An opponent raises from the button in a limit hold’em game, the small blind folds, and the hero calls in the big blind with AcKd. The flop is 7c6c2d.

Level 1

At Level 1, a person is only capable of determining the strength of their own hand. Holding AcKd on a 7c6c2d flop, he will understand that he has A-high.  If faced with a bet from his opponent, he will have little idea how to proceed with the hand.

Level 2

At Level 2, a person can read their own hand strength, as well as consider a possible holding for his opponent. In this hand example he might think, “well my opponent raised preflop so he probably has a pair of some sort, and all I have is A-high.”

Level 3

At Level 3, a person can read his own hand strength, as well as consider a possible range of holdings for his opponent. In this case he will realize that AK-high is very often the best hand on this flop vs a button stealer. An aggressive button stealer will be open-raising with perhaps the following range:

{22+, A2s+, K2s+, Q2s+, J3s+, T6s+, 97s+, 86s+, 75s+, 65s, 54s, A2o+, K6o+, Q7o+, J7o+, T8o+, 97o+, 87o, 76o}.

Vs this range, AcKd has 57% equity, i.e. it is a slight favorite vs the button stealer on this particular flop. A level 3 player would never consider folding this flop, but he may be unsure exactly how to best proceed with the hand.

Level 4

Finally, at Level 4, a player is considering his own range of hands vs his opponent’s range of hands at all decision points. Operating at this level becomes absolutely necessary if your opponent is also at level 3 or level 4.

A Level 4 player again realizes that his hand is a favorite on this flop. He also knows that there are many hands in his own big blind defense range (other than AK) with which he would like to check-raise as a semibluff (flush draws and straight draws) and for value (pairs). Because of the large number of possible straight and flush draws, he knows his Level 3 or Level 4 opponent will be hard pressed to fold A-high or even K-high if none of the draws fill in on the turn or river. This makes check-raising the flop with AK-high for value an attractive option for how to proceed with the hand.*

Because of the drawy dynamic nature of the board, he can extract maximum value with the best high card hand (AK-high) when his opponent has a weaker A-high or K-high hand, and he can also possibly induce rebluffs from his opponent’s drawing hands to win the maximum when the draws miss.

A Level 4 player will be attacking this flop relentlessly with flush draws {XcXc}, straight draws {98, T8, T9, 85s, 54s}, pairs {7x, 6x, 33+}, and a few high-card hands for thin value.

Fairly often, a check-raise on this flop will lead to a bigger loss than if the hero had played more passively. This does not concern a Level 4 player. A Level 4 player is thinking about the value of his overall strategy with his entire range on this particular flop, not the value of this single particular hand in this particular instance.

*In some cases with highly specific reads on your opponent, it would be best to remain passive with the AK on the flop. For example, if your opponent tends to bluff all the way through the river when checked to, but would fold often vs a flop check-raise, then staying passive would be the best option to simply induce bluffs on all streets.