Part 2 · Lesson 5 of 25 · Free
Reading hands as distributions
His raise says AA, AK, 77 or 22. Four hands, but not equally likely: one of them makes up more than half of his range. You almost never know an opponent's exact hand, so you weigh every hand he could hold by the number of ways it can be dealt, its combinations, and by how likely he is to play it this way.
The hand
Flop. You bet top pair with A♠ Q♠, and the Tight-aggressive player raises. He raises here with AA, AK, 77 and 22, and nothing else.
Predict first
Which hand is he most likely to hold?
- A set: AA, 77 or 22
- AK
- All four are equally likely
Show the answer
Answer: AK
AK has 8 combinations left, more than AA, 77 and 22 together (1 + 3 + 3 = 7). Cards you can see remove combinations.
Working it out
Count what is left. Two aces are visible, yours and the board's, so AA has 1 combination of its 6 and AK has 2 × 4 = 8 of its 16. One seven and one deuce are on the board, so 77 and 22 have 3 each. In total 1 + 8 + 3 + 3 = 15, and AK is 8 of them. Your ace is a blocker: without it he would have 3 combinations of AA and 12 of AK.
Narrow the range street by street with each action, then compare your hand with the whole range, weighted by combinations. Card removal matters most when value hands and bluffs are close in number.
Formula
Pairs: C(4,2) = 6 combinations; unpaired hands: 4 × 4 = 16 (4 suited, 12 offsuit). One card of a rank visible: pairs 3, unpaired 3 × 4 = 12
Check your understanding
The board shows one king, and you hold one ace. How many combinations of AK can he hold?
Show the answer
Answer: 9
Three aces left × three kings left = 9.
You hold one seven and the board shows another. How many combinations of 77 can he hold?
Show the answer
Answer: 1
Two sevens are left: C(2,2) = 1.