Erich Friedman: each round i secretly write down either the number 1 or 2, and you guess which. if you guess correctly, you get that many points. otherwise you get 0 points that round. after 4 rounds, you win if your total is 3 or more points. otherwise i win. who is favored, you or me? both players know the result of each round after it is over, and before the next round begins. --a simpler game has an infinite number of rounds (or just one) and goal is to maximize total points per round. Optimum strategy in simpler game is "you" guess "1" with probability P and "2" with probabiilty=(1-P) "I" provide "1" with probability A and "2" with prob=1-A Expected payoff for "you" = P*1*A + (1-P)*2*(1-A) optimum parameter choices: A=P=2/3 payoff with those choices = 6/9 = 2/3 point per round. (sorry to be boring...) -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)