Second Example

Draw poker, seven players, jacks to open, pass and back in. The ante is 7 chips, the limit 2 before the draw, 4 after the draw. Dealer is G. A, B, C, D pass. E opens for 2 and all players from F through C drop.

D holds 10-9-8-7-K. The odds are still 5 to 1 against his making a straight. The pot offers 9 chips against the 2 he must pay to call, or 4 1/2 to 1. He cannot win by pairing because E has at least jacks. The odds against him are greater than the odds he is offered and he throws in his hand.

These are the simplest possible examples (though both of them happen frequently) and in most cases closer figuring will be necessary. The examples were purposely made simple to illustrate the basic theory of the application of mathematics to poker. Mathematics in poker can be very useful—in fact, some knowledge of the odds is essential—but nothing can be more damaging than placing slavish reliance in the mathematical probabilities. Events always alter the a priori assumptions. For example, in a seven-hand game of draw poker it is useful to know that two aces should be the best hand, normally, before the draw; but if you hold the aces and three players have already come in before you, you must assume or at least suspect that your two aces are not the best hand; and if one of those players has raised, you can be fairly sure that they are not the best hand.