------ Original Post ------

Hi! I've spent a lot of time researching and trying to understand game theory, and game theory optimal (GTO) over the last little while. I believe that there are some rather large misconceptions about it, and I'm going to clarify a bit better what it is, and what it isn't.

Let's start with the simpler part of this. What is "game theory"? Essentially, it is any theory related to how to play a game. That's it, nothing too fancy here. I thought game theory required advanced mathematics or something to understand. Although many game theories do include math in them, it is not in essence what game theory is.

Ok then, so what is "game theory optimal"? Taking off from the math idea, I thought that it was an idea of how to play in a way that was unbeatable. No. Although playing a game theory optimal strategy would be unbeatable by definition, it is not the goal.

A game theory optimal strategy is any strategy in any game that makes the "best" possible move at every point where there is a decision to be made.

I used to think that game theory optimal and exploitative strategies were different. I thought that somehow there was this competition to see which one was "better". I was wrong. Exploitative play is a required part of game theory optimal.

I'm going to use a simpler game to illustrate my points here. Let's take rock-paper-scissors. An unbeatable strategy would be to throw each of your three options that has no detectable patterns to it so that your opponent can't beat you. So GTO would be to just pick one of your options are random every time, right?

The problem with the idea of picking everything at random is that you will also never "win". You can't win, and you can't lose. Worse yet, if whatever you're doing to pick one of these at random isn't random (i.e. it's biased), then your strategy is open to being exploited. In essence, if you employed this strategy perfectly, you would never win or lose. If you don't employ this strategy perfectly, you can lose, but you can't win.

Game theory optimal isn't looking to not lose though. It's looking to win! To take a look at what people have done to try and beat rock-paper-scissors, I suggest taking a look here (Rock Paper Scissors Programming Competition).

There's a key difference between a strategy that can't lose, and a winning strategy. The winning strategy still "looks" random to their opponents (any patterns generated are undetectable to their opponents), and also takes advantage of any patterns they find in their opponents' play.

When I first started learning about this, I thought there were two ways to play poker. One was GTO, and said that you want to be unbeatable. The other was exploitative, and said you want to beat your opponents. The "real" GTO uses both. You are both trying to exploit your opponents' weaknesses, and also not be able to be exploited. That is the goal, and the way that you would be able to create a true game theory optimal strategy.

I look forward to any questions and comments you may have!

Mike

------ Added June 6th, 2013 ~9am ET ------

This thread has generated some interesting thoughts, and I'm going to revise some of what I've said.

"Game Theory Optimal" is an answer to one of the following questions (and depends on who you ask):

    -    How do I maximize my EV to the greatest extent that is possible?

    -    How do I play unexploitably?

No one will ever be able to answer either of these questions. No strategy can truly be called "game theory optimal" that is not the true final solution. That's a bit of a bold statement, but I'm going to show why that's true.

First, let's start with something simpler. What is the game of poker? That's the key to understanding why proof is not possible.

In poker we are dealt cards, we make betting actions, and are probably trying to win. Although that creates a very large number of possibilities, they are still finite. But poker is more than that. Poker is played out with people. I have more options than "bet/raise/fold". I can also give or receive additional information that would be useful in game. I can act quickly or slowly. I can talk. I can listen. I can see.

There is an inherent flaw with any theory that creates a solution without taking into account the possible choices that we can make as people to give and receive information. By no means am I saying that mathematical "proofs" aren't useful, because they can be. What I'm getting at is that they can only prove something if the game of poker is sanitized as to not include anything it is that we do that makes us people.

Originally when I wrote this, I was claiming that exploitable play should be considered a part of game theory optimal. Now I'm changing my stance. Now I claim that no strategy should be called game theory optimal without taking into account everything that people can do during the course of a game (such as giving or receiving of information), as that is an integral part of poker. Without taking that into account, there can be no proof.