Game Theory Optimal Poker

I frequently hear conversations about the benefits of game theory-optimal (GTO) poker. People say that if you aren’t playing a GTO strategy, your opponents can exploit you. True! If you are playing a GTO strategy and they aren’t, they have negative equity. Generally false. Playing a GTO strategy is the surest way to make a lot money playing poker. Really, really false!

Let me illustrate this by examining a simple situation. At the end of a no-limit hold’em hand, there is $200 in the pot. You and your one opponent both have $200 remaining in your stacks. You will have the best hand half the time and the worse hand the other half. You know when your hand is best and when it isn’t, while your opponent always has a mediocre hand that he isn’t sure about. He checks. Let’s construct a GTO strategy. Here are some possible strategies.

1. Never bet.
2. Always bet.
3. Always bet your winners, but only your winners.
4. Bet your winners, and some, but not all of your losers.

If you never bet, you win half the time. Your average gain is half the pot, or +100. If you always bet, he will quickly learn to always call. Your result is the same, except you win 200 more on your winners and lose 200 more on your losers. You still average a gain of 100. If you only bet your winners, he will quickly learn to always fold. You won’t win anything more with your winners, so you’ll still average 100 per hand.

Now let’s look at strategy, betting all winners and some losers. Say you play 100 hands. Suppose you decide to bet one of your losers. Your opponent should still always fold, but now you win 200 51 times and get nothing back only 49 times. Now your average win have increased to 102. Suppose you decide to bet ten of your losers, he should still always fold. Now you win 60 and lose 40. Your average is now 120. Now suppose you try betting 20 of your losers. He should still fold. Now your average per hand is +140. If you bet 25 of your losers, and he always folds, you will now be +150. If he always calls, you will also be +150. But if you start to bet 30 of your losers, he should always call. Now you are back to winning 140 per hand. Without going through a lot of math, betting all your winners and half your losers is a game theory-optimal strategy. You will average 150 per hand, and nothing he can do will hurt you. He can always call, always fold, or follow some middle path, and you will always win 150. That is your GTO strategy. He can’t exploit it.

But think about it. If your win is fixed, you can’t exploit him either. If he always folds, you could bet every time, and win 200 per hand. Or if he always calls, you could just bet your winners. Then you’d make 400 half the time or 200 per hand. When your opponent makes mistakes, you win more money with an exploitative strategy than a GTO strategy. The only problem is that by playing an exploitative strategy, you leave yourself open to exploitation by a good, observant opponent.

Have we gone in a circle only to arrive back where we started? No, we have learned that you make more money against bad players using an exploitative strategy. You do best against perfect players by using a GTO strategy. As if you didn’t know already: you should find bad opponents, those who make exploitable mistakes, and avoid games with perfect opponents, who don’t. Texture you strategy to be generally close to GTO, but still vary enough to exploit their weaknesses. In the example above, GTO strategy was to bet all your winners and 50 percent your losers. Tweak it, so that against people who call too much you bet 35 percent of your losers, not 50 percent. Against players who fold too often, bet 65 percent not 50 percent.

The other problem with playing a GTO poker system is that no one has been able to calculate exactly what it is. (Yes, a GTO strategy can be found for a few simple situations, but not much more.) Even if someday a full GTO strategy is worked out, it would be too long and complicated for anyone to remember and apply. Your best sequence of plays under the gun might change significantly with small changes in the stack size of the button or the big blind. You might have to play a random mix of strategies that includes not only folding, calling or raising, but also raising every legal amount from a minimum raise to a shove. ♠

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.