30 October 2008
Rocket Engine at Ad Astra
Not at Ad Astra Games actually, but they put me on to the story. Actually, it's not so much of a story as it is just potentially really cool.
29 October 2008
Tater Titan!
An amusing Warhammer 40K project, and I'll never look at Mr. Potato Head in the same way again. Ladies and Gentlemen, the Eight Wonder of the world ...
A work still in progress. Check out the whole sequence of construction pictures (so far) at IRONDOG studios.
The Tater Titan!
A work still in progress. Check out the whole sequence of construction pictures (so far) at IRONDOG studios.
28 October 2008
If Battletech were a Card Game
One day I was pondering the question of Battle Value in Classic Battletech (CBT), which is a complex sort of mathematical problem, and then I had one of those deep thoughts: If CBT were a game that people gamble on, then this complex problem would have been worked out long ago.
A basic principle that serves me well both personally and professionally, it that when I don't really understand something, it is usually because I have not property considered the basics of the problem. The solution is to tear the problem apart - simplify the problem down to something that is understood. Then, and only then, you can try to understand the more complex question. I started thinking about the basic properties of CBT as a game, so I could look for other games with known mathematical properties.
So how do I simplify CBT? By throwing out components of the game that don't matter to the most basic mechanics of the game. Start with a one-on-one game. Get rid of the Map - no movement, no terrain, no ranges (or all the same range). Make all weapons the same (or consider only one weapon). Get rid of initiative, ammo, heat, critical hits and pilot hits, seperate hit locations (consider just one), critical hits, the distinction between armor and internal structure. (Did I miss anything?)
Now, consider what is left: A mech has been reduced to one big pile of "points", representing how much damage it can absorb before it is destroyed. It can attack and has some probability of doing some amount of damage "points" to another Mech (another pile of points) controlled by another player. Simplified this way, CBT is in a class of point scoring games. In this case a game where you try to score points against the other player, like Hearts. Scoring for yourself or against the other player isn't actually relevant, it just a matter of reaching a particular point total before the other player does.
Point scoring games are EVERYWHERE. I already mentioned Hearts, but I thought there might be a better match, so I kept looking for other games with more in common. In CBT we use a Mech Sheet to keep track of these points ...
... and some card games also involve a board to keep track of points too, like this one from Cribbage. The similarities do not end there: CBT has rules for weapons and movement on a map which affects how weapons can come into play, and dice are used to randomize the results. Cribbage has rules for how cards can be played and the points scores for each play, and the shuffle to randomize the results.
So, what I am (finally) getting at is the game of Classic Battletech has much in common with other point scoring games such as Cribbage. The rules of play are very different. No one would ever mistake the rules of CBT for the rules of Cribbage, but these games share a common mechanic which makes them mathematical cousins. This was the sort of link I was looking for; a link between CBT and a well understood game where the math has already been worked out.
While this describes one aspect of what I was looking for, it still doesn't give me quite what I needed. It did, however, put me on the right track for something important: Metal Fatigue.
Continued ...
A basic principle that serves me well both personally and professionally, it that when I don't really understand something, it is usually because I have not property considered the basics of the problem. The solution is to tear the problem apart - simplify the problem down to something that is understood. Then, and only then, you can try to understand the more complex question. I started thinking about the basic properties of CBT as a game, so I could look for other games with known mathematical properties.
So how do I simplify CBT? By throwing out components of the game that don't matter to the most basic mechanics of the game. Start with a one-on-one game. Get rid of the Map - no movement, no terrain, no ranges (or all the same range). Make all weapons the same (or consider only one weapon). Get rid of initiative, ammo, heat, critical hits and pilot hits, seperate hit locations (consider just one), critical hits, the distinction between armor and internal structure. (Did I miss anything?)
Now, consider what is left: A mech has been reduced to one big pile of "points", representing how much damage it can absorb before it is destroyed. It can attack and has some probability of doing some amount of damage "points" to another Mech (another pile of points) controlled by another player. Simplified this way, CBT is in a class of point scoring games. In this case a game where you try to score points against the other player, like Hearts. Scoring for yourself or against the other player isn't actually relevant, it just a matter of reaching a particular point total before the other player does.
Point scoring games are EVERYWHERE. I already mentioned Hearts, but I thought there might be a better match, so I kept looking for other games with more in common. In CBT we use a Mech Sheet to keep track of these points ...... and some card games also involve a board to keep track of points too, like this one from Cribbage. The similarities do not end there: CBT has rules for weapons and movement on a map which affects how weapons can come into play, and dice are used to randomize the results. Cribbage has rules for how cards can be played and the points scores for each play, and the shuffle to randomize the results.So, what I am (finally) getting at is the game of Classic Battletech has much in common with other point scoring games such as Cribbage. The rules of play are very different. No one would ever mistake the rules of CBT for the rules of Cribbage, but these games share a common mechanic which makes them mathematical cousins. This was the sort of link I was looking for; a link between CBT and a well understood game where the math has already been worked out.
