Poker Hand Probabilities: The Odds of Every Hand (Exact)

Most odds tables online are copied from one another, decimals and all. We computed these from scratch: closed-form combinatorics for the classic five-card table, then a full enumeration of all 133,784,560 seven-card hands with the same open-source evaluator that powers our odds calculator. If you need the ranking order itself first, the hand rankings chart has it; this page is about how likely each rung of that ladder actually is.

Five-card poker hand probabilities

The classic table: deal exactly five cards from a 52-card deck and there are C(52,5) = 2,598,960 equally likely hands. Each row shows how many of those hands make each rank, the probability, the odds, and the chance of that hand or anything better:

Three things worth actually remembering. First, high card is the most common hand — 50.12% of all five-card deals make no pair at all. Second, the ranking order is rarity in disguise: a full house (3,744 ways) beats a flush (5,108 ways) beats a straight (10,200 ways) precisely because each is harder to make. Third, everything from a straight up adds to less than 1% — 0.759% of hands are a straight or better.

Texas Hold'em: odds by the river (7 cards)

Hold'em deals you two hole cards plus five community cards and lets you use the best five of the seven. That changes every number. We enumerated all C(52,7) = 133,784,560 seven-card combinations and classified each by its best five-card hand:

The headline flip: with seven cards, one pair overtakes high card as the most common outcome (43.82% vs 17.41%), and 82.59% of river hands make a pair or better. Two pair or better happens 38.77%of the time — better than one river in three. Note these are the odds for a single player's seven cards dealt at random; they say nothing about whether the hand wins. For head-to-head numbers see the preflop matchup odds, and for the frequency of two big hands colliding — set over set, flush over flush — the cooler odds hub.

Your two hole cards: the preflop lottery

Before any of the above matters you get two cards from C(52,2) = 1,326 possible combinations. The exact chances of the starts players care about:

The one that surprises people: any two suited cards arrive 23.53% of the time, but a specific premium like AK suited is 1 in 331.5. And a pocket pair — the start of every set-mining plan — is only 1 in 17 hands, which is why patience is a strategy and not a personality flaw.

Methodology

• • 5-card table: closed-form combinatorics (e.g. full house = 13 × C(4,3) × 12 × C(4,2) = 3,744), then independently verified by enumerating all 2,598,960 five-card hands with our open evaluator. Both methods agree on every row, and the ten counts sum to exactly C(52,5) = 2,598,960.
• • 7-card table: full enumeration of all C(52,7) = 133,784,560 seven-card combinations, each classified by its best five-card hand with the same evaluator used by our equity tools. The counts sum to exactly 133,784,560. No Monte Carlo, no sampling error.
• • Hole cards: direct enumeration of all C(52,2) = 1,326 starting combinations. Suited connectors are counted as the 12 adjacent-rank pairs 32s through AKs, one per suit.
• • What the numbers mean: each table is the distribution for one player's randomly dealt cards. Probabilities of winning depend on opponents and are a different calculation — that is what the odds calculator does.

Common questions