GT-NO: Poker Strategy Isn’t Apples And Oranges

By playing a GTO strategy, you are guaranteed to win, which is why many of the world’s best players are gravitating towards it. But while it will win against a table full of amateur or low-stakes players, it will also leave a lot of money on the table. In this series we look at ways to spot exploits in your opponents and maximize your win rate.

Game Theory Optimal (GTO) strategies can be used for almost any game. Poker is just one of them.

For instance, suppose you and I choose between two fruits, say apples and oranges. We secretly write down apples or oranges on a piece of paper, and then compare them.

If we both wrote the same fruit, you give me $3. If you wrote oranges and I wrote apples, I give you $5. If you wrote apples and I write oranges, I give you $1.

If we choose our numbers randomly, then this is an even game. But because we don’t, one of us might be able to predict the tendencies of the other one and have an edge.

For instance, if I think you are 70% to write oranges, I will write oranges and have a 70% chance to win $3 and a 30% chance to lose $5. That’s an EV of 60 cents.

If you think there is an 80% chance I will write oranges, you will write apples and win $1 80% of the time while losing $3 20%. Your EV would be 20 cents.

But rather than try to predict what you will do, I can fall back to the GTO strategy. Which in this case means that I write oranges with a probability of two-thirds. If I do that and you write apples, I will win $3 one-third of the time when I also write apples, and lose $1 the other two thirds of the time. My EV is one-third of a dollar.

If instead you wrote oranges, I would win $3 two-thirds of the time and lose $5 one-third. Again, my EV would be one-third of a dollar.

Thus, in this game I can guarantee myself a profit of 33.3 cents on average per game, and there is nothing you can do about it.

If we played many games and you always wrote apples, I would average exactly the same profit as I would if you always wrote oranges. And importantly, I would make 33.3 cents per hand even if you played any type of “mixed strategy.”

Do you see this? If you don’t, I ask you to consider your oranges and apples separately. Since they both average giving me that same 33.3 cents, mixing up your strategy rather than always writing the same fruit, it doesn’t change anything. (Which is why it is simple algebra to calculate GTO strategies in games like this.)

Also notice that it would not help you in the slightest if I told you exactly what my strategy was. I will average a third of a dollar times the number of times we play. Such is the nature of GTO.

BUT if I used any other strategy and told you about it (or if you could deduce it), that would be a different story.

For instance, if you knew or suspected that I was writing both numbers with equal frequency, you would know (if you know GTO) that I am writing apples more often than GTO would tell me to.

So you should EXPLOIT that by writing oranges more often. In fact, you should write oranges every time!

Do that and you lose $3 half of the time but win $5 the other half. There’s the GTO strategy you could have used that kept your loss down to 33.3 cents per hand no matter what I did, but it would be insane to use it once you are pretty sure that I am straying from my GTO strategy.

In this case you moved your EV from minus 33.3 cents all the way up to plus a dollar.
And, of course, these same concepts can be applied directly to poker. It’s more of an apples-to-apples comparison, no oranges required. More next issue. ♠

David Sklansky is the author of The Theory of Poker, as well as nearly two dozen other guides on gambling, poker, and other games. The three-time WSOP bracelet winner’s latest book, Small Stakes No-Limit Hold’em: Help Them Give You Their Money, is now available on Amazon. You can contact Sklansky at [email protected].