Hi, Andrew,

I read your article at http://www.twoplustwo.com/magazine/i...el-thinker.php and I found it very interesting. In fact, I believe this is a critical topic not very often discussed over here.
I have some questions for you though. What would you say it woud be a good way to train yourself to have a good command on your levels of thinking? I find myself too often stucked in level 1, playing my hand like a robot, making bad calls and bad value bets. Other times, stuck in level 2, making those hopeless bluffs (I almost never sowplay though). But there are those times when I am playing my A game, when I feel I can clearly "see" what my opponents are betting with, and when I am capable of representing successfully a a strong hand, make correct checks, and make succsful thin value bets.
I would like these kind of play to be the rule more than than the exception. What woud you say are good things to do to improve this area of my game?

Yours

A poker enthusiast.

Good article.

nice read, ty.

Very interesting.

I have some doubts though. It's "easy" to know more or less if you're opponent is on level 1 or 2. However when you have a good opponent and you have to start thinking in deeper levels... How do you know at what level he really is? It seems so easy to get wrong and just go one level up and down and screw your conclusion. The information is "noisy" and any mental "fluctuation" could make your opponent change his level without even realizing he did so. What I mean is that this is very nice in theory, but I believe that once you try to get in deeper levels things can go wrong prety easily making you a nonsense player.


What do you think?

@Moneylover

I like your description of how you feel you are sometimes at Level 1, sometimes Level 2, then your "A" game. I definitely have those days as well.

But (and I don't mean this as criticism) are you sure you're not just being results-oriented when deciding if you are playing your "A" game or not? In other words, have you ever felt you were playing your "A" game but had horrible results? Presumably not, but are you really playing better during those times or are your results just better?

i think this is a good point, but if you are on a level 3 thinking and are exercisng the techniques suggested to pick the best option then you will be making the long term 'best' option in that situation. You talk about the players levels fluctuanting randomly due to many reasons, and this will of course affect your results, but as ever poker is a game of high variance and you just hav to make the correct choice knowing it will be profitable in the long run.

On a side note i also found that thinking about this while playing stops u playing like a bot, it keeps your mind active on the game and reduces leaks.

Thanks for the kind words all. I'm glad you enjoyed the article.

OP,

It's probably not what you want to hear, but the answer is "practice". Even when you aren't in the hand, you should work on putting your opponents on ranges and narrowing those down every time they take action. If you have trouble focusing on this, then you probably aren't in the best mindset to be playing. For advice on consistently playing your A game, and for recognizing and quitting when you aren't, I'd strong recommend Tommy Angelo's Elements of Poker.

FoldHellmuth,

This article was written to answer exactly the question you're asking. I know it can be tempting to throw up your hands and say, "Oh this is all so imprecise and speculative, you can never be sure, I'm just going to play my hand," but I think that's sloppy poker. Just because you can't be certain doesn't mean you shouldn't try your best.

As for what happens as players start thinking on higher and higher levels, I tried to address that at the end of the article as well. The answer is that both players' play approaches the game theoretically optimal. This is the "outside" to thinking on higher and higher levels, playing in a way that cannot be exploited no matter what your opponent is thinking or doing.

Awesome

+1.

Do you think there is a limit to the number of levels of thought that are meaningful? Like... a double-bluff is basically just not-a-bluff plus extra psychology, yes? So past a certain point it becomes more about how clearly you think at each level...

When you say "theoretically optimal", it sounds like you are thinking in a Nash equilibrium sort of sense... is that right?

Yes, I think that game theoretically optimal play (which I think would be an extremely complex Nash equilibrium for NLHE, but I'm really outside of my expertise in discussing this stuff) is the limit that players approach as they start thinking on higher and higher levels to adapt to each other.

nice

This is interesting. In particular because there has been a related discussion going on in the beginners' questions about range and level thinking: http://forumserver.twoplustwo.com/32...inking-849829/

"Level's" is the most overrated thing in poker since .5/1$

It should be range vs. percieved range. Understanding villains thought process to determine his range and how he percieves yours. Many of my close decisions are decided by game flow, not levels, thus you would be unable to put me on a level. Furthermore even when players can be described as playing a certain level, the level changes in different situations, for example facing a c/r to your cbet on a 822r flop players are able to think much more deeply then getting c/r on a QT9s 6o in a 3 bet pot, this is because one situation you have seen many times and one you havent and so with the given timebank you can consider fewer variable in the unfamiliar case and so depth of levels will be less.