While this describes one aspect of what I was looking for, it still doesn't give me quite what I needed. It did, however, put me on the right track for something important: Metal Fatigue.
Continued ...
Hammer's Slammers: Game Mechanics
Oops.
This is a post I started working on some time ago, but held off because I was rethinking the problem. I was looking at it earlier today and must have accidentally clicked on "publish" instead of "save". Too late though, because Google already latched onto it and is trying to link to it, therefore I will add a few comments and put it out for show. This is also a test of the what sorts of graphs I can do in Google Documents (henceforth GD).
This was SUPPOSED to be a post about a way to put a value on units in the game, which can be used to help create balances scenarios in the Hammer's Slammers game I wrote about previously. The game includes such values already to help in designing your own scenarios. Ultimately this is a preliminary post to talking about Battle Value in Classic Battletech, but it needs more work.
---
---
First and most obviously, It's not yet possible to have two different lines on a single graph using GD. I tried to work around this by making a single line with a few points that do not display, and ... well ... it's a mess. The X-axis is log-base-2 of the Attack/Defense ratio. This begs an explanation I haven't given yet - this ratio of attacker-to-defender strength which you look up on the Combat Results Table, roll the dice, and determine if the defending unit(s) are unaffected, disrupted, or destroyed. The Y-axis is the natural log of the odds of the units being disrupted (upper line) or destroyed (lower line), where the odds are the probability P, divided by 1-P, or odds = P/(1-P).
---
The point of all this is that the battle effectiveness of units in Hammer's Slammers can described by a relationship which is roughly linear on a logarithmic scale. Statisticians like these sorts of relationships because there is a lot we can do to describe them. Unfortunately is just describes the effects of a single attack, and I really want to try to put a value on the unit in a game, not just in a single attack. To do that, I will need to discuss survival distributions, and that is a topic for another day.
---
How is that for a broken post?
This is a post I started working on some time ago, but held off because I was rethinking the problem. I was looking at it earlier today and must have accidentally clicked on "publish" instead of "save". Too late though, because Google already latched onto it and is trying to link to it, therefore I will add a few comments and put it out for show. This is also a test of the what sorts of graphs I can do in Google Documents (henceforth GD).
This was SUPPOSED to be a post about a way to put a value on units in the game, which can be used to help create balances scenarios in the Hammer's Slammers game I wrote about previously. The game includes such values already to help in designing your own scenarios. Ultimately this is a preliminary post to talking about Battle Value in Classic Battletech, but it needs more work.
---
---
First and most obviously, It's not yet possible to have two different lines on a single graph using GD. I tried to work around this by making a single line with a few points that do not display, and ... well ... it's a mess. The X-axis is log-base-2 of the Attack/Defense ratio. This begs an explanation I haven't given yet - this ratio of attacker-to-defender strength which you look up on the Combat Results Table, roll the dice, and determine if the defending unit(s) are unaffected, disrupted, or destroyed. The Y-axis is the natural log of the odds of the units being disrupted (upper line) or destroyed (lower line), where the odds are the probability P, divided by 1-P, or odds = P/(1-P).
---
The point of all this is that the battle effectiveness of units in Hammer's Slammers can described by a relationship which is roughly linear on a logarithmic scale. Statisticians like these sorts of relationships because there is a lot we can do to describe them. Unfortunately is just describes the effects of a single attack, and I really want to try to put a value on the unit in a game, not just in a single attack. To do that, I will need to discuss survival distributions, and that is a topic for another day.
---
How is that for a broken post?
26 October 2008
Anatomy of a Blackhawk H - Part I
A project I'm working on for a friend.
This finished miniature is the be a Clan Blood Spirit Blackhawk H, posed in mid-jump.
And this is the progress so far.
See the complete gallery here.
[For the OTHER pictures of a hawk I took today, check this out.]
 |
| From GBR: Anatomy of a Blackhawk H |
 |
| From GBR: Anatomy of a Blackhawk H |
See the complete gallery here.
[For the OTHER pictures of a hawk I took today, check this out.]
23 October 2008
Virtual Theft, Real Law
Netherlands say virtual goods are property
from Raph's Website
UPDATE - from the Telegraph
from Raph's Website
Yet another country has come down on yet another side in the ongoing “virtual goods are property” debate. This time it’s the Netherlands.[More]
UPDATE - from the Telegraph
Woman arrested after virtual murder
A woman in Japan has been arrested after she murdered her virtual husband in a computer game.
22 October 2008
Facebook Games Finances, Revisited
In a previous post I detailed methods for determining the best way to invest your "money" in many of the game apps on Facebook. I worked out a few more details on how to account for some other costs I had not yet considered. That gets complicated though, so I think I will start with the conclusion and give the details later.
