Evaluating Your Play: Part VIII

Game theory tells us that there are two strategic categories. If you feel that your opponent can consistently outguess you, you should follow a random strategy that neutralizes his advantage. This randomization allows you to get the exact equity you are entitled to. It is known as an optimal mixed strategy. For example, you have to guess whether you opponent will select heads or tails. If he seems to be outsmarting you, you can simply flip a coin and know you will be right half the time. His advantage is neutralized. The other type of strategy attempts to exploit weaknesses in his play. If you are right in diagnosing his weakness, you can do much better by not randomizing. You have to guess if he will select heads or tails, but you know he always picks heads. Now you can exploit his weak strategy and win every time.

Poker is much more complicated than guessing heads or tails. In fact, it is way too complicated to analyze completely using game theory. There are some situations in which it is possible to calculate a game theoretical optimal strategy. Let’s assume your heads-up bets on the river are value bets, which occur when you have the best hand, and bluffs, which occur when you have the worst hand. Your opponent only calls or folds. What does game theory tell us? If you are making a pot-sized bet, the optimum ratio is two-thirds value bets to one-third bluffs. If you are only making a half-pot sized bet, then the optimum ratio is three-quarters value bets to one-quarter bluffs. I want to emphasize that if you follow these game theory guidelines, no one will be able to exploit you, but you won’t be able to exploit anyone else either.

The poker equivalent of the simpleton who always selects heads is the player who never bluffs. In the ancient days of high-draw poker in Gardena, we used to ask who was stupider — Mrs. Guggenheim who never bluffs after she draws one, or the Unlucky Expert with trip aces who calls when she draws one and then bets. You want to avoid being either Mrs. G or the Unlucky Expert. In general, you want to bluff and try to catch bluffs approximately the percentage of the time that game theory would suggest, but if your opponent is predictable, then you want to exploit his tendencies. Against someone who never bluffs, only call for value with very strong hands. Against someone who bluffs a lot, you can call with some pretty weak ones. Likewise, against a frequent caller, bluff less and against a frequent folder bluff more.

In an earlier column in this series, I suggested it was very valuable to carry a few index cards and a pen to note interesting situations for further analysis. It is probably a good idea to keep track of how often you bluff and how often you value bet. Also note how often your river calls catch an opponent bluffing. Whether you are trying to follow a game theory optimal strategy or an exploitative one, you should be getting caught bluffing some of the time. If you like to make pot-sized bets on the river, they need to work half the time for you to show a profit. If you find your bluffs are working eighty percent of the time, you are not bluffing enough. If you call a pot-sized bet with a hand that can only beat a bluff, you need to be right more than one-third of the time to show a profit. If your river calls with bluff-catcher hands work fifty or sixty percent of the time, you are not calling enough. When you don’t bluff often enough, you are playing a sub-optimal strategy, and your opponents can exploit it by folding more often against your river bets. If you don’t call on the river often enough, you are playing a sub-optimal strategy, and your opponents can exploit it by bluffing more often against you.

My experience has been that in small-to-medium stakes games, opponents who haven’t shown great strength don’t call enough when you make a half-pot to full pot-sized river bet. This is especially true when the river cards haven’t helped their hand and the board looks scary. Unless you know your opponent is a frequent river caller, try bluffing more often. At the end of a session, review your notes or at least try to mentally evaluate your performance as a bluffer and as a bluff catcher. ♠

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.