Level-Headed Thinking

by Andrew Brokos
Originally Published in Two Plus Two Internet Magazine, November 2007 issue

An important aspect of winning poker is adapting to the level on which your opponent is thinking. Most serious poker players understand that this is theoretically true but have trouble putting it into practice. This month, I want to talk about what these levels of thinking are and how they should influence your play.

Levels
When I refer to levels of thinking about poker, I mean the depth with which a player is thinking about a given situation and the factors he is considering. These levels can be broken down as follows:

Level 1– What do I have? This player thinks about absolute rather than relative hand strengths. He bets, calls, folds or raises based solely on where his holding falls on the scale of poker hands without regard for situational factors such as what hands are possible, what his opponent might have, or what he has represented. The sizing of his bets and timing of his decisions also tend to be commensurate with his hand strength. Only the absolute worst players are pure Level 1 thinkers, though many poor players revert to this thinking in certain situations.

Level 2– What does he have? This player tries to get a read on his opponent’s holding and then plays his own hand accordingly. If he bluffs, it is because he knows he suspects is beat and not because he has consistently represented a strong holding on earlier streets. When he bets for value on the river, it is because his hand is strong relative to the board and to his opponent’s range of hands rather than relative to the range he has himself represented. Most players think on Level 2 most of the time.

Level 3– What does he think I have? These players are conscious not only of what they have but of what they have represented. They think dynamically about your hand range based on how you have played in light of the information they know they have given you about their own hand. They will recognize, for instance, that you failed to bet or raise when there were many possible draws on the board, and therefore give you less credit for a big hand. They will also make thin value bets when they know they have shown a lot of weakness and bluff when they have shown a lot of strength earlier in the hand. Most mid-stakes winning players are primarily Level 3 thinkers.

Level 4– What does he think I think he has? The Level 4 thinker is a truly tricky opponent who gets inside your head and thinks about his play in light of the information you have about him and his hand and also the information that you know you have given him about your hand. The best example I can think of for this is a player who folds a pair to your river bet after you checked and called the flop and turn and all the obvious draws missed on the river. If his reasoning is that you think he will think you are bluffing and therefore would not bluff but would make a thin value bet, then he is employing Level 4 thinking.

You can imagine the progression from here and how intricate the mind games can get between two top-notch players. However, few players successfully employ Level 4 and above thinking regularly, in part because it is not often necessary.

A Level 3 Call
This hand occurred during an online heads up match with $3 and $6 blinds and $600 effective stacks. My opponent, a good but not great player, raised to $18 on the button, and I called with Kc 6c from my BB. The flop came 9h 6d 4c, giving me middle pair with a good kicker and a back door flush draw. I checked and called a bet of $28.

A 7c on the turn improved my flush draw, and I checked again. My opponent also checked, and the river was the 8s. This was a bad card, not so much because was an overcard to my pair, but because it put four to a straight on the board. I checked again, and my opponent bet $70 into a pot of about $74.

Because I expected this player to be thinking on Level 2, as even most good players do when it comes to value betting the river, I figured he would not make a thin value bet here. My passive play had represented a weakish one-pair hand that would be pretty scared by the river. Thus, I expected his range to consist of exactly straights and bluffs. I further determined that this was such a good card for him to bluff that he would bet hands like Ace-high that had some but very little showdown value, since my hand looked a lot like a small pair.

This was Level 3 thinking on my part: I considered the likely strength of his hand and also the kind of hand I had represented. A Level 4 thinker could exploit me here by value betting something like two pair. I did not think this player would be capable of that, however. I called the bet, and he showed me 2h 4h. As I suspected, he had put enough thought into my possible holdings to realize that even though he had a pair he could probably only win the pot with a bluff. He was using Level 2 logic with his river bet, and by thinking one level ahead of him, I made the correct decision.

Overthinking
Now let’s see what happens when I try to apply Level 3 thinking to a Level 1 thinker. This hand is also from a $3/$6 heads up match with $600 effective stacks, but against a much weaker opponent.

I raised to $18 with 8c 7h on my button, and my opponent made a re-raise to $36, which I called. The flop came 7s 5s 5d. He checked, and I checked as well, a bit suspicious of his tiny re-raise pre-flop.

The turn was the 8h. He bet $45, and I called. The river was the 9d, and he bet $120 into a pot of about $162.

At this point, I made two flawed assumptions about my opponent. The first was that my his tiny pre-flop re-raise would almost always come from high cards such as a big pair or a big Ace. Thus, I wasn’t particularly concerned about my opponent having a 5, 6, or 9 in his hand. The second was that his sizable river bet would be either a big hand, probably trips or better, or a bluff, but that it would be not a medium-strength hand such as an overpair. I called and lost to 9c 3c.

Against a Level 2 thinker, the above assumptions would be reasonable. But here, I now believe my opponent was operating on Level 1, at least on the river- I have no idea what he was thinking pre-flop. He bet hard because he had top pair, and he gave no consideration to what kind of hand he had represented, what was possible on this board, or what I might have or call him with.

Because I overthought the situation, however, he achieved the same result as a tricky Level 4 player. He found a good spot to make a thin value bet representing a bluff when he had in fact made top pair, an implausible hand given his actions on previous streets.

Conclusion
I chose to focus this article on river decisions because they eliminate the added complexity of implied odds, reverse implied odds, semi-bluffing, pot control, and hand protecting that factor into the action on earlier streets. River play is a pure mind game where you need to figure out the thought process behind an opponent’s bluffs, calls, and value bets.

I stated earlier that few players regularly employ Level 4 and higher thinking, and this is in part because it isn’t often necessary. Your objective should be to think one and only one level beyond the level at which your opponent is thinking. Better players will adapt more quickly to you, but if you haven’t got him figured out right, then a weaker opponent can be just as tricky. If you’re a level behind, then you’re getting outsmarted.
But if you’re more than one level ahead, then you’re giving your opponent too much credit and overthinking certain situations.

Since there are many more bad players than good players out there, the latter is a more common problem. It is also, thankfully, a much easier problem to fix.

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