Chances Are: Part VIII: An Effective Bluff

Math is a very good servant, but a very poor master. When you use math correctly, it will frequently guide you to making the correct play. Do not, however, become a slave to math. Poker is very situational, and there are many situations in which you must throw the math out the window and focus on what is actually happening at the table.

In the last column, which discussed methods of combining chances when more than one event must occur, we discussed why it is usually wrong to bluff multiple opponents. To recapitulate: when there is only one opponent, you have to estimate the chance of his folding compared to the pot. For example, if you make a pot-sized bet, your risk of losing a pot-sized bet and your gain, winning the pot, are equal. If he folds more than half the time you will show a profit. Let’s say he folds 70 percent of the time and that for easy calculation the pot is 100. You win .7 times 100 and lose .3 times 100. Seventy minus 30 equals 40. A very profitable play. Now, let’s say that there are two opponents. You now need them both to fold. As stated in the beginning of the paragraph, this is .7 times .7. They will both fold only .49, or less than half the time. This bet would show a tiny loss. (.49 times 100 minus .51 times 100 equals minus 2.) What about three opponents? With two, we squared the chances (.7 times .7). With three opponents, we have to cube the chances (.7 times .7 times .7). This is only equal to .34. This is a very bad bluff. It will clearly lose a lot of money. Thirty-four percent times 100 minus .66 times 100 equals minus 32. Against one opponent you showed a 40 profit. Against two you broke even. Against three you lost 32. This illustrates why it is very dangerous to bluff multiple opponents. Most players instinctively realize this and tend not to bluff in these spots. This means that you have to be much more careful about calling someone who bets into a lot of opponents. He’s probably not bluffing.

You have just read how the mathematics makes bluffing multiple opponents a bad play (negative equity). Now I will discuss a very common situation in which it is a very good play. In a deep stack, no-limit game, you are in the big blind. A sensible player raises under the gun, the button calls, the small blind calls and you call with Q J. The flop is 9 8 3. Your gutshot and backdoor-flush draw give you some outs, but your chance of hitting isn’t very good. The small blind checks, you check hoping for a free card. The raiser bets about three-quarters of the pot. The button calls quickly. The small blind folds, and it’s back to you. You read the initial raiser for a big pair, or less likely, two high cards like A-K or A-Q. You also noticed the button’s quick call. If he had a strong hand, he might have paused to think about raising. If he had a medium to weak hand, he might have paused to think about folding. His quick call makes you think he is on a draw – most likely spades.

It is clear that you should make a substantial bluff raise. The raiser made a fairly obligatory continuation bet, but even if he has aces or kings, your check-raise has to scare him. He certainly doesn’t want to lose a big pot to your set. And the fact that there is another player behind him makes him think his call is even more dangerous since he has to beat two opponents. On a good day, he’ll fold and the button will call with his draw. Then a blank will hit on the turn and you will bet enough to force him to fold. Even though it is usually a questionable play to try and bluff two opponents, here the situation made it clearly correct. Note that the while the presence of the third player in the hand normally is bad for attempting a bluff, it actually adds power to this play. The player with the strong hand is caught in the middle, and he will frequently fold. This play is technically a semibluff, since you can win even if called. A ten or two running hearts will probably give you the nuts, and even a queen or jack might put you ahead. Variations of the situation described in this column occur all the time. Be on the lookout for them. In the next column I’ll discuss a much less frequent situation where blindly following the math will lead you astray. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful games player. He has been a full-time gambler for over 35 years. With two WSOP bracelets and few million in tournament cashes, he is easing into retirement. He currently devotes most of his time to poker. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City – The Library near Houston and Doc Holliday’s on 9th St. are his favorites.