To BE A REALLY GOOD POKER PLAYER it is essential to have a fair idea of the direct probabilities underlying various situations in poker in order to use them as a guide to one's general course of action. But one should always bear in mind that in the final bet or bets the psychology of one's opponents is much more important than any of the direct mathematical probabilities.

I was fortunate to learn this at the age of fifteen. In the fall of 1987 by dint of some judicious maneuvering I managed to get myself in the army. I wasn't much of a soldier, but I did receive a thorough military training in the principles of poker, my chief instructor being an old sergeant who used to come out the big winner in practically every game. Naturally, I made a study of the sergeant's military tactics, and pretty soon I discovered his simple system.

The game was Table Stakes Stud, although the table stakes were commensurate with the soldiers' thirty dollars a month. Occasionally, however, after seven or eight of us had cornered most of the company's money, the game might run into fair figures.

My first line on the sergeant's theory came when a player showing the king, queen, jack, and ten of spades tapped him and the sergeant called with a pair of threes and won a big pot. I asked him about that the next day and he said, "Well, in that spot this other fellow was going to bet whether he had them or not, and I couldn't afford not to call"

The next time we played I had aces back to back against his kings. Two other aces had appeared during the course of the early rounds, but when I tapped the sergeant on the last round he turned up the king he had in the hole and threw his hand away without hesitation. I didn't ask him why he did it because I didn't have to. I put two and two together and said to me, "The sergeant didn't call because he figured it was such a foolish time to bluff that I must have that case ace in the hole."

The sergeant's theory-which might be summarized as, "To hell with the mathematics-it's the money that counts!"-has worked for me ever since. But, strangely enough, it proved his undoing in the final two-day game that preceded our discharge. By this time I had learned that he liked his theory so much that he made the mistake of never departing from it in the slightest. Accordingly, whenever he made a logical bet I called him, knowing he might be bluffing. But when he made an illogical one I dropped, knowing that he wasn't bluffing. Whenever it looked like a poor time for me to bluff him I did so with perfect safety, while if it looked like a good time for me to bluff him I'd have to have an "immortal" before I would throw a chip into the pot.

Mathematics of Draw Poker

There are 2,598,960 possible Poker hands in a fifty-two card deck. This is the number of combinations of fifty-two things taken five at a time and is equal to the product of. The numbers fifty-two, fifty-one, fifty, forty-nine, and forty eight divided by the product of the numbers one, two,) three, four, and five. Table I shows the division of these! hands into categories.

Two Pairs

There are seventy-eight possible combinations of two pairs, ranging from the highest (aces and kings) to the lowest (threes and deuces). Of these seventy-eight combinations, twelve are aces up, eleven kings up, ten queens up, nine jacks up, etc.

Accordingly, it is important to note that if you have tens and nines, which look like two fairly good-sized pairs, actually the chances are that if another player has two pairs, they will be better than yours, the reason being that forty-two of the seventy-eight combinations are jacks up or better.