Poker Hand Probabilities: A Complete Mathematical Reference

In a standard 52-card deck, there are 2,598,960distinct five-card hands. Every poker probability begins with this number. The relative rarity of each hand type follows directly from combinatorics, rarer hands beat more common hands because rarer hands are harder to make.

Five-card hand frequencies

More than 50% of all random five-card deals are high-card hands. One pair covers another 42%. If you have a pair, you are already beating the majority of random five-card combinations.

Texas Hold'em starting hand probabilities

There are C(52, 2) = 1,326possible starting hands.

Outs and the rule of 4 and 2

After the flop (two cards to come):
  Win probability ≈ (number of outs) × 4%

After the turn (one card to come):
  Win probability ≈ (number of outs) × 2%

Common out scenarios:
  Flush draw         → 9 outs → ~36% (flop), ~18% (turn)
  Open-ended straight→ 8 outs → ~32% (flop), ~16% (turn)
  Gutshot straight   → 4 outs → ~16% (flop),  ~8% (turn)
  Two overcards      → 6 outs → ~24% (flop), ~12% (turn)

Pot odds and calling decisions

Required win% = Call Amount / (Pot Size + Call Amount)

Example: Pot = $100, Opponent bets $50, you call $50 to win $200 total.
Required win% = 50 / (100 + 50 + 50) = 50/200 = 25%

Flush draw win% ≈ 36% > 25% required → CALL is profitable
Gutshot draw win% ≈ 16% < 25% required → FOLD is correct

Our Poker Evaluator calculates this for you: enter your pot size and call amount after running a simulation, and the tool tells you whether a call is profitable given your current win percentage.