More About Bluffs and Bluffing: Part II

In my recent column on bluffing, I wanted to give you some guidance as to whether you were bluffing too often or not often enough. In order to start this process, I gave you a “mission.” This was your mission: For the next few weeks, when you decide to bluff, always bluff the same percentage of the pot. (I’d recommend all your river bluffs be 75 percent of the pot.) Try to track how many bluffs work, how many fail, and your net winnings or losing on those hands. Hopefully this was not a Mission Impossible. Now let’s look at what your results mean. (If you didn’t undertake the mission, why not start now?)

Assuming you bet 75 percent of the pot as a bluff on the river, you need to win 3/7 of your bluffs to break even. 3/7 is around 43 percent. To illustrate this, if the pot was 400 and you bet 300, then you gain 400 when your bluff works and lose 300 when it fails. Thus if you succeed with three out of seven bluffs, you win 1,200 on those hands. But you also fail four out of seven times so you lose 1,200 on the losers, and breakeven overall. This analysis may seem simplistic. We haven’t mentioned game theory, optimal bluffing frequencies or any very complex concepts, just how often you have to win to break even. Your goal should be to make money on your bluffs, and game theory isn’t necessarily applicable to real opponents in real situations.

Before I continue, I want to emphasize that even though you want to make money on your bluffs, it is not bad to break even. Bluffs have an advertising value. When your opponents know you bluff, they are more likely to pay off your good hands. It is much harder to play against opponents who bluff fairly often. Bluffers create problems. They give you tough decisions. Therefore you want to bluff and give your opponents tough decisions. If you give them enough tough decisions, they will make mistakes.

If you wait for really good bluffing opportunities, you will win a high percentage of your bluffs. Let’s suppose the results of your mission showed that you bluffed 10 times and won 80 percent of your bluffs. Using the figure of a 400 pot and a 300 bluff, your profit was eight times 400 minus two times 300 or a net of 2,600. My guess is that you are being much too selective, and missing a lot of good bluffing opportunities. Your opponents aren’t paying off your good hands often enough, and your bluffs are working too often. If you start bluffing three times as often, but you only win 60 percent of your bluffs, you’ll do better. Your profit now is 18 times 400 minus 12 times 300 or a net of 3,600. Now your opponents are under a lot more pressure to call your value bets.

What if you had increased you bluffing frequency even more? Let’s say you bluffed 50 times, but only won half of them. Now your profit on your bluffs slips back down to 2,500. On the other hand, you opponents will definitely be paying off a lot of your value bets. (Remember they are now calling you half the time, while in the first case they were only calling 20 percent of the time.)

Game theory enables us to calculate the “optimum” bluffing frequency. When a player bluffs at that optimal frequency, there is no strategy his opponent can follow that takes advantage of these bluffs. The opponent can call every time or fold every time or flip a coin, but nothing helps. If you bluff too much, your opponents gain by calling every time. If you bluff too little they gain by folding every time. In the real world, as opposed to the world of game theory, you want to bluff opponents who fold too much and avoid bluffing those who call too much. This doesn’t mean you should ignore game theory. Knowing the optimal bluffing frequency will keep you from making a major mistake.

You are betting 75 percent of the pot. Sometimes you are bluffing and sometimes you are betting for value. If you bluff 30 percent of the time and value bet 70 percent, then you don’t care what your opponent does. If he always folds, he breaks even. If he always calls, 30 percent of the time he wins 700 (your 300 bet and the 400 in the pot), but 70 percent of the time you are betting with the best hand and he loses his 300 call. Thus over 10 bets, he wins 700 times three and loses 300 times seven. Whether he always calls or always folds, he breaks even.

It seems simple in theory, but in real life there are a lot of problems executing this plan. Not all your value bets will win. Sometimes they have an unexpectedly good hand, and you lose. Not all of your bluff are really bluffs. For example, you have A 3, and the flop was 10 7 2. The turn is the Q and the river is the 2. You bluff with your missed flush draw and he folds. His hand was 9 8, a straight-flush draw that missed. So your ace-high was really the best hand. You thought you were bluffing, but you were really value betting — hoping for a call. Keeping in mind that 30 percent is the correct theoretical percentage of the time you should be bluffing, a player with a reasonably good table feel, should be able to bluff more than 30 percent of the time, and still show a profit on his bluffs.

For next week, let’s modify your “mission.” When you decide to bet on the river, always bet the same percentage of the pot. Remember some of these bets are value bets and some are bluffs. (I’d recommend all your river bets be 75 percent of the pot.) Try to track how many bluffs work, how many fail, and your net winnings or losing on those hands. Also track your value bets. When tracking value bets, don’t include the money in the pot already. An uncalled value bet is worth nothing. You were already going to win what was in the pot if you checked. This is the opposite of a bluff, in which you weren’t going to win the pot by checking, but only by betting. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With 2 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.