Thoughts On Game Theory: Part Seven

In the last column we looked at the ratio of bluffs to value bets for various bet sizes and the minimum defensive frequency (how often you must call to prevent your opponent from profitably betting any two cards) according to game theory.

Let’s review the theory for a pot-sized bet on the river, and then discuss some traps and situations where knowing game theory is only the first step to making good decisions. 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, so in these games it is 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 for 100 pot-sized bets, 67 percent should be value bets and 33 percent should be bluffs. If your opponent makes a pot-sized bet on the river, you must defend (call or raise) at least half the time or they can profitably bet anything.

This sounds very simple, but it is not. In real life, as the bettor, you have to know when to value bet, and you have to choose which of your probable losers you should use as bluffs. As the defender, you have to decide which of your bluff catchers should be calls and which should be folds.

In theory, value bets always win if called. In actual play, you aren’t always sure you have the best hand. Most of your value bets are made with hands that rate to be the best hand when called. Emphasis on the when called! How well your hand does against your opponent’s whole range is irrelevant. The important factor is how well it does against his calling range.

Years ago, David Sklansky illustrated this with a cute example from seven card stud. On the river, your board shows 7 7 7 7 and your opponent shows 6 6 8 9. Your quad sevens can only be beaten by a straight flush. Your opponent would need to have exactly Q J and 10 in the hole to beat you, since you have the 7 blocker, this is very unlikely.

You are a huge favorite to have the best hand. Should you value bet? Absolutely not! He sees your quads. He will only call with a hand that beats you, so your bet can never gain, but on rare occasions will lose. Unfortunately, most situations aren’t this clear. In no-limit hold’em, you will often face a difficult decision with top pair (or even second pair) and a reasonable kicker. It is hard to know how often your opponent will call with a worse hand.

Some of the factors in making this decision are your range, his range, the nature of the board, the previous action, your table image, and his table image. If your range rates to hit the board strongly, your opponent may not make loose call. If his range includes a lot of hands that beat yours, your hand may not be best. If you have played the hand very strongly, betting the whole way, he may not call with a marginal hand. If you have under-represented your strength, there is a much better chance of getting a call. If you are perceived as a maniac or a frequent bluffer, you can value bet more often with more marginal hands. If they look on you as a nit, your marginal value bets may not be profitable (but your bluffs should be.) If your opponent is a calling station, value bet more. If they only call with good hands, then avoid thin value bets. If they love to bluff, it may be best to check in hopes of inducing a bluff.

This discussion hasn’t even touched on bet sizing. Do you think he will only call a small bet with his marginal hand? If you make a huge bet, will he think you’re bluffing?

The decision of whether to value bet, and if so, how large that bet should be is one that occurs with a very high frequency and is absolutely crucial to your success as a player. Unfortunately, there are no simple rules, and everyone makes mistakes.

There are two more very important situations we have to cover. Unless you’re a lot luckier than I am, you will frequently have a very weak hand. Even if you know you want to have about one-third of your bets be bluffs, you have to decide which hands, which opponents, and which situations are right to bluff. Likewise, even knowing you have to call at least half the time to ‘keep your opponents honest,’ knowing when to call with a bluff-catcher and when to fold quietly is critical.

In the next column we will look at these situations. In the meantime, remember that Game Theory is a tool that can enable you make correct decisions about the appropriate frequencies for various actions. But it should only be one tool in your toolbox, and you shouldn’t become its slave. ♠

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.