to 400. The basic random event in Battletech is about 3 bits, and 400 repeat random events adds about log2(400) or 8.6 bits, for a total of 11.6 bits.

Sooooo ... now that I've gone through all that, it seems that the information in a game is just log2 of the number of random events, plus a few bits of overhead. Does this mean anything all? I need to think on that.

Here is a partial answer: A game doesn't need any randomness at all, it could be completely strategic, like Chess. Add just a little bit of randomness, the whole game may depend on just a few rolls of the dice. As randomness increases the law of averages will come into play - Games like Risk and Battletech have many dice rolls - so many that the average effect of many rolls is almost always more important than single roll. Too much randomness, and players lose the ability to affect the outcome. The trick is getting is the right balance of randomness, and I don't think there is a formula for that.

PS: My friend Ashely also recently noted that it might be a good idea to eliminate any rolling of the dice that doesn't significantly add to the game. Wisdom!

Dice and Information
Dice and Information, So What?
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01 January 2011

New Years Blogolutions

IT has been a pretty good year, all in all. I didn't accomplish all I wanted - I only wrote 61 posts (not counting this), which is considerably less than the 149 I wrote in 2009, but many of those went into depth or required considerable research and preparation. That is also 61 posts while contending with a super-busy year at work and home, so I shouldn't complain. I have also made some new friends, which is always good.

StatCounter tells me I've had 25,381 page loads, 17,168 unique visitors, 14,364 first time visitors, and 2,804 returning visitors in 2010. This is actually down somewhat from 2009, but I've been less active, and 2009 included the remains of massive traffic spike I got from the Blog-of-Note in December 2008. Google stats tell me I now have over 200 RSS subscribers - Thanks everybody!

(and the ball drops - 10 - 9 - 8 - 7 - 6 - 5* - 4 - 3 - 2 - 1 - Happy New Year!)
(* about this point I jump up to kiss my wife and nearly knock over my painting tray in the process. If what you do on New Years Eve is a preview of what you will do in the New Year, then apparently I'm going to be spending a lot of time kissing my wife and cleaning up disasters. Could be worse!)

What I hope to do in 2011:

I think I've got one or two more good Lanchester's Laws posts in me, which ought to really nail that topic down. I might even use some historical data and do some of my own modeling, which would be good for a whole new series. I have a nagging doubt about the existing Lanchester's models - I think there may be something fundamentally wrong about the existing historical analyses, and I want to take my own poke at the problem. I'm probably wrong, but doing my own research on this idea could be fun.

The Lanchester posts have helped me see how point system can be built, and I've already written bit of this, but I want to consolidate this into a few concise posts detailing what I know about how it should work, and what parts are still open questions. This has been one of my long term goals, but now that I am finally within reach it is opening up new questions, so the quest will continue.

I want to write games. I have that grand idea in my head of writing my master game that combined every idea I have ever had (and that's a lot) into a single game, and I just know that's a bad idea. I need to write some smaller games and practice expressing these ideas in a form that others can try.

I really really need to get back to my painting again. When time is short my painting tends to fall by the wayside. Having a wet palette helps though, and I've got space clear in the basement for what is supposed to be our painting studio.

I need ... to get to bed! Goodnight and Happy New Year. Keep those dice rolling!

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