Thoughts on Game Theory: Part Eight

In the last column, we discussed pot-sized river bets for value by the last player to act, and the minimum defensive frequency against them (how often you must call to prevent your opponent from profitably betting any two cards) according to game theory.

I use a pot-sized bet in these examples not only because it is a common bet size, but because many games like Omaha are played pot-limit, making it the maximum bet you can make. Game theorists have calculated that when making a pot-sized bet on the river, you should have twice as many value bets as bluffs. Thus, out of 100 pot-sized bets, 67 percent should be value bets and 33 percent should be bluffs.

Obviously, you will reach the river as the last player to act more often then you want to value bet. River betting frequency should depend on your table image and perceived strength of your opponent.

Let’s say you reach the river 100 times. You have hands you feel are worthy of a value bet 40 times. (As discussed, you only want to value bet when you will be a favorite if he calls.) Since game theory tells you to have twice as many value bets as bluffs, you need to find 20 hands with which to bluff out of the 60 hands you have decided not to value bet.

So there will be 40 hands you just show down. These 40 hands will consist of hands that you think have a reasonable chance of winning a showdown against your opponent’s entire range. Hands that are not so good that you think they will be a favorite when called. In general, these are hands with one pair or worse. The often include ace or king high hands that have missed. Let’s there are 20 of these hands which are relatively strong, but not worth a bet.

To recap: we reach the river 100 times. We value bet 40 times. We have hands with reasonable showdown value 20 times. This leaves 40 more leftover hands. Game theory tells us we should bluff with half of them. The big question is which 20 should we select as bluffs and which 20 should we sadly show down expecting to lose?

There are three ways to select hands to bluff with. The first is the table situation, the second is your opponent’s tendencies, and the third is the actual cards in your hand.

Table Situation: Bluffs are generally more effective in situations where you are likely to have a hand that would value bet. These are cases where you have a range advantage and have played the hand strongly. It also occurs when you have played a hand weakly, checking and calling, and the river brings a possible straight or flush that you might hold. Your pot-sized river bet may get him to lay down a reasonable hand fearing you drew out on the river.

Opponent’s Tendencies: You remember that the minimum defensive frequency for a pot-sized bet is 50 percent. If you expect him to call less frequently, you should always bet. Imagine that he only calls 40 percent of the time. Now a pot-sized bet will show a net win of 20 percent of the pot. (The 60 percent you win minus the 40 percent you lose.)

In reality, it is impossible to know their actual defensive calling frequency in every situation. You should, however, have a general feel for which opponents are calling stations and which are very tight. Don’t try to bluff calling stations. Never! There is no surer way to burn up your money than to try to bluff someone who always calls.

As a bluffer you will feel sick when the calling station rakes in the pot with a marginal hand, and says, “I had to keep you honest.” In live games, you can frequently tell when your opponent has given up and is ready to fold. (Although some people with strong hands may pretend weakness to elicit a bluff.)

Actual Cards You Hold: This raises the complicated topic of blockers which I will save for the next column. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. 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.