[MarkGritter]

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In this program, how much information does A have about B's range of hands and vice versa? If he knows a lot, like tendencies (strong middles, etc), then this can go back to exploiting additional information and probably doesn't have a lot to do with the game itself. Like, for instance roshambo can be played 'perfectly' (even money) by randomizing what you throw, but if you know your opponent heavily favors rock, you can win way more often than your fair share.

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In this experiment, each player has perfect information about the other's range of hands and strategy. That is how they calculate the best option for each of their hands--- by evaluating what the opponent may have and how we will play it.

There's no question that CP2-7 does have a game-theoretic solution. What I'm aiming at here is a somewhat smaller goal, to see if CP2-7 actually has a "fixed" best arrangement for every hand, or if the game-theoretic solution must involve randomization (or at least nonlocal thinking.)

In the smaller games explored in these experiments, either player could arrive at a stable game-theoretic strategy by randomly picking among their top choices for a hand each time (using suitable weights--- not necessary 50/50.) Then the other player would find no common tendencies to exploit.