Poker hand combinations: full table with probabilities

Most players know the ranking ladder — few know the denominator. Texas Hold'em has C(52,5) = 2,598,960 distinct five-card outcomes once all cards are known. Every hand category is a slice of that pie, not a vibe. When you know exact combo counts, bluff-catchers, set-mining, and «is this draw worth it» stop being folklore.

Why combo math beats «I feel lucky»

A flush draw on the flop is ~35% to complete by the river — not «about a third» in the abstract, but 9 outs × 4% − 2% rule with known error bounds. Set over set happens roughly ~12% when both players hold pocket pairs — small enough to hurt, large enough to plan stack depth. Discipline is knowing the number before the bad beat story writes itself.

Hold'em-specific: made hands vs five-card catalog

The table above counts best five of seven. Preflop, AA is 6 combos; AKs is 4; AKo is 12 — 16 total AK combos, which is why blocker logic works. Postflop, nut flush counts shrink when Ah is on board or in your hand. Always subtract dead cards from the combo universe.

• Pocket pairs: 6 combos each rank — 66 on a 6-high board caps villain sets hard.
• Suited hands: 4 combos — flush draws and blocker bluffs scale with remaining suits.
• Offsuit broadways: 12 combos — wider preflop ranges, more domination spots.
• Full house vs full house: rare at 0.144% five-card rate, common when both players play pairs and boards pair.

The ledger trick for study sessions

When reviewing hands, tag spots with required equity vs actual combo count. Example: pot-sized call needs ~33%; gutshot from flop is ~17% with one card — automatic fold unless implied odds are documented. My spreadsheet column «combo check» flags any call where I never wrote the outs × 2% estimate. Compliance beats hero calls.

I remember when I called «because straights were due»

I remember snap-calling a pot bet on J-T-4 with Q9 — open-ender, 8 outs, ~32% by river, but I needed ~38% facing pot-sized pressure with reverse implied odds. I said «straights were due this session» — classic gambler's fallacy. Ledger later showed 11 similar calls in one month; EV ≈ −4.2 buy-ins at $2/$5. The table did not owe me a straight; math owed me a fold.

Print the combo table, run ten review hands on NUTS POKER this week, and log required equity before every call on a draw. Rankings are kindergarten; denominators are where discipline starts — NUTS POKER tables reward players who count combos, not players who count bad beats.