Steve
03-04-2003, 04:27 AM
I created a simple one-card poker game and was surprised at the optimal strategy. Here is the game: Two players, they each ante $1. Player A (the dealer) deals a single card to each, and then he is allowed to CHECK, or BET exactly $2. If he checks, they compare cards and the higher card wins the antes. If he BETs $2, Player B is allowed to CALL $2 or FOLD. (If player B calls, the higher card wins the pot; if he folds player A wins the antes).
The deal then shifts to the other player, who now becomes "Player A". [Note that Player A is always the only aggessor, Player B can only play passively.]
Ok, being a game theory nut, when I first created this game I assumed the following: That since Player A is making a bet of exactly the pot size, player B will have to call at least 50% of the time, or player A will show an automatic profit by bluffing. Doesn't that sound correct? But it is in fact wrong, because the optimal strategy for player B (as far as game theory is concerned) is to call with his best 4/9, or roughly 44%, of hands.
The optimal strategy for player A was also unexpected. I expected he should bet at least his best 25% of hands. But actually his optimal strategy is to bet his best 2/9 (approx 22%) of hands, and his worst 1/9 (approx 11%) of hands (as a bluff).
Game theory fans, any comments? I derived these optimal solutions mathematically and tested them with a C++ simulation.
The deal then shifts to the other player, who now becomes "Player A". [Note that Player A is always the only aggessor, Player B can only play passively.]
Ok, being a game theory nut, when I first created this game I assumed the following: That since Player A is making a bet of exactly the pot size, player B will have to call at least 50% of the time, or player A will show an automatic profit by bluffing. Doesn't that sound correct? But it is in fact wrong, because the optimal strategy for player B (as far as game theory is concerned) is to call with his best 4/9, or roughly 44%, of hands.
The optimal strategy for player A was also unexpected. I expected he should bet at least his best 25% of hands. But actually his optimal strategy is to bet his best 2/9 (approx 22%) of hands, and his worst 1/9 (approx 11%) of hands (as a bluff).
Game theory fans, any comments? I derived these optimal solutions mathematically and tested them with a C++ simulation.