This game is similar to "rock, paper, scissors" in that two players independently pick one of the six things, and if one thing somehow "beats" the other, then that player wins. If both players pick the same thing, they repeat until someone wins.
Life grows on Earth.
Water douses Fire.
Air resists Cold.
Life drinks Water.
Fire consumes Air.
Cold freezes Water.
Earth smothers Fire.
Life breathes Air.
Fire and Earth both warm Cold.
Air and Water both erode Earth.
Fire and Cold both destroy Life.
Water displaces Air.
A program that plays this game has a single set of probabilities for picking each of the six things. Assuming that the program's opponent knows what these probabilities are, what probabilities will give the program the best chances of winning?
What if the rules of the game are changed so that "Water displaces Air" is replaced with "Air ripples Water"?
(In reply to Compliments, and corrections
by Steve Herman)
Thank you. I can't tell you how far a little compliment goes. It is certainly appreciated!
I believe that the correct solution has been reached among the comments, and I would
post the official solution, but I'm still trying to think of a simple
way to explain it. Puzzles should be baffling, but solutions
should not. ;-)
Posted by Tristan
on 2005-06-22 01:11:32