How to Spot a Level 3 Thinker

One of my first articles for Two Plus Two Magazine, Level-Headed Thinking, was a brief introduction to the various “levels” of thinking about poker and how they should affect your decision-making at the table. When teaching and coaching, I regularly talk through a hand by explaining that against a Level 1 thinker I would do one thing, but that if I thought my opponent were on Level 2, then I would do something else instead.

In other words, when giving advice about a hand that someone else played, I feel like I can explain what factors to consider and how to respond given a certain read or set of assumptions, but only the player at the table can supply the read itself. One of my students recently asked me a question that gave me pause: “How am I supposed to know which level my opponent is thinking on?”

I hemmed and hawed a bit and told him that you just sort of get a feel for these things, but I knew this was an inadequate answer, and I resolved to think through some of the concrete evidence that I use to form such reads. What you’ll find here is the result of that exercise, an attempt to organize some of the most common behaviors that you can observe in your opponents that will give you clues as to how they think and play.

Level One Thinkers: Clueless Calls and Reverse Value Bets

Playing well on the river, moreso than on any other street, requires considering your opponent’s likely hands and what your own hand might look like to him. A Level One thinker who fails to consider these factors betrays his thought process, or lack thereof, when he makes bad plays on the river.

For all examples in this article, assume a $.50/$1 NLHE game with $100 effective stacks.

Example 1. Player A raises to $3 in first position, and Player B calls on the Button. The flop comes K [club] J [diamond] 8 [club], Player A bets $6, and Player B calls. The turn is the Q [diamond], Player A bets $12, and Player B calls. The river is the 9 [club]. Player A checks, Player B bets $25, and Player A calls with A [heart] A [spade].

In this example, it sure looks like Player A is not seeing anything beyond the fact that he has pocket Aces. Every draw that was out on the flop got there by the river, and Player A is also losing to KQ, KJ, QJ, KK, QQ, JJ, TT, JT, KT, QT, T9, T8, 98, 99, and 98. Basically, Player A is behind a huge portion of Player B’s range. The Aces are purely a bluff-catcher, and it’s hard even to put Player B on a hand that needs to bluff the river. One call like this is enough for me to label a player a Level One thinker.

If we change the example slightly so that Player A has position on the river, Player B checks to him, and A chooses to bet $10 into a $43 pot with his Aces, I’d be nearly as comfortable labeling him a Level One thinker. Once again, there seems to be no consideration of his opponent’s range or what hands will call this bet. It sure looks like Player A’s thought process is roughly, “I have Aces, so I’m going to bet.” If A were out of position, we could possibly interpret the small bet as a blocking bet, but when he has the option of checking the hand down but chooses to “value” bet it, that’s just Level One thinking.

Level Two Thinkers: Hopeless Bluffs and Questionable Slowplays

The Level 2 thinker knows about hand reading and tries to use it to his advantage. He considers his opponent’s possible holdings, but doesn’t give his opponent credit for being able to do the same. That works well against Level 1 thinkers, who actually aren’t trying to do any hand-reading of their own, but it sometimes results in losing plays against higher-level thinkers. These latter are what you want to be on the lookout for.

Example 2. Player A raises to $3 in first position. Player B re-raises to $12 on the Button, and Player A calls. The flop comes 5 [club] 4 [spade] 7 [diamond]. Both players check. The turn is the 9 [spade]. Player A bets $20, and Player B calls. The river is the 3 [diamond]. Player A bets all-in for $68 into a $65 pot. Player A shows Ace-King and loses to Player B’s pair of Queens.

The most logical explanation for this hand is that when Player B called the turn, Player A realized his Ace-King was no good and that B probably had a big pair. When the possible straight draw got there on the river, Player A tried to represent it with an all-in bluff. Player B realized that Player A has few if any 6’s in his range for calling a large re-raise pre-flop and thus correctly caught the bluff.

Player A is employing Level 2 logic here. He has an accurate read on Player B’s hand but fails to consider what his own hand looks like. If Player B is a Level 2 thinker, he will likely interpret the big river bet as either a straight or a bluff, and since there are few 6’s in Player A’s range, he won’t fold anything better than Ace-King.

Example 3. Player A raises to $3 in first position, Player B calls on the Button, and Player C calls in the Small Blind. The flop comes T [club] T [diamond] 6 [club]. Player C checks, Player A bets $5, and Player B raises to $15. Player C cold-calls the raise out of the SB, and Player A folds. The turn is the 2 [heart], and both players check. The river is the 8 [diamond], Player C bets $25, and Player B calls. Player C shows AT for three-of-a-kind but loses to Player B’s 9 [club] 7 [heart], which rivered a straight.

Player C was obviously unlucky to lose this pot to a rivered gutshot. However, his Level 2 play set him up for this by allowing Player B to freeroll the turn and river. Player C correctly read Player B’s raise as either a very strong hand (possibly but doubtfully stronger than his own) or a bluff. It seemed logical to him that he could slowplay his hand and expect Player B to continue bluffing or value betting worse hands. The problem was that Player C’s cold-call on the flop was an extremely suspicious red flag that prompted Player B to put on the brakes with his draw.

To be fair, it is hard for Player C to avoid giving off strength in this spot no matter what he does (aside from folding,which would indeed be deceptive!). Re-raising has several advantages over cold-calling, though. For one thing, it probably allows Player C to represent at least a slightly wider range than a call does. He might occasionally re-raise here as a semi-bluff, but this is an unlikely spot to call with anything except a very strong hand.

More importantly, the re-raise charges Player B for the information he is getting. The cold-call would be fine if Player B could be expected to continue with his bluffs, but here it announces so much strength that Player B is able to shut down and hope for a miracle on the turn or river. Although the draw will usually miss, Player C cannot count on getting any more money from Player B the times that it does. The only time that more money will go into the pot is on the rare occasion that Player B catches the miracle card, in which case Player C no longer has a winning hand.