Fair points, Huggy, but I don't think that means that levels are irrelevant. I agree that you can't pigeonhole someone as being purely a Level X thinker, but there are also players who are incapable of thinking about what they are representing in a remotely sophisticated way and others who are thinking constantly about that. It is definitely valuable to know which is which and to adjust your play accordingly. If you have a further read about how a player will think about a specific situation, that's obviously very valuable as well.

It seems to me that not thinking about your opponent's level can leave you open to exploitation. In the example that Hubby gave above when the flop comes if your opponent knows that in one case you are familiar with the play he can do something unexpected to try and throw you off.

Agree with RvsPR the overrated part is a bit much.

What I have. What do I think my opponents have. What do I think he thinks I have.

I never go outside this when playing...do you think its a mistake?
I feel I get the best reads when thinking like this.

Nice read.

Great Article. and very helpful in identifying villains.

A remember someone telling its best to be just one level above our villain, otherwise we level ourselves.

This is a must read for all serious poker players.

nice read

Well, if the decission becomes very "noise", then even in the long run we won't obtain anything right. The key concept is if you are making the right choice more often than not. Then of course in the long run it is +EV.

Hi Foucault,

I totally agree on working on levels 1, 2 and 3. But I think we all agree the deeper we go the more mistakes we can do and trick ourselves. Of course working on this is also a training and it is probably very useful. About the optimality issues I am not sure I understand what are the conditions. When you speak about optilimality what exact information do you consider known by each player?

Great article.

I think what is missed here is the obvious. You have an opponent who typically plays level 2. There are situations where this player is capable of level 3 thinking. In some simpler situations, higher level thinking is possible with this player. Although, he may also some across some situations where it is so complex for him, he is not even able to play level 2 in that hand. This can happen in back to back hands.

The important thing to recognize is that in most hands, he plays level 2 poker and adjust accordingly.

In this context "optimal" doesn't mean most profitable against a particular player or type of player. Game Theoretically Optimal, or GTO, means unexploitable. Here's an example:

It would take about 2 minutes for an intelligent person to develop a tic-tac-toe strategy whereby he would never lose. In fact, against any other intelligent person, the game would always be a draw. If you were playing high stakes heads up tic tac toe against John Nash, this would be the correct strategy for you to employ. He is never going to make a mistake, so the best you can hope for is to force draw after draw.

But if you were playing against my 3-year old cousin, you might do better off employing a different strategy that takes advantage of the fact that the kid sucks at tic tac toe. He's just awful. This would NOT be a GTO strategy. You'd be playing in a way such that a better player could take advantage of you and beat you. But this particular 3-year old just sucks so hard that he isn't going to take advantage of that, and the GTO strategy that focuses on forcing a draw doesn't give you the opportunity to take advantage of his abysmal planning.

GTO strategy is much more complex, possibly unsolvable, for NLHE. Until you know which mistakes your opponents are making, or at least have reasonable basis for a guess, then you should try to play in a balanced way that won't make a big mistake no matter how they are playing. This means betting or raising your strongest hands, checking or calling medium strength hands, and folding or bluffing your weakest hands.

Once you know that a guy is a station, you can bluff him less and value bet him more. This is no longer GTO strategy. If he stops being a station, continuing to play this way will cost you money. However, if he keeps stationing, then you will make more money exploiting his looseness than you would if you were playing GTO.

So optimal in this sense doesn't assume any information at all about how your opponent is playing. In fact, it's the best strategy when you don't have any information to go on, or in situations where you don't expect to have an edge in the leveling game.

Foucault,

Good stuff man!

I agree with the range vs pcvd range discussion. Although I think I want to add.
You're able to judge one's level of thinking a lot better when you can factor in dynamics.

e.g. your example 4 is a hand you can't "observe" and then draw a conclusion. There needs to be some history to judge about that hand. Player B didn't raise flop nor turn, which are both great occassions for player B to raise with strength and semibluffs.
So if it is a spot without much history I would think that two pair is near the strongest part of player B's range. Actually I would encourage player A to check-call this river, in the first place to get some reads and history, in the second place because I would assume that player B's river range is heavily weighterd towards pair+draws, combo draws that he didn't want to semi-bluff raise on flop or turn. When checked-to player B gets a good opportunity to turn weak hands like 76 into a bluff.

Moneylover:
I think you have a more basic leak.
IMO you need to focus more on your opponents, their ranges, and their betting patterns. It is a more underlying problem in your game than your level of play. You seem to be paying more attention at the table some days when you say you play your "A game". Look at your session log of wins/losses and find the times your are most attentive and try to play at those times. It seems as though you are choosing bad spots to value bet/bluff. Also, try to isolate the players at the table that are rarely folding to bluffs and value bet them more.

very good read i appreciate this