An opponent’s hand is unknown, but the list of hands they could hold is finite and can be counted. Counting those possibilities turns a vague worry such as “he might have a set” into a comparison of numbers. The skill rests on two ideas: how many ways each type of hand can be made, and how the cards you can already see remove some of them.
Counting ways to make a hand
A standard deck has 52 cards, so there are 52 × 51 ÷ 2 = 1,326 possible two-card holdings. Dividing by 2 reflects that dealing the ace of spades then the king of hearts gives the same hand as the reverse order. The same idea underlies the difference between permutations combinations in any counting problem: when order is irrelevant, divide it out.
Three shapes cover everything:
- Pocket pairs. Each rank has 4 cards, and choosing 2 of them gives 4 × 3 ÷ 2 = 6 combinations. So any specific pair, such as queens, has 6.
- Suited unpaired hands. Choose a suit and take both ranks in it: 4 combinations. Ace-king suited is 4.
- Offsuit unpaired hands. Each of the 4 aces can pair with each of the 3 kings in a different suit: 4 × 3 = 12 combinations.
So ace-king in total has 4 + 12 = 16 combinations, while a specific pair has only 6. The three shapes together account for every holding: 13 × 6 = 78 pairs, 78 rank pairs × 4 suited = 312, and 78 × 12 = 936 offsuit, which sum to 1,326.
Card removal
Every card you can see is a card your opponent cannot hold. Suppose you hold the ace of hearts and king of clubs. The opponent now draws from the remaining 50 cards, which can form 50 × 49 ÷ 2 = 1,225 holdings. Compare some hands before and after:
| Opponent hand | Combinations with no cards known | Combinations after you hold A♥ K♣ |
|---|---|---|
| Aces (AA) | 6 | 3 (three aces remain) |
| Kings (KK) | 6 | 3 |
| Ace-king (AK) | 16 | 9 (3 aces × 3 kings) |
| Ace-queen (AQ) | 16 | 12 (3 aces × 4 queens) |
| Queens (QQ) | 6 | 6 |
Your own cards make premium pairs and ace-king rarer for the opponent, while queens are unaffected. The relative share of queens in the opponent’s possible hands has therefore risen. This is why a blocker is described as a card that makes certain holdings less likely, not impossible.
The reasoning is a form of conditional probability: the chances change because of what you know. It is also the same logic as drawing without replacement, where each card removed changes the make-up of what remains.
The board removes combinations too
Community cards work the same way. Say the flop is K♠ 7♦ 2♣ and you still hold A♥ K♣. One king is on the board and another is in your hand, so only the king of hearts and king of diamonds remain unseen. An opponent can make a set of kings in just 1 way (K♥ K♦). A set of sevens needs two of the three remaining sevens, so there are 3 combinations. Sets of deuces are also 3.
Top pair with a king is also scarce for an opponent: 3 aces × 2 kings = 6 combinations of ace-king remain. Without seeing any of these cards, an opponent would have had 16 ways to hold it.
Blockers and flush possibilities
Blockers also matter for flushes. Suppose the board has three spades and you hold the ace of spades. Without your ace, there are 10 unseen spades, and an opponent holding two of them makes 10 × 9 ÷ 2 = 45 flush combinations. With your ace removed, 9 spades remain, giving 9 × 8 ÷ 2 = 36. Your single card removes 9 of the 45, which is one fifth.
That one-fifth reduction is real, but notice it leaves 36 combinations. A blocker shifts the odds modestly. It does not say the opponent lacks the hand.
Weighting combinations by behavior
Raw counts assume every holding is equally likely. In practice, opponents fold some hands before the flop and bet others in particular ways. A player who would never call a raise with a weak offsuit hand reduces that hand’s weight to zero in the count. Judging opponent patterns this way is much less certain than arithmetic. A small number of observed hands is a thin basis for removing combinations from a list.
Putting counts to use
Counting combinations supports other calculations. If an opponent’s betting range contains 6 combinations of strong hands and 3 of weak ones, then the strong hands make up two thirds of that range, about 67%. This kind of ratio feeds into decisions about calling and bluffing, and into hand equity estimates against a range rather than a single hand.
Treat the results as estimates. The counts are exact, but the assumptions about what the opponent would do with each hand are guesses. Poker outcomes remain uncertain even when the counting is right, and wagering money can lead to losses. If gambling is a problem for you, a local support service can help.