Combinatorics

Counting the exact number of card combinations that make up a range.

Combinatorics: Counting the exact number of card combinations that make up a range.

There are 1,326 ways to be dealt two cards from 52, which collapse to 169 distinct hands once suits that play identically are grouped together.

Those counts are the tool for range work. Offsuit hands are three times as common as their suited versions, so a range of "any two broadway cards" contains far more offsuit combinations than suited ones, and its equity reflects that.

The same counting answers questions people usually estimate. A specific pocket pair is 6 combinations in 1,326, or one deal in 221. Aces or kings together is one in 110, which is the honest response to an opponent who always seems to have it.

Where the numbers come from

Related terms in poker

  • Pot odds — The price a call is getting, compared against how often it needs to win.
  • Outs — The cards remaining that would improve your hand to a likely winner.
  • Equity — Your share of the pot, meaning how often you win it if the hand plays to showdown.
  • Implied odds — The money you expect to win later if your draw comes in, beyond what is in the pot now.
  • Position — Where you act in the betting order, and the largest structural edge in poker.
  • Button — The dealer position, which acts last on every postflop street.

Where an entry quotes a number, that figure comes from the computed sections of this site rather than from another glossary, so the definition and the derivation cannot drift apart. Each entry links to the page where the number is worked out.