Many expert players believe their bluffs should have negative expectation. They see them as a form of advertising that will lead to their being called on other occasions when they do have the best hand. However, I believe pure bluffs should have no worse than zero expectation as I shall explain in more detail in a later chapter At the same time, I agree that bluffs are an important part of a player's game. If you never bluff, your opponents will always know you have a legitimate hand when you bet. They will be likely to play correctly on the basis of what you have in your hand, which is to their advantage and your disadvantage, according to the Fundamental Theorem of Poker
Since it is correct to bluff occasionally so that you don't give away too much information when you bet with a legitimate hand, the question is when to do it. Clearly, you cannot establish a regular pattern of bluffing. Observant opponents will soon pick it up, and you will be caught bluffing too often to make it profitable.
Rather than try to guess when to bluff, especially against tough players, use your cards to randomize your play. (See Chapter Nineteen, "Bluffing and Game Theory.") In early betting rounds, with more cards to come, the most convenient and profitable way to use your cards is to bluff when you have the kind of semi-bluff hands I have been discussing. Then you are still bluffing occasionally, you will get all the advertising you need, but you have the extra advantage of sometimes winning even when you do get caught.
There are numerous situations where a pure bluff would not work often enough to be profitable, but where a semi-bluff is more profitable than simply checking and hoping to draw out and win in the showdown. Suppose you are playing $10-$20 hold 'em. After six cards your hand has fallen apart; you have no win. There is one more card to come and $60 in the pot. So if you bet $20 as a pure bluff against a single opponent, you are getting 3-to-1 for your bet when he folds, The key question, then, is whether that opponent will fold often enough to make a bluff profitable in terms of the pot odds you are getting. Let's say you expect he will fold 20 percent of the time. That is, he will call four times out of five and fold once. Thus, the odds against getting away with a bluff are 4-to-l, while you are getting only $60-to-$20 or 3-to-l odds when you bet. Therefore, the play has negative expectation. In the long run it is unprofitable. (This is assuming you give up your bluff when you're called and don't bet on the end.)
Now instead of a busted hand with one more card to come, let's assume you are holding a hand that you assess as having a 30 percent chance of winding up the winner - something like, say, a four-flush and a small pair. Again there is $60 in the pot, and you figure you have a 20 percent chance of stealing that $60 right there if you come out betting against a single opponent. Readers should see intuitively that a semi-bluff bet now turns into a profitable play. In fact, it is more profitable than simply checking and hoping to win in the showdown.
To make this point absolutely clear, we'll do some arithmetic. We'll assume that if you check after six cards, your opponent will check behind you, and we'll ignore bets on the end on the assumption that you will fold when you don't make your hand and your opponent will fold when you do. We'll take 100 identical situations where you check and hope to draw out and 100 situations where you make a semi-bluff bet.
Take checking first. With $60 in the pot and a 30 percent chance of winning, you will average winning $60 30 times for a total of $1,800.
What happens when you bet? Well, since your semi-bluff has a 20 percent chance of making your opponent fold, you will average winning $60 immediately 20 out of the 100 times you try it for a total of $1,200. Of the 80 times your opponent calls your bet, you will average winning $80 (the $60 already in the pot plus the $20 called) 30 percent of the time and losing your $20 bet 70 percent of the time. That works out to an $80 win 24 times and a $20 loss 56 times for a net win of $800. So after 100 identical situations, you will average winning $1,200 when your opponent folds, plus $800 when he calls for a total of $2,000, which is $200 more than you would win by checking. That comes to only $2 per hand, but it is with such small edges that you increase your hourly rate and your profits at the end of the month and the year.
The important thing to notice from this example is that both a pure bluff by itself and a value bet by itself would be wrong. Had you bet as a pure bluff, you would be getting only 3-to-l odds for a wager that has only one chance in five of winning. Had you bet only for value - that is, with the certainty your opponent will call - you would also be making an incorrect play since you have estimated that you are a 7-to-3 underdog. You are wagering even money (your $20 bet for a $20 call) when the odds are 21/3-to-1 against your winning. However, the combination of the two possibilities - namely, winning with a bluff or winning by improving to the best hand - makes a semi-bluff bet not just a good play but a mandatory one.
Just as a semi-bluff bet can be profitable, so too can a semi-bluff raise. Suppose in hold 'em you start with
Everybody checks. The next card is the
which gives you a flush draw and an inside-straight draw (not to mention a straight-flush draw). If someone now bets, you should raise. Even if that person folds only 20 percent of the time, the combined possibilities of winning right there and of making the best hand when he calls turns raising in this spot into a more profitable play than just calling. In general, when there is a possibility of winning the hand right there, even a slight one, it is important to bet - or raise. What's more, sometimes when you think you are semi-bluffing, you are actually betting the best hand. Another consideration when deciding to semi-bluff is the size of the pot. The larger the pot, hence the bigger the pot odds you are getting, the smaller your chances of getting away with a semi-bluff need to be to make the play profitable. Game theory suggests the opposite - that you should bluff less with a larger pot, assuming expert opponents. However, in practice most players do not adjust their calling strategy correctly to the size of the pot, which makes both semi-bluffs and pure bluffs more profitable when the pot is large.
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