Poker Combinations: Count Every Hand

How many poker combinations are there preflop?

A 52-card deck can deal two unordered hole cards in 1,326 ways. The calculation is 52 × 51 ÷ 2. Division by two removes duplicate orderings because A♠K♥ and K♥A♠ describe the same holding. A standard 13 × 13 range grid compresses those exact deals into 169 hand classes.

GTO Wizard reaches the same total: 78 pair combinations, 312 suited combinations, and 936 offsuit combinations. The 169-grid count and the 1,326-combo count answer different questions. A grid names hand types; combinations count the exact cards.

How do you count pocket-pair combinations?

Any pocket pair starts with six combinations because you choose two suits from four. AA can appear as A♠A♥, A♠A♦, A♠A♣, A♥A♦, A♥A♣, or A♦A♣. The same six-way pattern applies to KK through 22.

A visible card changes the count fast. If you hold A♣K♣, only three AA combinations remain: A♠A♥, A♠A♦, and A♥A♦. Two visible aces leave one possible pair. Three visible aces leave none. Players often remember the starting count and forget to remove the cards in their own hand.

This matters when a tight player 4-bets. Suppose you assign AA and AK to the value range while holding A♣Q♣. AA has three remaining combinations. AK has 12. Treating the two labels as equally likely would distort the range before you consider how often that opponent chooses each action. Our poker blockers guide covers the card-removal effect in bluffing and calling spots.

How do suited and offsuit combinations work?

An unpaired hand has 16 combinations before you split it by suitedness. Four are suited because both cards must share one of four suits. The other 12 are offsuit. AKs therefore has four combinations, AKo has 12, and AK without a suffix includes all 16.

This three-to-one ratio explains why raw hand labels mislead. A player who opens both AKo and AKs reaches the flop with offsuit AK three times as often before card removal and action frequencies. Upswing Poker’s hand-combination primer uses the same 6-4-12 counts and shows how range software displays the total.

How do blockers change poker combinations?

Remove every exact combination that uses a card you can see. Holding K♦Q♦ leaves three KK combos, 12 AK combos, and three QTs combos. Your king removes half of the original KK combinations. It removes four of the 16 AK combinations. Your queen of diamonds removes Q♦T♦ from the four suited QTs combinations.

SplitSuit demonstrates those same counts in its combos and blockers lesson. The arithmetic stays simple when you count unseen cards. For two different ranks, multiply the remaining cards of the first rank by the remaining cards of the second, then separate suited combos if the range calls for them.

Action removes combos too, although it does so through strategy instead of physical impossibility. A player may open all four A5s combinations but 4-bet only half of them. Your range model should carry two A5s combos into the 4-bet branch. Preflop Wizard’s poker hand ranges guide explains how mixed frequencies work inside a range.

How do you count a preflop range?

Add the combinations for every hand, then apply blockers and action frequencies. A range of QQ+, AK contains 18 pair combos (six each of QQ, KK, and AA) plus 16 AK combos, for 34 combinations before you see your cards. That total gives each holding the weight the deck actually assigns it.

A 2012 Two Plus Two discussion starts with the same 1,326 total and shows why players need to state whether they mean preflop starting combinations or later board runouts. Keep the unit attached to the number. A hand class, an exact combo, and a five-card outcome are separate counts.

How do combinations improve a real preflop decision?

Consider a 100bb cash game. The cutoff opens, you 3-bet A♣5♣ on the button, and the cutoff 4-bets. You estimate a value range of QQ+ and AK, plus some A5s bluffs. Your ace removes three AA combos and four AK combos. Your five removes A♣5♣ itself and leaves three possible A5s combinations before action frequency.

Start with the 21 remaining value combinations calculated above, except your hand has no queen blocker, so QQ returns to six. The value range becomes 24 combos: six QQ, six KK, three AA, and nine AK. If the cutoff uses half of the three available A5s hands as bluffs, the model adds 1.5 weighted bluff combos. That range stays heavily value weighted.

The count does not decide the hand alone. Pot odds, position, stack depth, rake, and the opponent’s actual frequencies still matter. Combo work prevents one common error: seeing four hand labels in the value range and one bluff label, then assuming a four-to-one ratio. The deck and mixed strategies assign the real weights. Use our 4-bet strategy guide to place that count inside a complete preflop plan.

How should you practice counting combos?

Memorize 6-4-12, then count one narrow range at a time. Start with a hand such as QQ+, AK. Add your two hole cards and recount it. Next, add a flop and remove every impossible holding. Write the exact suit combinations until you can see the count without listing them.

Keep range selection and combo counting separate during early practice. First decide which hands reach the action. Then count how many remain. Mixing those tasks invites double counting, especially when a hand uses a partial frequency. Record half of four suited combos as two weighted combos, even when the solver chooses different suits in different formations.

Pair the arithmetic with the free GTO preflop charts. Pick one opening position, count the pair, suited, and offsuit sections, and compare the result with the range percentage. Then drill that formation in Preflop Wizard so the combinations connect to folds, calls, raises, and 3-bets.

Poker combinations FAQ