But Erich's version has complications that make it more challenging. First is the finiteness, and our goal is not to maximize our expected point total, but our chance of surmounting the three-point threshold. Second is the chance for both players to alter their play based on the state of the game so far. There are few enough parameters here (moves remaining, points needed to win) that a 2-D plot of the game value is possible and feasible. It will be interesting to see how it differs from Warren's 'base level' strategy. I'd also like to see how the strategy differs from the simple game of two players competing for most points in N moves, or first-to-reach-100, where the move choice is either to flip a coin, or accept an average score for that move. Here's some _real_ game theory! Rich ------ Quoting Warren Smith <warren.wds@gmail.com>:

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)

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