Poker Combinatorics: Counting Combos

Combinatorics — "combos" — is the math of counting how many specific ways a player can hold each hand. It's the precise version of range thinking, and it turns vague reads ("he probably has it") into countable odds ("he has three times more value than bluffs here").

The basic counts

Before any cards are removed:

• A specific unpaired hand (like AK): 16 combinations — 12 offsuit and 4 suited.
• A specific pocket pair (like QQ): 6 combinations.
• A specific suited hand (like A♠K♠ exactly, or "suited" as a class): 4 suited combos for the hand class.

These numbers are the building blocks for counting how much of each hand type a range contains.

How blockers change the count

Every card you (or the board) hold removes combos from the opponent's range:

• Holding one ace drops their AA combos from 6 to 3, and their AK combos significantly.
• Board cards do the same — a king on the board reduces how many kings they can hold.

This is why blockers matter: they literally subtract combinations, shifting the ratio of value to bluffs in a range.

Using combos in a decision

The classic application is a river call. Count, roughly, the opponent's value combos versus bluff combos given the line. If a pot-sized bet needs you to win 33%, you call when bluffs are at least about a third of their betting combos and fold when they aren't. Your own blockers nudge that count toward calling or folding.

You don't need exact math live

Strong players estimate combos quickly rather than computing exactly. The habit of asking "how many ways can he have value versus bluffs?" — and adjusting for what your cards block — is what matters at the table.

The takeaway

Combinatorics makes range thinking precise: count value vs. bluff combos, adjust for blockers, and compare to the price. It's the engine under disciplined river decisions.