# What is my hand’s poker equity?

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).

- Page: https://www.acalculator.org/game/poker-equity-calculator
- JSON spec: https://www.acalculator.org/game/poker-equity-calculator.json
- Version: d08ea6426339

## Default answer

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

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| hand1 | Your hand | Your hand: two cards, rank then suit, such as Ah Kh (T or 10 for ten; c, d, h, s for the suits). |
| hand2 | Opponent’s hand | Opponent’s hand: two cards, rank then suit, such as Ah Kh (T or 10 for ten; c, d, h, s for the suits). |
| board | Board | The community cards dealt so far: none, the 3-card flop, 4 with the turn, or all 5. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| equity1 | Your equity | Your share of the pot on average: your chance to win plus half the chance of a tie. |
| equity2 | Opponent’s equity | The opponent’s chance to win plus half the chance of a tie. |
| win1 | You win | The share of boards on which your best 5-card hand is better. |
| win2 | Opponent wins | The share of boards on which the opponent’s best 5-card hand is better. |
| tie | Tie | The share of boards on which both best hands are equal and the pot is split. |
| cards1 | Your cards | Your two cards in standard form: rank (T for ten) then lower-case suit, such as Th Td. |
| cards2 | Opponent’s cards | The opponent’s two cards in standard form, such as As Kc. |
| method | How it was counted | Exact (every remaining board), or before the flop estimated (exact without flushes, flush boards sampled). |
| hand1Now | Your hand now | Your best 5-card hand on the board so far (shown from the flop on). |
| hand2Now | Opponent’s hand now | The opponent’s best 5-card hand on the board so far (shown from the flop on). |

## 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.

## Assumptions

- 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.

## Worked examples

1. hand1 = Ah Kh, hand2 = Qs Qd, board = Qh 7h 2c gives equity1 = 25.555556%, win1 = 25.555556%, tie = 0%, method = Exact: every one of 990 possible boards, hand1Now = High card, hand2Now = 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. hand1 = Ah Kh, hand2 = Qs Qd, board = Qh 7h 2c 3d gives win1 = 15.909091%, win2 = 84.090909%, method = 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. hand1 = As Ks, hand2 = 2c 2d, board = Ah 2h 7c Kd 9s gives win1 = 0%, win2 = 100%, equity1 = 0%, hand1Now = Two pair, hand2Now = Three of a kind. Source: hand calculation in content.mdx: three 2s beat aces and kings.
4. hand1 = Ah Ad, hand2 = Kc Ks gives equity1 = 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).

## FAQ

### 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.

## Sources

- Wikipedia, List of poker hands (hand rankings): https://en.wikipedia.org/wiki/List_of_poker_hands
- Wikipedia, Poker probability (Texas hold ’em): https://en.wikipedia.org/wiki/Poker_probability
- Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, section 3.2, combinations: https://math.dartmouth.edu/~prob/prob/prob.pdf
- National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/