30 September 2008

The Physics of Racing

When my son got a Sony PlayStation of Christmas back in 2000 or so, we also purchase some games to go along with it. One of these was Grand Tourismo 2. I picked up the manual and started browsing through it so I could play well enough to be a worthy challenge for a young video game fanatic. I was in for a surprise; a very few pages of a rather thick manual were dedicated to the games and controls. The rest of it was instructions on how to drive a car at racing speeds.

I had been away from most video and computer games for several years at this point, and I found GT2 to be a very impressive combination of great (at the time) graphics and real world physics. Parts of the GT2 manual included a significant discussion of the physics involved, and I soon found myself studying this in some depth. I found a great resource for this: Brain Beckman's Physics of Racing Series. This great series of article told me everything I needed to know, and soon I was creating spreadsheet to optimize the gear spacing for the cars in my GT2 garage, getting that extra bit of performance out of them. My son thought I was crazy, spending all that time thinking about playing the game instead of just playing it, but I had a great time.

We still have the PlayStation and thee versions of the GT2 game, but I haven't tried to play in years. I did get a lot of pleasure from playing it, but after a "driving" session I always felt like I didn't have anything to show for my time (the same goes for most computer games I've since tried). I finally decided to focus my free time or other activities that give a bit more back; Specifically miniatures and tabletop gaming. I still think about that game a lot though, so maybe it's time to revisit it.

28 September 2008

Roman d20 at ZOI

Matthew Kirschenbaum notes the recent sale of 2000 year old polyhedral dice.

From - Zone of Influence - A game studies blog (mostly tabletop)

There is quite a bit of interesting info on this blog (or linked from), so I'll likely have more posts referring to it in the future.

25 September 2008

Gold Key Star Trek Comics

Wowio.com is offering free books online. Some of the most popular at the moment are the 1960's Star Trek comics by Gold Key. Much more to see as well.


[Hat Tip: io9.com]

22 September 2008


Some of my miniatures work -

+++ Photo credit Sam Snell (Wasp on CBT boards)

Which I gave away as part of a local contest, but I'm trying to do something similar now, so I'm pulling out the pictures. (Thanks Sam!)

21 September 2008

Standard Deviations From The Beaten Path

The increasing famous Andrew Ferguson takes an intuitive and cleaver approach to derive the Binomial distribution. From: Standard Deviations From The Beaten Path.

19 September 2008

Wet Dice

I got busy in the kitchen collecting data for my little experiment. I rolled them in batches of 16 (all of my new dice) and did ten sets, so my actual sample size was N=160. The result was 18 sixes, when I expected 160/6 = 26.67, so this is actually less than I should find on average. This brings up a detail glossed over yesterday; This is a two sided test with equal probability of detecting outcome greater OR lesser than the assumed fair value (0.1667). In my zeal to test if these dice are rolling higher than expected I ignored the other possibility that they might roll lower - a possibility that cannot be ruled out and should not be excluded. I did set up the test to allow this the possibility, but I didn't explain it as such.

It seems that I need to state the assumptions of my experiment more formally.
There is an assumption I didn't state last time; that all of these dice are identical in the probabilities of the result (identically distributed). It could be that some of my dice consistently roll high and other roll low, which tend to cancel each other out and confound my experiment.

18 September 2008

Lucky Dice versus the Water Test

Last night at the weekly gaming session, something a bit unlikely happened. We played the first 5 turns of a Battletech game, and I won the initiative roll all 5 turns. Now without going into the details of the game the initiative roll occurs at the beginning of each turn, and consists of a player from each side rolling two 6-sided dice, and the side with the highest total "wins" (re-roll on ties). This gives 50% chance of winning the initiate on any given turn. The chance of doing this 5 times in a row from the beginning of the game is 0.5^5 or about 3.1%. Some luck!

I was probably just lucky, but then I got to thinking: Having left home in a hurry that morning and forgetting to bring my regular dice, I picked up a new set at the store. (This was not from any real need, because my friends would have loaned me dice. I just try to spend money at the store that provides our gaming space.) These new dice were smaller than the one I usually use, and I wonder if these might actually be unfairly weighted, with the missing plastic (where the pips are) making rolls of higher numbers more likely (because the 1-pip side is heavier than the 6-pip side). This would also be true of regular size dice too, but perhaps the uneven weighting would be more pronounced with these smaller dice.

Loaded dice have a weight inside it closer to the side intended to be down. I had a pair of these when I was a kid (from a "magic kit" I think), and I recalled how my brother showed me the "water test" (Thanks John!). If you have ever seen loaded dice thrown on a hard surface, you might notice they bounce in a noticeably unusual fashion, but still don't always land on the weighted side. If you drop loaded dice into water though, the heavy side ends up on the bottom almost every time. I don't expect that these dice are so heavily loaded I will see a strong effect, but doing a standard statistical experiment "in the water" ought to amplify any unfairness - if it exists.

To simplify things a bit, I will drop a bunch of dice into water and count how many six-pips come up, reasoning that if my dice are unbalance then this is the mostly likely result. I could do this without the water too, but my thinking is that even a small unbalancing of these dice will be much easier to detect in this manner, therefore I don't need a terribly large sample size. A "fair" die will come up 6 with 0.1667 probability. With a little bit of calculation I can up with a sample size estimate on 121 die rolls. This will give me at least 80% chance of detecting a statistical difference if the water test results come up with 6's with .2667 probability (or more), and a no more than a 5% chance of this happening purely by chance (2.5% actually). I'll get my hands wet tonight, and report the results tomorrow.

If any statisticians are paying attention, this is a two sided test, but I could probably justify a one-sided test here. I have a professional aversion to one-sided test though. My calculations were based on a normal approximation.

11 September 2008

Why Giant Battling Robots?

Why, you might ask, should anyone be interested in giant battling robots? There's is a long story there, but I'll try to keep it short. I like games, and I like studying the statistical aspects of games. My early interest in playing games lead to my interest in computers, and eventually to a serious study of statistics and a career. My favorite game is Battletech, now officially "Classic Battletech" (CBT), a tabletop game played with paper, pencils, and dice, where pieces represent 30-meter tall bipedal war machines. I find it an interesting game or many levels.
I had been working out the mathematics of minor aspects of the game for a long time, but a few years ago I started to get really serious about understanding the mathematical properties of this game, and others. Along the way I've discovered some ways that games relate to the real world too. I am finally ready to starting sharing some of what I have learned, so I hope someone else finds this interesting too. Stick around, it should be fun!