Here is the problem: You can buy "lots" that give you a permanent income, and you can buy 1, 5, or 10 lots at once for a fixed price for each lot. The price per lot goes up for every lot you already own, so buying 10 lots at once save money - if you can afford it in the first place. Is it better to buy lots one at a time, thus increasing your income a little much sooner? Or, should you save your money for the big purchase of 5 or 10 lots later on?
Here's the scoop: Again there are two (three Sir!) three things to consider: your current income, your savings or Cash-on-Hand to spend, and the amount of income you will gain (per lot) from a new purchase.
1) If you have NO savings, then the strategy is very simple. If the income gained from the purchase of 1 lot is greater than 10% of your current income, then you should purchase 1 lot as soon as possible. If the gained income is less than 10%, then you should save up to purchase 10 at once.
2) If you have some savings, but less than needed to purchase 5 lots, and the income gained from 1 lot is greater then 10% of you, then you should purchase 5 lots as soon as possible. If you have more than enough save for 5 lots, then wait until you can buy 10.
3) If the income gained from the purchase of 1 new lot is less than 10% of your current income, then you should always save up for a purchase of 10 lots.
4) If you won't be playing again for a "long" period of time, don't be afraid to buy anything you can, because it ALWAYS pays itself off eventually.
If you noticed (in 2) there is a fuzzy line between buying 1 and buying 5, you are correct: There is more to it, and ways to determine exactly what you ought to do and how soon you should do it, but it requires a lot of nasty calculation. The advice above is simple, requires only trivial math, and always works. I'll give those nasty details next time (but not tonight, it's late).
Here is the problem: You can buy "lots" that give you a permanent income, and you can buy 1, 5, or 10 lots at once for a fixed price for each lot. The price per lot goes up for every lot you already own, so buying 10 lots at once save money - if you can afford it in the first place. Is it better to buy lots one at a time, thus increasing your income a little much sooner? Or, should you save your money for the big purchase of 5 or 10 lots later on?
Here's the scoop: Again there are two (three Sir!) three things to consider: your current income, your savings or Cash-on-Hand to spend, and the amount of income you will gain (per lot) from a new purchase.
1) If you have NO savings, then the strategy is very simple. If the income gained from the purchase of 1 lot is greater than 10% of your current income, then you should purchase 1 lot as soon as possible. If the gained income is less than 10%, then you should save up to purchase 10 at once.
2) If you have some savings, but less than needed to purchase 5 lots, and the income gained from 1 lot is greater then 10% of you, then you should purchase 5 lots as soon as possible. If you have more than enough save for 5 lots, then wait until you can buy 10.
3) If the income gained from the purchase of 1 new lot is less than 10% of your current income, then you should always save up for a purchase of 10 lots.
4) If you won't be playing again for a "long" period of time, don't be afraid to buy anything you can, because it ALWAYS pays itself off eventually.
If you noticed (in 2) there is a fuzzy line between buying 1 and buying 5, you are correct: There is more to it, and ways to determine exactly what you ought to do and how soon you should do it, but it requires a lot of nasty calculation. The advice above is simple, requires only trivial math, and always works. I'll give those nasty details next time (but not tonight, it's late).
IO9 reviews Vade Mecum: the CthulhuTech Companion
From IO9.com:
What happens when ancient evils awaken in the year 2085? One seriously f-ed up RPG campaign setting. The world of CthulhuTech revolves around the Aeon War, an ongoing struggle between hideous aliens, otherdimensional horrors, freaky cultists and vast conspiracies. And they all have battle tanks and giant mechs. But the core rulebook wasn't enough to describe this dark future, so Vade Mecum: the CthulhuTech Companion delves even deeper into this world of sanity-destroying rituals and twisted technology.LINK to more
10 October 2008
Messing about with Google Documents
I can create forms, and maybe do something with them?
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http://spreadsheets.google.com/pub?key=pkUU00qOcikYQ4Oj8W7pUDg
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http://spreadsheets.google.com/pub?key=pkUU00qOcikYQ4Oj8W7pUDg
09 October 2008
Invasion of the Air-Eaters
BoardGameGeek recently featured a review of a game I own, but haven't played in a long time.
http://www.boardgamegeek.com/article/2700343#2700343
http://www.boardgamegeek.com/article/2700343#2700343
08 October 2008
RPGBomb.com Games Day Milwaukee!
RPGBomb.com Games Day Milwaukee!
Held at:
ADVENTURES IN GAMING!
9115 W. Oklahoma Ave.
Milwaukee, Wi 53227
Saturday December 6th, 2008
11am - Midnight*
Admission $5
Held at:
ADVENTURES IN GAMING!
