Guides Reading the Player, Not the Hand
Counting His Hands: Combos and Blockers
"He could have a flush" is not a read. "He has six flush combos and nine top-pair combos, and I block two of the flushes" is a read, and the arithmetic behind it takes about ten seconds once you know the three numbers it rests on.
The Three Numbers
| Hand shape | Combos | Why |
|---|---|---|
| Pocket pair | 6 | four cards, choose two |
| Suited | 4 | one per suit |
| Offsuit | 12 | sixteen total, minus the four suited |
Everything else is addition. AK is 16 combos before any cards are known. Aces is 6. That ratio alone explains why a raiser has AK far more often than he has aces, and why treating a big raise as "probably aces" is usually wrong by a factor of nearly three.
The Board Removes Cards
Every card on the board takes combinations out of his range. An ace on the flop cuts pocket aces from 6 combos to 3 and cuts AK from 16 to 12. Two aces on the board leaves exactly one combination of aces.
This is why paired boards change everything. On a K-K-4 flop, kings are down to one combination, which means the hand everyone is afraid of is nearly impossible, while the pocket fours are still at 3 combos and every K-x is live.
Your Own Cards Remove Cards Too, and That Is a Blocker
A blocker is a card in your hand that reduces the number of ways your opponent can hold a specific hand. Holding one ace cuts his aces from 6 to 3. Holding the ace of spades on a three-spade board removes every nut-flush combination from his range.
The practical uses are narrow and real.
- Bluffing. The best bluff hands hold the cards that make his calling hands. Holding the ace of the flush suit means he has the nut flush zero percent of the time, which makes a large river bluff far more likely to get through.
- Bluff catching. If you hold cards that block his value hands, his range shifts toward bluffs, so your marginal hand goes up in value. Holding a card that blocks his draws does the opposite.
- Folding. When your hand blocks nothing he is bluffing with, your bluff catcher is worse than it looks.
The Combos and Blockers drill runs the whole count on generated spots: six per pair, four suited, twelve offsuit, and then your cards start deleting his. Counting what he can still have is one of those skills that is entirely mechanical and almost never practiced.
A Worked River Spot
Board is K-9-4-2-7 with three hearts. He has bet all three streets. What can he actually have?
Flushes: he needs two hearts. If his range included the suited broadway hearts and suited connectors, that is maybe five or six combinations. Top pair: K-x with a decent kicker, and since one king is on the board, each K-x offsuit hand is down to 9 combos and each suited one to 3. Sets: kings is 3 combos, nines 3, fours 3.
Now the point. If you hold the ace of hearts, you have removed every flush combination that contains the ace, which is often half of them. His flushes just dropped from six combinations to three, and the same river call is now a materially different decision. That is the difference between a feeling about a board and a number.
Doing This at the Table Without a Calculator
Nobody counts full ranges in real time. What works is counting one class of hands, the one the decision turns on.
You do not need to know his entire range on that river. You need to know how many flushes he can have and how many top pairs, because the call is a comparison between those two groups. Ask one question and count one group. That is a ten-second calculation and it is available to anyone who has memorized six, four and twelve.
Pair it with the break-even math and the two together answer most river decisions: how often does he need to be bluffing for this call to be right, and how many bluffing combinations does he actually have left.
Questions People Ask About This
How many combinations of each poker hand are there?
Six for any pocket pair, four for any suited hand and twelve for any offsuit hand, which is sixteen total for any unpaired holding before the board removes cards.
What is a blocker in poker?
A card in your own hand that reduces the number of ways your opponent can hold a specific hand. Holding one ace cuts his pocket aces from six combinations to three.
Why does a paired board change so much?
It removes almost all of the trips combinations people fear. On a king-king flop, pocket kings is down to a single combination while every king-x hand is still live.