OT: Game Theory/Statistics

[geoschmo]

Suicide Junkie said:
There is quite a simple way to show that there is no guaranteed draw.

Put all your tokens down, and pretend I get lucky.

If your biggest pile of tokens is less than 9, I could have put 10 in every box and win 10 to zero.
If your biggest pile of tokens is 9 or more, I could have used the same distribution of tokens as you, except for zero against your biggest box, and +1 against all the other boxes. Meaning I win 9 to 1.

Therefore, no matter how many tokens your largest pile has, there is a possibility of me winning.

While I agree with your conclusion there are some problems with how you got there. First of all, each player has an 100 tokens and there are ten boxes. Simple division should show you the lowest possible number you can have for your biggest pile is 10, not 9. And that's if yo udivide them evenly. If any pile has less then ten then at least one other pile must have more than ten.

Secondly, each player has an equal numebr of tokens, so it's also impossible to outscore an opponent 10 to zip. The highest possible winning score would be 9 boxes to 1.

Geoschmo