acalculator

What is my hand’s poker equity?

Enter both hands and any board cards to see each hand’s share of the pot at showdown. The results are mathematics, not advice.

Your numbers

Leave empty before the flop, or type 3, 4 or 5 cards such as Qh 7h 2c.
Your equity
46.03%

Ah Kh against Qs Qd has 46.03% equity.

Opponent’s equity
53.97%
You win
45.84%
Opponent wins
53.78%
Tie
0.38%
Your cards
Ah Kh
Opponent’s cards
Qs Qd
How it was counted
Estimated: exact without flushes, 1,000 flush boards sampled

Your equity: 46.03%. Ah Kh against Qs Qd has 46.03% equity.

The results are maths only. They are not betting advice or a promise of a return. Bet only what you can afford to lose. For help with gambling, call 1-800-GAMBLER. Terms of use

How to calculate

Computes the equity of two Texas hold’em hands against each other: the chance each wins or ties by the river, exact once the flop is out and estimated before it (exact on boards without a flush, sampled where a flush is possible).

Example with the default inputs (Your hand Ah Kh, Opponent’s hand Qs Qd): Ah Kh against Qs Qd has 46.03% equity.

Method: Equity = P(win) + P(tie) ÷ 2 over the boards that can still come: every board exactly from the flop on; before it, every board without a possible flush exactly (grouped by board ranks) plus 1,000 seeded samples of the boards where a flush is possible.

  • Heads-up: two known hands, each playing its best 5 of 7 cards under standard poker hand rankings. Suits never break a tie.
  • All unseen cards are equally likely; no other player’s folded cards are known.
  • Before the flop the equity is exact on every board where no flush is possible and estimated from 1,000 seeded samples of the boards where one is (standard error at most 0.46 percentage points); from the flop on it is exact.
  • Equity is the share of the pot won on average if both hands go to showdown; it ignores betting.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Your hand Ah Kh, Opponent’s hand Qs Qd, Board Qh 7h 2c gives Your equity 25.555556%, You win 25.555556%, Tie 0%, How it was counted Exact: every one of 990 possible boards, Your hand now High card, Opponent’s hand now Three of a kind.Source: exact count of the 990 turn and river pairs (253 wins), Python 3 cross-check in the progress log
  2. Your hand Ah Kh, Opponent’s hand Qs Qd, Board Qh 7h 2c 3d gives You win 15.909091%, Opponent wins 84.090909%, How it was counted Exact: every one of 44 possible boards.Source: hand calculation in content.mdx: 7 of the 44 rivers (the hearts that do not pair the board) win
  3. Your hand As Ks, Opponent’s hand 2c 2d, Board Ah 2h 7c Kd 9s gives You win 0%, Opponent wins 100%, Your equity 0%, Your hand now Two pair, Opponent’s hand now Three of a kind.Source: hand calculation in content.mdx: three 2s beat aces and kings
  4. Your hand Ah Ad, Opponent’s hand Kc Ks gives Your equity 81.25549%.Source: exact enumeration of all 1,712,304 boards, Python 3 (progress log): 1,388,072 wins and 6,538 ties = 81.2555%; the page estimates the flush part from 1,000 boards, so 1% relative tolerance (under 2 standard errors at the 0.46-point bound)

How it works

Cards. Each card is a rank (2 to 9, T or 10, J, Q, K, A) then a suit (c, d, h, s, or ♣ ♦ ♥ ♠), in any case, with spaces and commas ignored: Ah Kh, 10d9d, Q♥ 7♥ 2♣. Each hand has exactly 2 cards and the board 0, 3, 4 or 5. A card used twice gives no answer.

Hand values. Each hand plays the best 5 of its 7 cards (2 in hand plus 5 on the board) under the standard ranking: straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, one pair, high card. Within a category, higher ranks win, then kickers. An ace plays high or low in a straight (A-2-3-4-5 is the lowest straight). Suits never break a tie; equal hands split the pot.

Counting. Over all boards that can still come:

  • Win = boards where your hand is better ÷ boards
  • Tie = boards where the hands are equal ÷ boards
  • Equity = win + tie ÷ 2 (and the same for the opponent; the two equities add up to 100%)

With 3, 4 or 5 board cards, the calculator deals every remaining board: C(45, 2) = 990 turn and river pairs on the flop, 44 rivers on the turn, 1 board on the river. The result is exact.