9115 W. Oklahoma Ave.
Milwaukee, Wi 53227
Saturday December 6th, 2008
11am - Midnight*
Admission $5
07 October 2008
Hammer's Slammers
Another game from my collection.
I don't think I had played this game since I was in high school, but my friend Leonard and I played a few games recently. This game is as I remembered it: Simple to learn and fast playing, with and an interesting variety of units to play - near invincible Supertanks, lightning fast Combat Cars, ferocious Mercenary Infantry, death-from-afar Artillery, and ... ... and a bunch of conventional units with the unfortunate job of trying to stop all those monsters. It sounds like an unfair fight, and it generally is. The mercenary units are the heroes of this game, but the scenarios are set up so that players must play very aggressively to meet set time limits. This results in fast paced battles with fierce close assault combats, much like the stories the game is based on.
Those stories deserve mention too. David Drake's Hammer's Slammers series are hard hitting tales of military science fiction told by a Vietnam veteran. In my mind the first collection of short stories is the best. Drake is not my favorite author, but his stories have stayed with me for nearly 30 years, and I can think of no higher praise than that.
A bit more information about the game. I contacted Mayfair games and verified that this game is no longer in print, and not likely to be back in print. A few copies can be found for sale. There is inaccurate information on several web sites (what a shock!) that Mayfair went out of business back in 1997, but anyone who has been playing their games already knew that. Thanks to Kim at Mayfair Games for replying to my questions.
I have something more in mind for this game; Its simplicity makes it a good choice to demonstrate some of the mathematics that applies to boardgames. I will be returning to this game periodically with examples that demonstrate the math at work in games.
=== Various links related to the post ===
Mayfair Games:
http://www.mayfairgames.com/
Detailed description of the Hammer's Slammers boardgame:
http://www.boardgamegeeks.com/game/4049
David Drake's Official Home Page:
http://www.david-drake.com/index.html
(Makes me wonder if there is an unofficial one)
Slammer's miniatures:
http://www.oldcrowmodels.co.uk/ocproducts.htm
Another Slammers game, in large scale:
http://www.hammers-slammers.com/index2.htm
Some large scale models (to go with the large scale game):
http://www.david-drake.com/hswargame.html
I don't think I had played this game since I was in high school, but my friend Leonard and I played a few games recently. This game is as I remembered it: Simple to learn and fast playing, with and an interesting variety of units to play - near invincible Supertanks, lightning fast Combat Cars, ferocious Mercenary Infantry, death-from-afar Artillery, and ... ... and a bunch of conventional units with the unfortunate job of trying to stop all those monsters. It sounds like an unfair fight, and it generally is. The mercenary units are the heroes of this game, but the scenarios are set up so that players must play very aggressively to meet set time limits. This results in fast paced battles with fierce close assault combats, much like the stories the game is based on.
Those stories deserve mention too. David Drake's Hammer's Slammers series are hard hitting tales of military science fiction told by a Vietnam veteran. In my mind the first collection of short stories is the best. Drake is not my favorite author, but his stories have stayed with me for nearly 30 years, and I can think of no higher praise than that.
A bit more information about the game. I contacted Mayfair games and verified that this game is no longer in print, and not likely to be back in print. A few copies can be found for sale. There is inaccurate information on several web sites (what a shock!) that Mayfair went out of business back in 1997, but anyone who has been playing their games already knew that. Thanks to Kim at Mayfair Games for replying to my questions.
I have something more in mind for this game; Its simplicity makes it a good choice to demonstrate some of the mathematics that applies to boardgames. I will be returning to this game periodically with examples that demonstrate the math at work in games.
=== Various links related to the post ===
Mayfair Games:
http://www.mayfairgames.com/
Detailed description of the Hammer's Slammers boardgame:
http://www.boardgamegeeks.com/game/4049
David Drake's Official Home Page:
http://www.david-drake.com/index.html
(Makes me wonder if there is an unofficial one)
Slammer's miniatures:
http://www.oldcrowmodels.co.uk/ocproducts.htm
Another Slammers game, in large scale:
http://www.hammers-slammers.com/index2.htm
Some large scale models (to go with the large scale game):
http://www.david-drake.com/hswargame.html
06 October 2008
05 October 2008
Financial Advice for Facebook Games
I got into Facebook recently, and started playing some of the games available there. I noticed that many games share a similar theme in how they operate, and many are simple variants on a basic game engine. One feature common to many is that you can invest your money into land or buildings which then return a regular income. What caught my interest here is that the best investment is not always obvious. I found several examples of where people had posted information about the ratio of income-to-cost (income-gained/cost), and suggested that the highest ratio will be the best investment. For example: if playing Dragon Wars a Meadow (the cheapest unit of land) initially costs $5000 and increases your income by $100 per hour. The income-to-cost ratio is then $100/$5000 = 0.002. The higher the ratio be better, but the cost goes up depending on the number of lots you already own (an additional 20% of the base cost for all the Meadows you already own). There is a “discount” if you purchase in lots of 5 or 10; This means you can save a lot of money in the long run - spending more efficiently - if you always buy in lots of 10.
