06 September, 2008

Axis and Allies Fishiness: Was Cassady Right?

So I dumped the logs of all of my active Axis and Allies games into a file and wrote a program that counts all of the die rolls. Here are the results for 20-some games and a total of 16,335 rolls:

1: 2,871 rolls
2: 2,790 rolls
3: 26,89 rolls
4: 2,625 rolls
5: 2,706 rolls
6: 2,654 rolls

This is really sketchy because, as you can see, there are a lot more of the lower rolls than there are of the higher rolls. The average roll is 3.457, when it should be 3.500. These may seem like small deviations, but statistically they are quite large. If you rolled an ideal die (with each side coming up exactly 1/6 of the time) 16,335 times, what is the chance that the die would come up showing "1" at least 2,871 or more times? 0.09%. Essentially, this means you'd have to roll a set of 16,335 dice 1,063 times in order to get 2,871 rolls of "1" in just one of the sets.

One explanation is that the game does not show any battles where neither the Attacker or the Defender gets a hit. I have suspected this for a long time and I used my program to check it. There were no battles where no one got a hit in any of my games. That's good enough for me...

1 comment:

Cassady said...

I. Love. You.

This is pretty amazing, and the depth of your analysis and the consideration it shows to actually care about this...well, I'm just touched.