acalculator

How good are my four hole cards?

Type both four-card hands and the board. The Omaha odds calculator counts every turn and river that can still come, like a PLO calculator, and gives each hand’s share of the pot. The results are mathematics, not advice.

Your numbers

Type 3, 4 or 5 cards such as Qh 7h 2c.
Your equity
50.37%

Ah Ad Ks Qs against Jh Th 9c 8c has 50.37% equity.

Opponent’s equity
49.63%
You win
50.37%
Opponent wins
49.63%
Tie
0%
Your cards
Ah Ad Ks Qs
Opponent’s cards
Jh Th 9c 8c
How it was counted
Exact: every one of 820 possible boards
Your hand now
One pair
Opponent’s hand now
High card

Your equity: 50.37%. Ah Ad Ks Qs against Jh Th 9c 8c has 50.37% 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 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.

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.

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.

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Your hand Ah Ad Ks Qs, Opponent’s hand Jh Th 9c 8c, Board Kh 7h 2c gives Your equity 50.37%, You win 50.37%, Opponent wins 49.63%, Tie 0%, How it was counted Exact: every one of 820 possible boards, Your hand now One pair, Opponent’s hand now 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. Your hand Ah Ad Ks Qs, Opponent’s hand Jh Th 9c 8c, Board Kh 7h 2c 3d gives You win 80%, Opponent wins 20%, How it was counted 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. Your hand Jh Th 4c 5c, Opponent’s hand Js Ts 6d 7d, Board Ah Kd Qc 2s 3h gives Tie 100%, Your equity 50%, Opponent’s equity 50%, Your hand now Straight, Opponent’s hand now 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. Your hand As Ks Qs Js, Opponent’s hand Ah Kh 2c 2d, Board Ts 9s 3h 4h 5d gives Opponent wins 100%, Your equity 0%, How it was counted Exact: every one of 1 possible board, Your hand now High card, Opponent’s hand now 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. Your hand Ah Ad 2c 3c 4d, Opponent’s hand Kh Kd Qs Js Tc, Board Ac 9h 9d gives You win 99.87%, How it was counted Exact: every one of 741 possible boards, Your hand now Full house, Opponent’s hand now 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

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 Ad Ks Qs, 10d9d8c7c. Your hand has 4 cards (or 5 for five-card Omaha), the opponent’s hand the same number, and the board 3, 4 or 5 cards. Each field holds up to 30 characters.

Hand values. Each hand plays the best 5-card hand made of exactly 2 of its hole cards and exactly 3 board cards, 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). Suits never break a tie; equal hands split the pot. Only high hands count (no hi-lo).

Counting. Over every set of cards that can still complete the board from the unseen deck (52 minus both hands minus the board), each equally likely:

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

With four-card hands there are C(41, 2) = 820 boards on the flop, 40 on the turn and 1 on the river; with five-card hands, C(39, 2) = 741, 39 and 1. Percents are shown rounded half up to 2 decimals.

Rules. Each message gives no answer:

  • "Your hand needs 4 cards (or 5 for five-card Omaha)."
  • "The opponent’s hand needs 4 cards, the same number as yours." (5 when your hand has 5)
  • An empty board: "Enter at least the 3 flop cards: this calculator counts every board from the flop on."
  • 1, 2 or more than 5 board cards: "The board has 3, 4 or 5 cards (flop, turn, river)."
  • "The same card appears twice."
  • Text that is not cards: "Your hand: “…” is not a list of cards such as Ah Kd (rank then suit)." (with the field’s own name and the text typed).

Shown as text. Your cards and the opponent’s cards repeat each hand in standard form: rank 2 to 9, T, J, Q, K, A, then the suit as c, d, h or s, separated by spaces. How it was counted reads Exact: every one of 820 possible boards (with a thousands comma above 999; 1 possible board on the river). Your hand now and the opponent’s hand now name each hand’s best category on the board so far: High card, One pair, Two pair, Three of a kind, Straight, Flush, Full house, Four of a kind, Straight flush.

Assumptions

  • Two known hands, head to head; folded cards are unknown.
  • Equity assumes both hands reach showdown; it ignores betting.

Worked examples by hand

A♥ A♦ K♠ Q♠ against J♥ T♥ 9♣ 8♣ on K♥ 7♥ 2♣. The aces have one pair now (A A with K 7 2, or K K with the board king); the other hand has high card. Counting the 820 turn and river pairs gives 413 wins and 407 losses: 50.37% against 49.63%. The connectors win often because many turns and rivers give them a straight or a heart flush.

Same hands, turn 3♦. 40 rivers: 32 wins and 8 losses, 80%.

A♠ K♠ Q♠ J♠ against A♥ K♥ 2♣ 2♦ on T♠ 9♠ 3♥ 4♥ 5♦. The first hand holds four spades but the board has only two, and exactly three board cards must play, so there is no flush; its best is high card. The second hand plays A♥ and 2♣ with 3♥ 4♥ 5♦ for a straight (A-2-3-4-5). The second hand wins: 0% for the first.

J♥ T♥ 4♣ 5♣ against J♠ T♠ 6♦ 7♦ on A♥ K♦ Q♣ 2♠ 3♥. Each hand’s best is J T from the hand with A K Q from the board, the same straight (the first hand’s A-2-3-4-5 is lower). Suits never break a tie, so the pot is split: 50% each, 100% tie.

Five-card Omaha: A♥ A♦ 2♣ 3♣ 4♦ against K♥ K♦ Q♠ J♠ T♣ on A♣ 9♥ 9♦. The first hand has aces full (A A from the hand, A 9 9 on the board). Of the 741 boards, it loses only when the turn and river are the last two kings (four kings): 740 wins, 99.87%.

Other questions people ask

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.