The cold-call even enables Player B to slow down correctly with some strong hands. Even if the same action occurs but Player C manages to win at showdown against a hand like T9 or JT, he still probably lost value against hands that would have stacked off on the flop but instead went into pot control mode because of the suspicious cold-call.

Level Three Thinkers: Thin Value Bets and Disciplined Checks

We’ve mostly identified Level 1 and Level 2 thinkers by their mistakes. Level 3 thinkers are sophisticated players and more likely to be recognized by particularly good plays they are able to make that would not occur to lower-level thinkers. Because they are aware of their images and the information that they’ve given off about their hands, Level 3 thinkers are able to recognize when their marginal hands are good enough to bet for value and when they are weak enough that they have more value as bluffs.

Suppose that in Example 2, instead of getting caught in a bluff with Ace-King, Player A won his opponent’s stack with a pair of Kings. A less sophisticated player might be afraid to value bet even an overpair, at least for full pot. After all, there is a four-card straight on the board, not to mention the many possible set and two-pair combinations. However, a Level 3 thinker might realize that Player B will expect few if any of these hands to be in his pre-flop range. Thus, he can make a big bet for value with one good pair, expecting his Level 2 opponent to misinterpret the bet as either a straight or a bluff and talk himself into a call with a worse pair.

Example 4. Player A raises to $3 one off the Button, Player B calls on the Button, and the blinds fold. The flop comes J [club] 8 [club] 5 [diamond], Player A bets $5, and Player B calls. The turn is the Q [diamond]. Player A bets $11, Player B calls. The river brings the 7 [club]. Player A checks, and Player B checks behind, showing 8 [diamond] 7 [diamond] for a rivered two pair to beat Player A’s Ace-Jack.

At first glance, it may seem awfully weak-tight for Player B not to bet his two pair for value when Player A checks to him on the river. If Player A is a good hand-reader and Level 2 thinker, though, there is reason to think he will virtually never check-call in this spot. For one thing, every draw that was out on the flop came in by the river, so it is unlikely that Player B will get to the river with many hands that need to bluff. This negates the value of checking to induce a bluff.

The weakest part of Player B’s range consists of one-pair and weak two-pair hands that are surely more likely to call a bet on the river than to bet themselves. Thus, Player A needs to decide whether his marginal hands are good enough to show a profit when one more bet goes in on the river. If they are, he should bet them himself. If they aren’t, he should either check-fold them or occasionally turn them into bluffs by either betting big or check-raising.

To protect his “check-and-give-up” range, Player A should also sometimes check very strong hands with the intention of check-raising. Thus, even with two pair, Player B cannot expect a bet to be called by many worse hands and has to fear both value check-raises and check-raise bluffs. Any hand that called his bet would be making a crying call hoping to beat only bluffs and very thin value bets. If Player B is a Level 3 thinker, he will realize that there are very few of the former in his range, and thus there should not be many of the latter, either.

In other words, eights and sevens is a strong hand relative to Player A’s range but actually fairly weak relative to Player B’s range, which includes a lot of straights and sets. A check here indicates a player who is aware of how his range is perceived by a hand-reading opponent.

Higher-Level Thinking: Mind Games and Game Theory

When truly top-notch players square off, crazy things can happen. An observer will see both players do things that seem nonsensical and possibly even bad. Usually, he will not be able to make sense of the reasoning behind these plays without in-depth knowledge of the history between the players involved. This, combined with the fact that so few players are consistently operating on such high levels, makes it generally a waste to spend too much time worrying about how to identify and combat such play. Just for fun, though, let’s quickly explore one possible scenario.

Suppose that in Example 4, Player B actually bets the river. Player A shakes his head patronizingly and explains to his opponent, “You’re such a Level 3 thinker. All your hands made at least a pair by the river, so you don’t need to bluff, and you know I know that, so you’re never value betting less than a straight either. But I know you know that,” he says smugly, folding a set of 5’s face-up. This is Level 4 thinking.

With a sly smile, Player B exposes his 87 and rakes the pot. “I know you know I know. That’s why I can bluff with this.” This is Level 5 thinking.

At some point, all of these mind games and leveling wars devolve into an endless chain of “I know that he knows that I know that he knows…” It’s enough to make you wonder how one great player can ever be sure that the reasoning behind his brilliant play isn’t as apparent to his opponent as it is to him, in which case said opponent would never take the bait or fall for the bluff.

This is where game theory comes in. When you know that your opponent is thinking on a certain level and no higher, you can exploit him. That is, you can take all of his assumptions into consideration and then do him one better. When he expects you to value bet, you bluff, and when he expects you to bluff, you value bet.

That’s all well and good when you know that you are out-thinking your opponent. The problem is that anything you do to exploit him also opens your own game up to exploitation if it turns out that he is out-thinking you. If he expects you to expect him to expect you to bluff, then he can fold to your value bet.

As your opponents get better and better, they get harder to exploit, and they draw nearer to game theoretically optimal (GTO) play. If some superhuman player, or more likely a computer, ever learns to play a perfect GTO game, it would be impossible to out-level him. He could tell you, “In this situation, I will be betting the following hands. With X and Y, I will fold to a raise, with A and B I will call a raise, and with my absolute best and absolute worst hands, I will re-raise.”

In other words, you could have perfect information about how he will play, and there were still be nothing you could do to exploit him. When you call, he is value betting just often enough. When you fold, he is bluffing just often enough. The best you can do is play an unexploitable strategy of your own, which is what you should strive to do against any opponent who is either completely unknown to you or whom you believe capable of thinking on a higher level than you do.