coin-matching game |Poker Strategy|

In the coin-matching game described above, the optimum strategy (for either player, as this is a symmetrical game) is to stack the coins at random, half of them heads and half tails. It is clear that if A, for example, stacked his coins with more heads than tails, B could do better than break even (in the long run) by stacking his coins with more tails than heads; in fact, if B put all of his coins so as to come up tails, he would be assured of a profit. Similarly, if A weights his stack toward heads, B can profitably weight his toward tails. (Of course if B guesses A's strategy wrong, A will win.)

However, if A aligns his stack on a 50-50 basis, the game will result in a draw (in the long run), no matter how B places his coins. (The reader should verify this for himself.) If A (say) does not adopt his optimal strategy (half and half) and instead weights his stack in one direction or the other, he is, in essence, gambling that he can outguess B. Use of the optimal strategy can guarantee A no worse than an even split (the "fair" result) in the long run.

Application to poker. When a "game theory situation" arises in poker, there is similarly an optimum strategy for each player. Just as in coin-matching a strategy consists of taking different actions (placing a coin as heads or tails) on a percentage basis, so in poker does a strategy consist of making a betting decision on a percentage basis. Some strategical questions at poker which can be analyzed on a game-theory basis are: How often to bluff; how often to call a possible bluff; how often to bet into a potential high-low call; how often to call high-low without an "immortal" in each direction.