# How good are my four hole cards?

Computes the exact equity of two Omaha hands against each other from the flop on: each hand’s chance to win or tie by the river, using exactly two hole cards and three board cards; five-card Omaha too.

- Page: https://www.acalculator.org/game/omaha-odds-calculator
- JSON spec: https://www.acalculator.org/game/omaha-odds-calculator.json
- Version: d132c675a387

## Default answer

Example with the default inputs (Your hand Ah Ad Ks Qs, Opponent’s hand Jh Th 9c 8c, Board Kh 7h 2c): Ah Ad Ks Qs against Jh Th 9c 8c has 50.37% equity.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| hand1 | Your hand | Your hand: 4 cards (5 for five-card Omaha), rank then suit, such as Ah Ad Ks Qs (T or 10 for ten; c, d, h, s for the suits). |
| hand2 | Opponent’s hand | Opponent’s hand: 4 cards (5 for five-card Omaha), rank then suit, such as Ah Ad Ks Qs (T or 10 for ten; c, d, h, s for the suits). |
| board | Board | The community cards dealt so far: 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 hand is better. |
| win2 | Opponent wins | The share of boards on which the opponent’s best 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 cards in standard form, such as Ah Ad Ks Qs. |
| cards2 | Opponent’s cards | The opponent’s cards in standard form. |
| method | How it was counted | How many boards were counted. |
| hand1Now | Your hand now | Your best hand on the board so far. |
| hand2Now | Opponent’s hand now | The opponent’s best hand on the board so far. |

## Method

Equity = P(win) + P(tie) ÷ 2 over every board that can still come, each hand using exactly 2 hole cards and 3 board cards.

## Assumptions

- Heads-up: two known hands. Each plays its best 5-card hand of exactly 2 hole cards and exactly 3 board cards, under standard high-hand rankings (no hi-lo split). Suits never break a tie.
- All unseen cards are equally likely; the result is exact from the flop on. Before the flop there is no answer.
- Equity is the share of the pot won on average if both hands go to showdown; it ignores betting.

## Worked examples

1. hand1 = Ah Ad Ks Qs, hand2 = Jh Th 9c 8c, board = Kh 7h 2c gives equity1 = 50.37%, win1 = 50.37%, win2 = 49.63%, tie = 0%, method = Exact: every one of 820 possible boards, hand1Now = One pair, hand2Now = High card. Source: Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands.
2. hand1 = Ah Ad Ks Qs, hand2 = Jh Th 9c 8c, board = Kh 7h 2c 3d gives win1 = 80%, win2 = 20%, method = Exact: every one of 40 possible boards. Source: Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands.
3. hand1 = Jh Th 4c 5c, hand2 = Js Ts 6d 7d, board = Ah Kd Qc 2s 3h gives tie = 100%, equity1 = 50%, equity2 = 50%, hand1Now = Straight, hand2Now = Straight. Source: Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands.
4. hand1 = As Ks Qs Js, hand2 = Ah Kh 2c 2d, board = Ts 9s 3h 4h 5d gives win2 = 100%, equity1 = 0%, method = Exact: every one of 1 possible board, hand1Now = High card, hand2Now = Straight. Source: Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands.
5. hand1 = Ah Ad 2c 3c 4d, hand2 = Kh Kd Qs Js Tc, board = Ac 9h 9d gives win1 = 99.87%, method = Exact: every one of 741 possible boards, hand1Now = Full house, hand2Now = Two pair. Source: Wikipedia, Omaha hold ’em (each player uses exactly two of four hole cards and exactly three board cards): https://en.wikipedia.org/wiki/Omaha_hold_%27em; Wikipedia, List of poker hands: https://en.wikipedia.org/wiki/List_of_poker_hands.

## FAQ

### How does Omaha differ from hold’em for the odds?

In Omaha each player gets four hole cards and must use exactly two of them with exactly three board cards. So four spades in your hand make no flush unless three spades are on the board, and a pair in your hand plus a pair on the board does not make three of a kind with a fourth board card.

### How is the equity calculated?

For every board that can still come, the calculator finds each hand’s best 5-card hand from the 6 ways to pick 2 of 4 hole cards and the 10 ways to pick 3 of 5 board cards, then counts wins, losses and ties. Equity is the win share plus half the tie share. On the flop there are 820 turn and river pairs with four-card hands; on the turn, 40 rivers.

### Why does it need the flop?

Before the flop there are 1,086,008 boards, each with 120 hand checks, which is too much to count on a phone. From the flop on, every board is counted, so the answer is exact.

### Does it work for five-card Omaha?

Yes. Type 5 cards in each hand. Each hand still uses exactly 2 hole cards, picked from 10 pairs. On the flop there are 741 possible turn and river pairs.

### Does it do Omaha hi-lo?

No. It ranks high hands only. In hi-lo the pot is split with the best qualifying low hand, which needs a different count.

## Sources

- Wikipedia, Omaha hold ’em (four hole cards; a hand uses exactly two hole cards and exactly three community cards). https://en.wikipedia.org/wiki/Omaha_hold_%27em (retrieved 2026-10-19)
- Wikipedia, List of poker hands (hand rankings). https://en.wikipedia.org/wiki/List_of_poker_hands (retrieved 2026-10-19)
- National Council on Problem Gambling, help and treatment (1-800-MY-RESET). https://www.ncpgambling.org/help-treatment/ (retrieved 2026-10-19)