Lesson One: Invest your money now, and it will eventually pay itself off. You cannot lose.
While the highest ratio might be the best available investment, it does not consider the time needed to save up money for a big purchase. Obviously investing in any sort of purchase will eventually pay for itself, but I think a more relevant metric is the time needed for the investment to pay for itself. If we flip this ratio over (Cost/income-gained) we get a measure of time. In the same Dragon Wars example above this ratio is $5000/$100 = 50, which I will refer to as Time To Payoff (T2PO). So after 50 hours the new income from the purchase repays the cost of the investment.
I would suggest that this T2PO ratio is a more intuitive way to judge how good a particular investment is - The shorter the payoff time the better. It also gives useful information about when you will accumulate enough money to make your next purchase of similar cost.
Now let’s consider when you should spend your money. It is more efficient to save your money until you can buy a lot of 10, but my intuition was that sometimes a small investment now would have a bigger payoff that a bigger investment later. This depends on your current income (CI) and your Cash-on-Hand (COH). If a purchase is going to cost (PCOST), and that is more than your COH, then you will have to save up for (PCOST-COH)/CI hours (round up) before you can make the purchase and then pay it off. I'll call this total Time Until Buy (TUB).
Example: Suppose your income (CI) is $500 per hour and you have $10000 to spend (COH). You can:
1) Purchase 1 meadow immediately, TUB+T2PO = 50 hours.
2) Purchase 2 lots immediately (one at a time), TUB+T2PO = 53 hours (rounding up).
3) Wait 3 hours and purchase 3 lots, TUB+T2PO = 58 hours.
4) Wait 16 hour and purchase 4 lots, TUB+T2PO = 74 hours.
5) Wait 20 hour and purchase 5 lots (at a discount), TUB+T2PO = 70 hours.
Here we see that 1 meadow has the fastest payoff, but 5 lots will pay off faster than 4. Buying 5 lots at once is more efficient, but we have to save up for so long to do it that we can do better by making a smaller investment sooner. All this of course depends on your current income, cash available, and cost of what you want to buy. The point is that sometimes a small investment made sooner will have a shorter payoff than one you have to wait for.
Lesson Two: You might do better if you wait, but don’t wait too long! Small investments made earlier might be better than saving your money for a long time.
I have mentioned that buying 10 lots at once is a better deal or more “efficient”, and this deserves more attention, because it implies that buying less than 10 lots at once is somehow inefficient. So far I have ignored this, but consider: If I purchase 2 lots instead of 5, I might get my investment back faster, but when we go to purchase more lots, it’s going to cost extra to do it. This is a little tricky because it considers the cost of a purchase I have not yet made. As an example, I will compare buying 2 lots now and 5 lots later, to the alternate of buying 5 now and 5 (prorated to 2) later, with the goal being to compare the cost to get to 7 more lots.
If I first by 2 lots and later buy 5, I pay $5000+$5500=$20500 for the first 2 and 5*$6,000=$30,000 the next 5, for a total of $55,500. On the other hand, if I buy 5 lots and then 5, I pay 5*$5000=$25,000 for the first 5 and (5*$6,000)*0.4=$12,000 for the next 2 (the 0.4 is the prorating), for a total of $37,000. The cost of making an inefficient purchase in this example is $55,500 - $37,000 = $18,500. You can make the less expensive purchase sooner, but you pay for it later.
I can take this inefficiency cost (ICOST) into account when calculating the time to payoff by adding the "cost of inefficiency" to the cost of the purchase. This represents that I will be paying that extra cost eventually. I can calculate an "Adjusted Time to Payoff" (AT2PO).
AT2PO = TUB+(PCOST+ICOST)/CI
Starting with the last example, and assuming I have enough cash to make either purchase immediately (Time Until Buy is zero), then purchasing 2 lots has AT2PO= 0+($20,500+$18,500)/$200 = 195 hours, while purchasing 5 lots has AT2PO = 0+($30,000+0)/$500 = 60 hours. The more efficient purchase pays off in one-third of the time. This measure (AT2PO) meets my expectation that the most efficient purchase should have the shortest payoff time.
Again, the benefit of the earlier payoff depends on how long you might have to wait until you can afford the purchase, and how often you check in to play the game and reinvest your money.
Lesson 3: Make efficient purchases if you can afford the cost and the time.
Buying in lots of 10 saves a lot of money in the long run, but unless you can devote your time to be able to make the most efficient purchase at the right time, it won’t save as much as you might gain by simply spending what you have immediately – and unlike the real world of real estate investment, you cannot lose money at this game!
I will follow up with a spreadsheet that actually does some of these calculations - Stay tuned.
