Let’s Talk About Game Theory

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In Chapter 4 of my book FossilMan’s Winning Tournament Strategies, I discuss the basics of game theory, and how it applies to poker. I want to summarize some of that discussion here, in case you haven’t yet had a chance to read the book.

Game Theory is simply a branch of mathematics that analyzes the strategies and choices in any game, and determines which of those decisions is optimal. If you can determine the complete Game Theory Optimal (GTO) strategy for a game, then with that strategy you are unbeatable.

For a game like poker, that doesn’t mean you win every hand, or even every session. But it does mean that in the long run, after luck evens out, you never lose. If your opponent were also playing perfect GTO strategy, then you would tie one another. If they are playing any other strategy, in the long run, you will win. However, not even the best computers have yet determined the GTO strategy for poker (though they are getting closer). And even if they get there, that strategy will be so complicated that no human brain will ever be able to memorize it.

So, you might be thinking, what does it matter? Well, the more you study and understand GTO strategy, the stronger and better your basic strategy will become. Basic strategy is what you apply in a poker game when you don’t know anything about an opponent or how they play. Are they too aggressive, too passive, too loose, too tight? Do they overplay suited cards preflop? Do they always semi-bluff their draws, or never bluff at all? Since you know nothing about them, you can only play your basic strategy. Therefore, the stronger your basic strategy, the closer it is to GTO, the better your results.

Once you get to know an opponent, you will find some mistakes and patterns in their play. You might also start to spot tells indicating when they’re strong or weak. Once you have enough confidence in these reads, you can move beyond your basic strategy, and make plays that diverge from it. If these modifications take greater advantage of the opponent’s mistakes, then this new strategy will be more profitable than your basic strategy, at least against this player. In the language of Game Theory, this is a Game Theory Exploitative strategy, as you are doing something different than your GTO strategy, to exploit the opponent’s weaknesses more effectively.

Here is a simplistic example. Imagine it is the first hand of a no-limit holdem tournament, and everyone is 300 big blinds deep. A player moves all-in preflop. Sticking to GTO strategy, you only call if you have A-A, which is what most of us would do. Now, on the next hand, this player again moves all-in preflop. And the next hand, and so on. At some point, it is obvious this player is doing this regardless of their cards.

However, a pure GTO strategy does not take into account how an opponent has played in the past. It only considers the bare facts of the game, such as stack size, blind size, position, action so far in this hand, and the like. As such, pure GTO strategy is still folding everything except pocket aces. In the real world, you would be much better off adjusting to this obvious pattern, and taking advantage by calling with some other hands. That is, you will modify your basic strategy, and make an exploitative decision to call with a range of top hands, not just aces.

In a more realistic example, suppose a player is the chip leader deep in the tournament, and is raising preflop a high percentage of the time. As such, you know they are unlikely to have a premium starting hand each time, meaning you can profitably adjust how you play against this aggressive chip leader. Let’s assume your stack is the right size (such as 15-20 big blinds), and you know this player enough to know that if you reraise all-in, they will only call with a reasonably strong hand. It might therefore be correct to reraise all-in, and take advantage of their loose opening range. If the numbers are right, you might do this even when holding a very weak hand. In contrast, if the person who raised is a very tight player, who also doesn’t like to fold once they enter a pot, you would probably be wrong to reraise all-in unless you had a very strong hand.

So, first, work on your basic strategy. You need to make it a strong, winning strategy on its own. More importantly, you have to really understand why it is a strong basic strategy. Only then will you be able to intelligently identify those situations where you can take advantage of an opponent’s mistakes, and win even more using a smart exploitative adjustment. Play Smart! ♠

Greg Raymer is the 2004 World Series of Poker main event champion, winner of numerous major titles, and has more than $7 million in earnings. He recently authored FossilMan’s Winning Tournament Strategies, available from D&B Publishing, Amazon, and other retailers. He is sponsored by Blue Shark Optics, YouStake, and ShareMyPair. To contact Greg please tweet @FossilMan or visit his website.