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Pot Size and Number of Opponents

THE GOOD AND BAD CARDS

One approach to poker is to raise when you have a very good hand and fold when you have a very bad hand. But what happens when you follow that approach? Let's say you have three aces rolled up on your first three cards in seven-card stud. That's the best possible hand you could have at that point. You put in a raise, and everybody folds. You have won a very small pot with a hand that potentially could have won a huge pot

The Cost of Giving Your Hand Away

This extreme example points up a basic poker dilemma. You want to make the most of your hands by maximizing your gains and minimizing your losses, yet what are you costing yourself when you play in such a way that your opponents should know what you have? The answer to this question is contained in the Fundamental Theorem of Online Poker Games, which states that every time opponents play a hand differently from the way they would have if they could see all your cards, you gain; and every time they play a hand the same way they would have played it if they could see all your cards, you lose.

The Fundamental Theorem indicates that when you play in a way that lets your opponents know what you have, you may be costing yourself substantially. If opponents know exactly what you have, they will never make a mistake except on very close mathematical decisions. The more your play gives away what you have, the less likely it is that your opponents will make a mistake. Yet you want them to make mistakes. Creating mistakes is, in a sense, the whole objective of the games. Clearly you might not want to raise immediately with three aces rolled up because you don't want your opponents to know what a strong hand you have. You want to win more money from them on later betting rounds. At the same time, never raising with a big hand could be a mistake too.

An interesting example of such a mistake came up toward the end of the 1977 World Series of Online Poker Games in a hand between two world-class players, Doyle Brunson from Longworth, Texas, and Bones Berland from Gardena, California. The games was no-limit hold 'em. Brunson had about $20,000 in front of him, and Berland, about $50,000. Before the flop Berland raised in early position, a hefty raise, and Brunson called him with two queens. The flop became J, 5, 2. Again Berland made a pretty good bet, and Brunson called him. On fourth street came another small card, and Bones made a gigantic bet, just about enough to put Doyle all-in. Doyle thought and thought and thought, and finally he pushed in his money and called.

Many people thought Brunson played incorrectly in calling with two queens. Berland was not about to bluff in this situation. These critics felt there was a great chance that Berland had two aces or two kings, and there were other hands he could have had that Doyle's two queens couldn't beat. Given the way he played it, the only hand Bones might possibly have that Brunson could beat was an ace, jack - the top pair on board with an ace kicker.
When Bones turned over his cards in the showdown, he had precisely ace, jack. Brunson won the hand with two queens and went on to win the world championship of poker that year. You asked Doyle afterward about his risky call. "Well," he said, "Bones couldn't have two aces or two kings because he never raised in early position with these hands before the flop. He would just call, hoping to re-raise, you know, on a slow play."

Here was a case, then, where a top player was given information because another top player played properly but with too much consistency. In no-limit hold 'em it is generally correct to slow play in early position with two aces or two kings. However, when Berland always played those pairs the same way, as he supposedly did, the information he gave away was much more costly than the money he figured to gain by playing the aces and kings properly every time.

To illustrate further the cost of giving away your hand, suppose you are playing head-up razz with no ante, no forced bet, and all the time in the world. You have decided, therefore, to play super-super-tight, folding everything except A, 2, 3 on your first three cards. With no ante it would seem you're a cinch to end up a winner, but the fact is a good player will slaughter you. He'll soon know you are playing only A, 2, 3, and he'll play his cards accordingly. He'll start off with slightly worse hands than yours, like three-card Ss and three-card 6s, but he'll wind up beating you on later plays since he'll know exactly what you have. He'll know when you pair up and when you don't, and he'll never make a mistake. On the other hand, though you start out with the better hand, you will make mistakes because you won't know what your opponent has. Thus, while in general it is correct to play very tight when there is no ante and no forced bet, by playing only A,2,3 in razz, you are giving away so much information that you don't stand a chance against a good opponent.