I've been hearing a lot about the different levels of poker thinking, and I feel compelled to sort out some of the misconstrued details.

First of all, it originally started getting popular with Sklansky's essay "Three levels of Expert Poker Thinking." We'll get back to that. What happened next, however, is that someone simplified it, and then proceeded to make it complicated again by turning it into something completely different than what it started as. Personally, I think it's gotten a little ridiculous.

First let me cover what I will call the "New Levels of Poker Thought."

1. What do you have?
2. What do you think your opponent has?
3. What does your opponent think that you think he has?

....and so on.

This is the general idea you see pasted all over the internet these days. Originally, in homage to Sklansky's essay, there were only these three levels of thought; now there are frequently four or five. As most of us already know, there are actually infinite levels of thought, so the number that one chooses to stop at is really of no concern.

In practice though, when battling wits in poker, I think there are really only two levels that matter: I like to call them "I know," and "he knows that I know." (Anything further just repeats; for instance: "I know that he knows that I know" is just "I know" all over again, and so on.)

For example, let's say that I have a flush, and I know I should bet x amount to get paid off. However, if my opponent knows that I know I should bet x to get paid off, then he'll fold to the obvious bet. So, if I know that he knows that I know I should bet x, then I should try to trick him by betting y. But wait - if my opponent knows that I know that he knows that I know I should bet x, then he'll know I'm trying to trick him and he'll fold to y. Therefore, if I know that he knows that I know that he knows that I know I should bet x, then I should go ahead and trick him into calling by betting x, just like I had planned on at the beginning... are you lost yet?

It's like that scene from "The Princess Bride," the one where Vizzini is arguing logically over which of the two glasses Wesley has poisoned. In poker, the outcome of a hand can be the much the same as the outcome of that scene - you might sit there and outthink your opponent, only to find he's poisoned both glasses anyway, and had no idea what you may or may not have thought anyway!

Which is why it's a little unnecessary, these "infinite levels of thought." In practice, for any player with some experience, there aren't infinite levels - there are only two: straightforward, or tricky. People always talk about going "just one level past their opponent", but how do they know they didn't actually fall three levels short - or five levels, or seven levels short? Maybe they actually went three, five or seven levels over - they would still have come to the same conclusion as they came to going "one level over;" see what I mean? No matter how many convolutions you put yourself through, all paths end here: either he knows that you know, or he doesn't. People act like they can read their opponents' minds, but with only a fifty-fifty chance of getting your opponent right, it's not that hard to stumble on the right answer.

Now, I'd like to revisit Sklansky's original "Three levels of Expert Poker Playing", to explore where these original "three levels of thinking" came from.

1. Expert Mathematical Strategy (What do I have?)
2. Expert Counter Strategy (What does my opponent have?)
3. Expert Mixed Strategy (What does my opponent think I have?)

Level 1 play, perfect mathematical strategy, is an automatic strategy that doesn't take into account your opponents' cards. Level 1 thinking is correct more often than not, and is best-suited for weak, loose games, where one of the advanced levels of thinking would be lost on your opponents. With a Level 1 strategy, you would always play a specific hand the same way in a specific situation.

Level 2, counter strategy, is determined by how your opponents are playing. Sometimes, taking advantage of what your opponents are doing is more profitable than what a pure percentage play would dictate. For example, you might bet a made hand against a passive opponent, but check the same hand versus his aggressive counterpart. With a Level 2 strategy, you would play a specific hand in a specific situation differently against different players - but you would always play it the same way in the same situation against the same player.)

Level 3 play, mixing it up, is for the toughest games. Against very tough players, it's sometimes necessary to play a specific hand differently, even in an identical situation, against the same opponent. What this usually means is reversing your previous actions, knowing that they have been observed - or knowing that your opponent is anticipating a reversal and therefore avoiding it.

Level 3 is obviously where we get back to the "I know" and "he knows that I know" type of thinking. But even Sklansky himself states, in his essay, that when playing with an opponent capable of this kind of advanced thinking, it's probably best to use game theory to randomize your actions.

Randomizing your decisions involves using irrelevant factors, such as the color of your cards or the second-hand of your watch, to influence your close decisions. For instance, you might decide that if three (of your five) cards are red, than you will bet the river - otherwise you plan on checking. This can be an important way to throw off an opponent who is capable of outthinking you.

It's important to note that mixing up your play shouldn't be done at the expense of making large mathematical mistakes. It's okay to make a slightly inferior play if it can be used to milk someone out of future profits, but one shouldn't veer too far from sound mathematical strategy in the name of deception.

I've read several articles lately, some that describe four levels of thinking; others talk about five and beyond - one of them even started with a Level Zero! But it's all regurgitation of the original idea of only three levels worth mentioning - and I doubt that any of those authors have ever read the original Sklansky essay. I just thought it was time to go back to the roots.

Good luck at the tables!

Sam @ Power Poker Course.




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