Ah, RPS -- possibly the greatest game ever. Or possibly not. Anyway, I may write more about it later, but for now I'm interested in finding a way to use RPS to select a winner from among three people with equal probability.

Playing two-out-of-three between one pair and then pitting the winner against the odd man out won't work, because it gives the odd man a 50% chance of winning while the other two have only a 25% chance each. Requiring the odd man to win two in a row against the winner of the pair reduces his odds to 25% and raises the odds of the other two to 37.5%. Is there a reasonable way to get the odds to 33% for each player, or is it impossible to do because of the nature of the game?