With no board cards there are C(48, 5) = 1,712,304 boards. The calculator estimates the equity in two parts:

  1. Boards on which no flush is possible, exactly. For each suit s, let m(s) = 5 − (the most cards of suit s in either hand). A flush of suit s is possible only on boards with at least m(s) cards of suit s. On every other board, both hands’ values depend on ranks only, so the calculator runs through every pattern of 5 board ranks, each counted as many times as it can be dealt from the unseen cards (the product of C(cards of that rank left, how many the board has)), and counts wins, losses and ties exactly as if no flush were possible.
  2. Boards on which a flush is possible, sampled. These boards (at most one suit can qualify on a 5-card board) number F = Σ over suits and j ≥ m(s) of C(unseen cards of s, j) × C(other unseen cards, 5 − j). The calculator draws 1,000 of them uniformly (suit and count j with chance proportional to their number of boards, then the cards by a partial Fisher–Yates shuffle, with the seeded generator Mulberry32, seed 20260928). On each it takes the real result minus the rank-only result for win, loss and tie, and adds the average change × F ÷ 1,712,304 to part 1.

The estimate has no bias. The change on one board is between −1 and 1, and F ÷ 1,712,304 is at most 14.47% (both hands suited in different suits), so the standard error is at most 14.47% ÷ √1,000 = 0.46 percentage points. The same hands always give the same answer.

Your cards and the opponent’s cards repeat the hands in standard form: rank 2 to 9, T, J, Q, K, A, then the suit as c, d, h or s, with a space between cards (10h 10D is shown as Th Td).

How it was counted. The text is exactly one of:

  • Exact: every one of 990 possible boards (3 board cards), Exact: every one of 44 possible boards (4 board cards), Exact: every one of 1 possible board (all 5 board cards; singular “board”);
  • Estimated: exact without flushes, 1,000 flush boards sampled (no board cards).

Hand now. From the flop on (3 or more board cards), it also names each hand’s best 5-card hand on the board so far with one of the category names above, written High card, One pair, Two pair, Three of a kind, Straight, Flush, Full house, Four of a kind, Straight flush. Before the flop it is not shown.

Assumptions

  • Two known hands, head to head; every unseen card is equally likely.
  • Equity assumes both hands reach showdown; it ignores betting and folding.

Worked examples by hand

A♥K♥ against Q♠Q♦ on the turn, Q♥ 7♥ 2♣ 3♦. 44 rivers are left. Q♠Q♦ already has three queens. A♥K♥ wins only with a flush: 9 hearts are unseen (13 minus A♥, K♥, Q♥, 7♥), but 2♥ and 3♥ pair the board and give the queens a full house, which beats a flush. So A♥K♥ wins on 7 of 44 rivers = 15.91%, and loses on 37 = 84.09%.

The same hands on the flop, Q♥ 7♥ 2♣. Counting all 990 turn and river pairs gives 253 wins and 737 losses for A♥K♥: equity 25.56% (exact). A♥K♥ has High card now; Q♠Q♦ has Three of a kind.

A♠K♠ against 2♣2♦ on A♥ 2♥ 7♣ K♦ 9♠. The board is complete. A♠K♠ has two pair (aces and kings); 2♣2♦ has three 2s, which is higher. The equity is 0% against 100%.

A♥A♦ against K♣K♠ before the flop. Exact enumeration of all 1,712,304 boards (Python 3, progress log) gives the aces 1,388,072 wins and 6,538 ties: equity (1,388,072 + 6,538 ÷ 2) ÷ 1,712,304 = 81.26%. The calculator gives 81.37%, 0.11 points away. For A♥K♥ against Q♠Q♦ the exact equity is 46.21% and the calculator gives 46.03%.

A note on gambling

These results are mathematics, not advice. Every hand can lose. If gambling is causing problems for you or someone you know, the US National Problem Gambling Helpline is 1-800-MY-RESET (call or text).

Other questions people ask

What is poker equity?

Your equity is your share of the pot on average if the hand goes to showdown: your chance to win plus half your chance to tie. With 60% equity, you win 60 of every 100 in the pot over many such spots.

How is the equity calculated?

The calculator deals every possible remaining board, ranks both hands’ best 5 of 7 cards on each board, and counts wins, losses and ties. From the flop on it counts every board exactly (990 on the flop, 44 on the turn). Before the flop there are 1,712,304 boards. It counts every board on which no flush is possible exactly, grouped by the board’s ranks, and samples 1,000 of the boards where a flush is possible.

How accurate is the estimate before the flop?

Only the flush part is sampled, and flushes are possible on at most 14.47% of boards, so the standard error is at most 0.46 percentage points and usually far less: for A♥A♦ against K♣K♠ the page is 0.11 points from the exact value. The sample comes from a fixed seed, so the same hands always give the same answer, in a few milliseconds.

What is the equity of aces against kings?

About 81% for the aces before the flop. Exact enumeration of all 1,712,304 boards for A♥A♦ against K♣K♠ gives 81.26%; the calculator gives 81.37%.

Can I enter a range of hands?

No. This calculator takes two exact hands. Equity against a range averages the equity against every hand in the range, weighted by how many ways each can be dealt.