New And Improved Wallet Game

[Jazza]

there was a post a little while ago about a game called wallet, which got me thinking about the game and the best way to play it

so here are the rules: you and an opponent choose how much money to put in your wallet, when you both have done this you put your wallets on the table, and the person who's wallet has the most money gets his money doubled by the loser (this was different in my other goofed up thread)

you both have infinite bankrolls, but have to choose a finite non-zero amount of money

so what strategy can you use to guarantee a minimum EV of 0?

also, i will create a contest for those who wish to enter:

everyone PM's me their prefered strategy (in the form of a probability distribution function), and after say 3 days i will see who's strategy is best overall, by having a round robin tournament between all participents

2 points for a win, 1 for a tie, and 0 for a loss

most total points wins

one thing to note is that the best strategy for the contest may not be the strategy that guarantees a minimum EV of 0

and btw i have tried to work out the answer (to avoid further embarrisment