Texas Hold'em equity calculator

How to use it

Put each player's two hole cards in a seat, and the community cards in the board box. The order of seats does not matter and neither does the order of cards within a hand. Any seat left empty is ignored, so a heads-up question needs only two seats filled. If you want to know how a hand fares against an unknown holding, type ? in a seat and that player is dealt a fresh random hand on every simulated deal.

The three numbers per player mean different things. Win is the share of deals that hand wins outright. Tie is the share where it shares the best hand with somebody. Equity is its long-run share of the pot: its wins plus its fractional part of every tie. Equities always add up to 100%; wins do not, because ties are left out.

Method: exact enumeration or seeded simulation

Every seven-card combination is scored by the same hand evaluator used on the hand rankings page, whose five-card frequencies are checked against the full 2,598,960-hand enumeration in this site's test suite. What differs is which boards are scored.

• Exact. When every hand is known and at least the flop is out, the calculator visits every possible completion of the board, each exactly once. Heads-up on the flop that is C(45, 2) = 990 turn-and-river pairs; on the turn it is the 44 remaining rivers. The answer has no sampling error at all.
• Simulated. Preflop, or when any seat is random, the number of possibilities runs into the millions or billions, which is too slow to redo on every keystroke. The page instead deals 10,000 to 200,000 random completions from the cards that are left, using the mulberry32 pseudo-random generator with a fixed seed. The same seed always gives the same answer, which is why the result does not flicker as you type. The standard error shown is √(p(1 − p) / n): roughly two thirds of re-runs land within one standard error of the true value, and nearly all within two.

Worked example: the default hand

The page opens on A♥ K♥ against J♠ 10♣ with a flop of J♥ 8♥ 2♣. Player 2 has top pair and is ahead right now. Player 1 has the nut flush draw and two overcards. Counting outs gives nine hearts for the flush plus three aces and three kings that make a pair above jacks: fifteen. The exact chance of hitting one of fifteen outs by the river is 1 − (32 × 31) / (47 × 46) = 54.1%.

The calculator says 53.43%, a little lower. The difference is real rather than rounding. An ace on the turn gives player 1 the lead, but a 10 on the river then hands player 2 two pair, and a king followed by a jack gives player 2 trips. Player 1 also wins a few boards that outs counting misses, such as a runner-runner straight with a queen and a 10. Outs counting is a good estimate; enumeration is the answer. The outs calculator shows how the rule of 4 compares at fifteen outs.

Preflop reference: common matchups

Exact heads-up preflop equities, each computed over all 1,712,304 possible boards with the same evaluator. The specific suits are shown because they matter by a fraction of a percent: a hand that shares a suit with its opponent has fewer flush chances.

Three-handed, A♠ A♥ against K♠ K♥ and Q♠ Q♥ comes out at 67.67%, 17.23% and 15.10%. Adding players always cuts the favourite's share: aces are roughly 81% against one pair but about 68% against two.

Where this stops being the whole story

Equity assumes every card is dealt with no more decisions. Real hands have betting on later streets, so the share of the pot a hand actually collects, sometimes called realised equity, can be higher or lower than the number here. A drawing hand that folds to a big turn bet never sees the river it was counting on.

It also assumes you know exactly what everyone holds. In practice you are weighing a hand against a range of possibilities; the random-seat option is the crude version of that (every hand equally likely), which is rarely how anyone actually plays. And a simulated answer is only as good as its sample size: for a close decision, switch to 200,000 deals or fill every seat and add a flop so the calculator can enumerate exactly.

This is a tool for studying the game's mathematics and settling arguments at a home game. It says nothing about any particular opponent, and no calculation makes a hand a sure thing.