[douglas]

It's a simple enough game I'm sure there's a reasonably easy (for a game theorist) to prove optimal strategy, but it's probably one of those situations where the optimum is to randomly pick which of some number of strategies to follow each game. Any given fixed distribution of tokens can be beaten, but if you came up with a pair of distributions A and B such that any way to beat A loses to B and any way to beat B loses to A, flipping a coin to decide which of A and B to use each time would guarantee you a 50% win rate.