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EXAMPLES OF THE FUNDAMENTAL THEOREM OF POKER

Example 1

Suppose your hand is not as good as your opponent's when you bet. Your opponent calls your bet, and you lose. But in fact you have not lost; you have gained! Why? Because obviously your opponent's correct play, if he knew what you had, would be to raise. Therefore, you have gained when he doesn't raise, and if he folds, you have gained a tremendous amount.

This example may also seem too obvious for serious discussion, but it is a general statement of some fairly sophisticated plays. Let's say in no-limit hold 'em you hold the and your opponent holds an offsuit

You check, your opponent bets, and you call. Now the ace of diamonds comes on fourth street, and you bet, trying to represent aces. If your opponent knew what you had, his correct play would be to raise you so much it would cost too much to draw to a flush or a straight on the last card, and you would have to fold. Therefore, if your opponent only calls, you have gained. You have gained not just because you are getting a relatively cheap final card but because your opponent did not make the correct play. Obviously if your opponent folds, you have gained tremendously since he has thrown away the best hand.

Example 2

Suppose there is $80 in the pot, and you have two pair. You are playing draw poker, and you bet $10, which we will assume is all you can bet. Your single opponent has a four flush - that is, four cards to a flush. The question is - are you rooting for him to call or fold? Naturally you want him to do what is most profitable for you. The Fundamental Theorem of Poker states that what is most profitable for you is for your opponent to make the incorrect play based on complete information about both hands. Since your opponent is getting 9-to-1 odds (his $10 call might win him $90) and is only about a 5-to-1 underdog to make a flush, it is correct for him to call because a call has positive expectation. Since it is correct for him to call, following the Fundamental Theorem, you are therefore rooting for him to fold.

This sort of situation comes up frequently. You have the best hand, but your opponent is getting odds good enough to make it correct to call if he knew what you had. Therefore, you want your opponent to fold. By the same token, it is correct for you to chase when you are getting sufficient pot odds. If you don't chase, you are costing yourself money and, therefore, making money for your opponent.

Example 3

Since it is correct for your opponent to call when he is getting sufficient pot odds, you can sometimes make an opponent fold incorrectly by showing more strength than you actually have on an early betting round.

You are fairly sure he has kings. You now proceed to make a pair of 6s on board, and you bet. Your opponent will almost certainly fold a pair of kings since he is afraid you have made aces up.

Some people might say, "Well, wait a second. Why don't You want your opponent to call as long as his pair of kings is worse than your two small pair?" The answer is that if there are cards to come and your opponent is getting proper odds, you do better to win the pot right there. A pair of kings versus two smaller pair needs very short odds to justify a call. Since your opponent would have been correct to call, you gain when you make him fold.
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