Block 05 · Poker Math: Pot Odds, Equity & Outs

Counting combos

Lesson 7 of 12 ~2 min read 20-question test

A "combo" is one specific two-card way to hold a hand, and every hand type has a fixed count. Master three numbers and you can weigh any range instead of guessing.

The three magic numbers

Poker math starts with counting. There are exactly 1,326 different two-card hands in a 52-card deck. Every specific holding falls into one of three buckets: a pocket pair has 6 combos, a suited hand has 4 combos, and an offsuit hand has 12 combos. Memorize 6 / 4 / 12 and you can size up any range on the spot.

Pocket aces: this is just one of the 6 ways to be dealt AA.

Why 6 for a pair

A pocket pair needs two of the same rank, and there are 4 of each rank in the deck. The number of ways to choose 2 cards from 4 is written C(4,2) = 6. So AA, KK, 77 — every pair — has exactly 6 combos: the six pairings of spade, heart, diamond, and club.

AKs (suited): 4 combos, one for each suit — one spade pairing shown here.
AKo (offsuit): 12 combos — 3 times as many as the suited version.

Card removal shrinks the count

The 6 / 4 / 12 counts assume all four cards of each rank are still hidden. The moment a card becomes visible — in your hand or on the board — it is removed from the possible combos. If you hold one ace, your opponent can only have 3 aces left, so their AA drops from C(4,2)=6 to C(3,2)=3 combos. This is the idea behind blockers.

An ace on the flop removes combos: opponent AA falls from 6 to 3, and AKo falls from 12 toward fewer.

Value combos vs bluff combos

Range reading is really combo counting. On the river, list the hands your opponent bets for value and the hands they bet as a bluff, then count the combos of each. If value combos far outnumber bluff combos, their bet is likely real and you should fold marginal hands; if bluffs are plentiful, you call more. The cards you hold act as blockers, subtracting combos from one side or the other.

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Hand 1 / 12 Score 0
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Before the test — remember
  • Each pocket pair = 6 combos, each suited hand = 4 combos, each offsuit hand = 12 combos.
  • Any two distinct ranks total 16 combos (4 suited + 12 offsuit); all 1,326 combos exist in a deck.
  • Cards you can see (your hand or the board) remove combos, cutting a pair from 6 to 3 to 1.
  • Comparing value combos to bluff combos tells you whether a bet is more likely strong or weak.
Lesson test · 20 questions

Test yourself

Answer them all — 16/20 to pass. Every answer gets an explanation.

Question 1 / 20 Score 0

How many combos does a specific pocket pair (like KK) have?

Review — all 20 questions & answers tap to expand
  1. How many combos does a specific pocket pair (like KK) have?

    Answer 6

    A pair is C(4,2) = 6 ways to choose two of the four cards of that rank.

  2. How many combos does a specific suited hand (like AKs) have?

    Answer 4

    A suited hand has one combo per suit, and there are 4 suits, so 4 combos.

  3. How many combos does a specific offsuit hand (like AKo) have?

    Answer 12

    Offsuit combos = 4 aces x 4 kings (16) minus the 4 suited pairings = 12.

  4. How many total combos exist for any two distinct ranks (all of AK)?

    Answer 16

    4 suited + 12 offsuit = 16 combos for any unpaired two-rank hand.

  5. How many two-card starting hands exist in a 52-card deck?

    Answer 1,326

    C(52,2) = 1,326 distinct two-card combinations.

  6. You hold one ace. How many combos of pocket aces can your opponent have?

    Answer 3

    With only 3 aces left, C(3,2) = 3 combos of AA remain.

  7. The board shows exactly one king. How many combos of KK are still possible?

    Answer 3

    One king removed leaves 3 kings, and C(3,2) = 3 combos.

  8. Two aces are visible between your hand and the board. How many AA combos remain?

    Answer 1

    With only 2 aces left, C(2,2) = 1 combo of AA is possible.

  9. The ace of spades is on the board. How many combos of AKs remain?

    Answer 3

    AKs has 4 combos (one per suit); removing the spade version leaves 3.

  10. Which has more combos: a specific pocket pair or a specific offsuit hand?

    Answer The offsuit hand

    An offsuit hand has 12 combos versus only 6 for a pair.

  11. For the same two ranks, how do offsuit combos compare to suited combos?

    Answer Offsuit is three times as many

    Offsuit has 12 combos and suited has 4, so offsuit is exactly 3x.

  12. What does the term 'blocker' describe?

    Answer A card you hold that removes combos from an opponent's range

    A blocker is a card you hold that makes certain opponent combos impossible.

  13. Which formula gives the number of combos for any pocket pair?

    Answer C(4,2) = 6

    Choosing 2 of the 4 same-rank cards is C(4,2) = 6.

  14. An opponent's river range is only AA and AKo. With no card removal, how many total combos is that?

    Answer 18

    AA has 6 combos and AKo has 12, for 18 total.

  15. Why does an unpaired hand make up more of a range than a pair?

    Answer Unpaired hands have 16 combos vs 6 for a pair

    With 16 combos vs 6, unpaired two-rank hands are far more numerous.

  16. If value combos greatly outnumber bluff combos in a bettor's range, you should generally:

    Answer Fold marginal hands more often

    More value than bluffs means the bet is likely genuine, so marginal calls lose.

  17. How many suited combos does any two-rank hand have, and why?

    Answer 4, one per suit

    Suited requires matching suits, and with 4 suits there are exactly 4 combos.

  18. A king and a queen of different suits are on the board (one each). How many combos of KQo remain?

    Answer 7

    With 3 kings and 3 queens left, total pairings 9 minus 2 suited (the two suits holding both a king and a queen) = 7 offsuit combos.

  19. You hold the ace of hearts. How many combos of AA can an opponent hold?

    Answer 3

    Removing one ace leaves 3 aces, so C(3,2) = 3 combos of AA.

  20. Counting combos in a range is most directly useful for:

    Answer Estimating how likely each holding is, to guide calls and folds

    Combo counts weight each holding's likelihood, driving sound call/fold decisions.