Lesson One: Invest your money now, and it will eventually pay itself off. You cannot lose.
While the highest ratio might be the best available investment, it does not consider the time needed to save up money for a big purchase. Obviously investing in any sort of purchase will eventually pay for itself, but I think a more relevant metric is the time needed for the investment to pay for itself. If we flip this ratio over (Cost/income-gained) we get a measure of time. In the same Dragon Wars example above this ratio is $5000/$100 = 50, which I will refer to as Time To Payoff (T2PO). So after 50 hours the new income from the purchase repays the cost of the investment.
I would suggest that this T2PO ratio is a more intuitive way to judge how good a particular investment is - The shorter the payoff time the better. It also gives useful information about when you will accumulate enough money to make your next purchase of similar cost.
Now let’s consider when you should spend your money. It is more efficient to save your money until you can buy a lot of 10, but my intuition was that sometimes a small investment now would have a bigger payoff that a bigger investment later. This depends on your current income (CI) and your Cash-on-Hand (COH). If a purchase is going to cost (PCOST), and that is more than your COH, then you will have to save up for (PCOST-COH)/CI hours (round up) before you can make the purchase and then pay it off. I'll call this total Time Until Buy (TUB).
Example: Suppose your income (CI) is $500 per hour and you have $10000 to spend (COH). You can:
1) Purchase 1 meadow immediately, TUB+T2PO = 50 hours.
2) Purchase 2 lots immediately (one at a time), TUB+T2PO = 53 hours (rounding up).
3) Wait 3 hours and purchase 3 lots, TUB+T2PO = 58 hours.
4) Wait 16 hour and purchase 4 lots, TUB+T2PO = 74 hours.
5) Wait 20 hour and purchase 5 lots (at a discount), TUB+T2PO = 70 hours.
Here we see that 1 meadow has the fastest payoff, but 5 lots will pay off faster than 4. Buying 5 lots at once is more efficient, but we have to save up for so long to do it that we can do better by making a smaller investment sooner. All this of course depends on your current income, cash available, and cost of what you want to buy. The point is that sometimes a small investment made sooner will have a shorter payoff than one you have to wait for.
Lesson Two: You might do better if you wait, but don’t wait too long! Small investments made earlier might be better than saving your money for a long time.
I have mentioned that buying 10 lots at once is a better deal or more “efficient”, and this deserves more attention, because it implies that buying less than 10 lots at once is somehow inefficient. So far I have ignored this, but consider: If I purchase 2 lots instead of 5, I might get my investment back faster, but when we go to purchase more lots, it’s going to cost extra to do it. This is a little tricky because it considers the cost of a purchase I have not yet made. As an example, I will compare buying 2 lots now and 5 lots later, to the alternate of buying 5 now and 5 (prorated to 2) later, with the goal being to compare the cost to get to 7 more lots.
If I first by 2 lots and later buy 5, I pay $5000+$5500=$20500 for the first 2 and 5*$6,000=$30,000 the next 5, for a total of $55,500. On the other hand, if I buy 5 lots and then 5, I pay 5*$5000=$25,000 for the first 5 and (5*$6,000)*0.4=$12,000 for the next 2 (the 0.4 is the prorating), for a total of $37,000. The cost of making an inefficient purchase in this example is $55,500 - $37,000 = $18,500. You can make the less expensive purchase sooner, but you pay for it later.
I can take this inefficiency cost (ICOST) into account when calculating the time to payoff by adding the "cost of inefficiency" to the cost of the purchase. This represents that I will be paying that extra cost eventually. I can calculate an "Adjusted Time to Payoff" (AT2PO).
AT2PO = TUB+(PCOST+ICOST)/CI
Starting with the last example, and assuming I have enough cash to make either purchase immediately (Time Until Buy is zero), then purchasing 2 lots has AT2PO= 0+($20,500+$18,500)/$200 = 195 hours, while purchasing 5 lots has AT2PO = 0+($30,000+0)/$500 = 60 hours. The more efficient purchase pays off in one-third of the time. This measure (AT2PO) meets my expectation that the most efficient purchase should have the shortest payoff time.
Again, the benefit of the earlier payoff depends on how long you might have to wait until you can afford the purchase, and how often you check in to play the game and reinvest your money.
Lesson 3: Make efficient purchases if you can afford the cost and the time.
Buying in lots of 10 saves a lot of money in the long run, but unless you can devote your time to be able to make the most efficient purchase at the right time, it won’t save as much as you might gain by simply spending what you have immediately – and unlike the real world of real estate investment, you cannot lose money at this game!
I will follow up with a spreadsheet that actually does some of these calculations - Stay tuned.
04 October 2008
Battletech Episode One: The Gathering Storm
Watching it now for the first time.
Some of this appears to be early computer generated animation, at least in scenes where the view is supposed to be provided "enhanced imaging".
