Poker is a game of probabilities. Knowing how often a flush draw completes, or the real chance of a royal flush, is what separates good decisions from guesses. This page collects the numbers that matter: hand frequencies, pre-flop odds, draw equity by outs, and a shortcut for calculating at the table.
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Royal flush 0.000154% · Straight flush 0.00139% · Quads 0.024% · Full house 0.1441% · Flush 0.1965% · Straight 0.3925% · Three of a kind 2.11% · Two pair 4.75% · One pair 42.26% · High card 50.12%. A flush is rarer than a straight, which is exactly why it outranks it — see flush vs straight.
Any pocket pair: 5.88% (1 in 17). Aces specifically: 0.45% (1 in 221). Suited connectors: about 3.9%. AK of any suit: 1.21%. At a nine-handed table a pocket pair is dealt roughly every other hand, which is why aces do not always hold up in a full pot.
Flop to river: 4 outs ≈ 17% · 8 outs (open-ended) ≈ 32% · 9 outs (flush draw) ≈ 35% · 12 outs ≈ 45% · 15 outs ≈ 54%. Turn to river is roughly half of each. Counting method explained on the outs page.
On the flop multiply your outs by four for equity through the river; on the turn multiply by two. A flush draw is nine outs, so 36% — the exact figure is 35%. Accurate enough to compare against pot odds and decide whether a call is profitable.
AA vs KK ≈ 82/18. AA vs AKs ≈ 87/13. Pair vs two overcards (coin flip) ≈ 55/45. AK vs QQ ≈ 43/57. Small pair vs big pair ≈ 18/82. Test any matchup in the odds calculator.
With two hole cards and five community cards the chance is about 1 in 30,940 — far more likely than the 1 in 649,740 figure calculated on five cards. Playing 100 hands an hour, that is roughly one royal every 300 hours.
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