Hmmm ... lots of torn sleeves on the left arm, vaguely Trek-ish.
The Elemental armor seems to be of about the right proportions than a person could actually fit in there - I like that.
Now for episode two!
More torn sleeves, and the old ones never get patched. Apparently needle-and-thread is another lost technology in the 31st Century.
03 October 2008
Red Dragon
[Mini and photo by Sam Snell]
Sam informs me this is one of the new plastic minis from the boxed set.
02 October 2008
See Jane Design Games
Dr. Jane McGonigal, that is. Sometimes Google is downright scary in its ability to predict things I might like to see. This showed up in my recommended feeds list today: AvantGame.
This web site goes along with it. Jane McGonigal is doing serious work on games. Meaningful games too. I think I'm jealous! :-)
Click here for info about her latest effort - Superstruct
(Having posted the link, I guess I'd better play!)
Jane McGonigal video presentation via The New Yorker:
"We're not trying to predict the future. We're making the future."
http://www.newyorker.com/online/video/conference/2008/mcgonigal
This web site goes along with it. Jane McGonigal is doing serious work on games. Meaningful games too. I think I'm jealous! :-)
Click here for info about her latest effort - Superstruct
(Having posted the link, I guess I'd better play!)
Jane McGonigal video presentation via The New Yorker:
"We're not trying to predict the future. We're making the future."
http://www.newyorker.com/online/video/conference/2008/mcgonigal
Aerotech units on the CBT map
A friend (you know who you are) was discussing the possibility of testing some alternate rules for Aerotech units playing on the Battletech map. I have had similar thoughts, so I'm going to share mine here.
[Camospecs diorama table at GENCON 2007, photo by me]
The map: Aerotech units move so fast relative the the standard CBT scale it's hard to get away from having separate maps. My though here is to place markers 16 hexes apart on the CBT map to indicate the center of the corresponding Aerotech map hexes (henceforth AeroHex markers). All Aerotech movement is done by Aerotech rules, with some adjustments to accomodate the CBT map. Aerotech units are considered to be approximately at the location of the markers, but are placed in a specific CBT map hex for the purposes of attacks.
Initiative:
1) All Aerotech units spend half of their movement first, with the side losing initiative making all it's moves first. Aero units moving through CBT map hexes may declare an attack on that hex.
2) Standard initiative then proceeds with Aero units as part of the sequence. Any Aerotech unit ending it's movement or declaring an attack within a hex should have it's miniature placed within 8 hexes of that AeroHex marker on the map. The controlling player may choose any hex, but facing must correspond to it's facing at the point when the attack was declared (exception, diving units may face down?, so that ground attacks all strike the front).
Declaration of fire:
Declaration of fire within specific hexes occurs during movement, but declaration against individual units occurs as part of the normal declarations.
Aero units: When Aero units declare targets, the controlling player must declare an "Attack Point" within 8-Piloting hexes of where it was placed at during movement or attack declaration, but no more than 8 hexes away from the AeroHex marker representing the Aerospace hex it is in. The same facing is maintained. For strafing attacks the Attack Point marks the (beginning/middle/end) of the strafing run.
Ground units: Ground units may declare fire against Aero units at any AeroHex marker they have moved through during the turn, or at the Attack Point. Treat the Attack Point as an additional Aerohex marker for the purpose of facing and range to target. The firing unit does not have to declare fire on the closest AeroHex marker.
Modified Facing: For the purpose of firing at Aero units, firing at the closest AeroHex marker to the firing unit, or any other marker on the "approach path", results in an attack on the front facing of the Aero unit. Attacks on the second closest (or further) markers on the "retreat path" are treated as attacks on the side or rear of the Aero unit, depending on the location of the ground unit relative to that marker.
Modified Range: Double the effective short, medium, and long ranges of all weapons for the purpose of air-to-ground and ground-to-air fire. Active ECM is considered to be effective within 8 hexes of any AeroHex marker on the flight path (but not the attack point). Do not double minimum ranges. Do not double the radius of area effect weapons.
The next thing is to reconsider the defensive movement modifiers for very high speeds. In a system using 2d6 the difference between a +4 and +5 modifier is much larger than the difference between a +2 and a +3. I am thinking that Aero units should have a completely different chart for this, and a finer gradation of modifiers. This last bit is a little tricky: I'm saying there need to be something like a +4.5 modifier, and an extra die roll to resolve the "fraction".
Example: If an Aero unit has a defensive modifier of +4.5, then resolve the attack as if this was a +4. If the attacker rolls exactly the target number, then there is a 50% change the attack will still miss, resolved by a d10 roll (roll 5+, with "0" counted as zero, not "10"). This could also be done with a d6 roll, but that requires an odd definition of "fraction" that isn't really important for this discussion. The new Aero movement modifier chart could then have meaningful modifiers that don't make them completely invulnerable on high speed passes.
Another thought might be to adjust air-to-ground modifiers for air movement, so that Aero units might need to slow down a bit to get decent shots on ground units. There is a certain fairness here that I like, because the Aero units can be still be fast and invulnerable if they want, but at the cost of combat ineffectiveness.
Time for me to go review the Aero rules again, and see what sort of alternate move-mod chart might be workable. I can check out the other rules I've forgotten about while I'm at it.
[Camospecs diorama table at GENCON 2007, photo by me]
The map: Aerotech units move so fast relative the the standard CBT scale it's hard to get away from having separate maps. My though here is to place markers 16 hexes apart on the CBT map to indicate the center of the corresponding Aerotech map hexes (henceforth AeroHex markers). All Aerotech movement is done by Aerotech rules, with some adjustments to accomodate the CBT map. Aerotech units are considered to be approximately at the location of the markers, but are placed in a specific CBT map hex for the purposes of attacks.
Initiative:
1) All Aerotech units spend half of their movement first, with the side losing initiative making all it's moves first. Aero units moving through CBT map hexes may declare an attack on that hex.
2) Standard initiative then proceeds with Aero units as part of the sequence. Any Aerotech unit ending it's movement or declaring an attack within a hex should have it's miniature placed within 8 hexes of that AeroHex marker on the map. The controlling player may choose any hex, but facing must correspond to it's facing at the point when the attack was declared (exception, diving units may face down?, so that ground attacks all strike the front).
Declaration of fire:
Declaration of fire within specific hexes occurs during movement, but declaration against individual units occurs as part of the normal declarations.
Aero units: When Aero units declare targets, the controlling player must declare an "Attack Point" within 8-Piloting hexes of where it was placed at during movement or attack declaration, but no more than 8 hexes away from the AeroHex marker representing the Aerospace hex it is in. The same facing is maintained. For strafing attacks the Attack Point marks the (beginning/middle/end) of the strafing run.
Ground units: Ground units may declare fire against Aero units at any AeroHex marker they have moved through during the turn, or at the Attack Point. Treat the Attack Point as an additional Aerohex marker for the purpose of facing and range to target. The firing unit does not have to declare fire on the closest AeroHex marker.
Modified Facing: For the purpose of firing at Aero units, firing at the closest AeroHex marker to the firing unit, or any other marker on the "approach path", results in an attack on the front facing of the Aero unit. Attacks on the second closest (or further) markers on the "retreat path" are treated as attacks on the side or rear of the Aero unit, depending on the location of the ground unit relative to that marker.
Modified Range: Double the effective short, medium, and long ranges of all weapons for the purpose of air-to-ground and ground-to-air fire. Active ECM is considered to be effective within 8 hexes of any AeroHex marker on the flight path (but not the attack point). Do not double minimum ranges. Do not double the radius of area effect weapons.
The next thing is to reconsider the defensive movement modifiers for very high speeds. In a system using 2d6 the difference between a +4 and +5 modifier is much larger than the difference between a +2 and a +3. I am thinking that Aero units should have a completely different chart for this, and a finer gradation of modifiers. This last bit is a little tricky: I'm saying there need to be something like a +4.5 modifier, and an extra die roll to resolve the "fraction".
Example: If an Aero unit has a defensive modifier of +4.5, then resolve the attack as if this was a +4. If the attacker rolls exactly the target number, then there is a 50% change the attack will still miss, resolved by a d10 roll (roll 5+, with "0" counted as zero, not "10"). This could also be done with a d6 roll, but that requires an odd definition of "fraction" that isn't really important for this discussion. The new Aero movement modifier chart could then have meaningful modifiers that don't make them completely invulnerable on high speed passes.
Another thought might be to adjust air-to-ground modifiers for air movement, so that Aero units might need to slow down a bit to get decent shots on ground units. There is a certain fairness here that I like, because the Aero units can be still be fast and invulnerable if they want, but at the cost of combat ineffectiveness.
Time for me to go review the Aero rules again, and see what sort of alternate move-mod chart might be workable. I can check out the other rules I've forgotten about while I'm at it.
01 October 2008
Giant Battling Robots With Tentacles
Catalyst Game Labs announces the release of Cthulhutech.
See also: johncoulthart.com
Cthulhu-Challenge, from Raincoaster.
See also: johncoulthart.com
Cthulhu-Challenge, from Raincoaster.
GENCON 2007 Pictures
I took a bunch of pictures in the Battletech room (and elsewhere) at GENCON 2007, and I finally remembered where I had these pictures stashed - out on Photobucket where they are nice and safe. Here's a link: http://s238.photobucket.com/albums/ff32/Trebuchet3025/
I also added a permanent link at the bottom of the page.
I also added a permanent link at the bottom of the page.
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