// PLO equity · 2-way · river

One heart is not a flush

All in on the river on Kh9h6h4h2c: 3h2hTs9s owns 100.0%, and AhKsQdJc owns 0.0% of the pot. The board is complete, so this is the one showdown.

Four hearts on the board, and the first hand holds the ace of hearts. In hold’em that is the nut flush. In Omaha a hand must use exactly two hole cards, so one heart makes nothing, and the hand with the three and two of hearts wins the pot. This is the most common misread at a new Omaha table.

Board

K♥9♥6♥4♥2♣

Hand	Equity	Wins	Splits	Equity bar
A♥K♠Q♦J♣	0.00%	0.00%	0.00%
3♥2♥T♠9♠	100.00%	100.00%	0.00%

The working

Cards out of the deck. 2 hands × 4 + 5 on the board = 13, which leaves 39 unseen.
Run-outs. The board is complete, so there is exactly one showdown and nothing to deal.
Exactly two plus three. On each board a hand plays exactly two of its 4 hole cards with exactly three of the five board cards: C(4, 2) × C(5, 3) = 60 five-card hands, and the best of them is its score. Across the deal that is 120 five-card hands, each one scored the way the engine scores it.
Equity. A board a hand wins outright is worth 1 pot; a split is worth 1 ÷ the number of hands sharing it. For 3♥2♥T♠9♠: (1 wins + 0 from 0 splits) ÷ 1 = 100.000%.
Check. Every board's pot goes somewhere, so the equities add to 100.000%.

The showdown, card by card

The five cards each hand plays. Every one is exactly two hole cards and three from the board; the other hole cards do nothing, whatever they would have made in hold’em.

Hand	Plays	With	Made hand
A♥K♠Q♦J♣	A♥K♠	K♥9♥6♥	Pair
3♥2♥T♠9♠	3♥2♥	K♥9♥6♥	Flush

Suits, a side card, a dead card, a different flop: in Omaha any of them moves these numbers. Open the deal in the calculator and change anything; it is dealt again in your browser.

Change the cards →

// what is computed, and what is assumed

Computed: every possible run-out, dealt from the cards nobody holds, with every hand scored under Omaha rules: the best of all its two-hole-card, three-board-card five-card hands. No sampling, so no error bars.
How it is scored: when the page loads, the engine scores every distinct five-card rank pattern and every flush once, into a lookup table the calculator reads. That table is tested against the engine on all 2,598,960 five-card hands, so every comparison is the engine’s own.
High only. Omaha hi-lo (eight or better) splits pots between a high and a low hand; that is not computed here, so do not read these numbers for PLO8.
Assumed: everyone sees the showdown. Equity is each hand's share of the pot if nobody folds and no more money goes in. In pot-limit that is exact once everyone is all-in; with chips behind it is a starting point, not a verdict.
Specific hands only. Omaha ranges hold hundreds of thousands of combinations, so equity against a range is not here.
Input: cards as rank then suit, spaces optional: As Ah Ks Kh, or AsAhKsKh. Every hand needs the same number of cards: four for PLO, five or six for the bigger variants.

More Omaha spots

Spot	Game	Street	Favourite	Equity	Boards dealt
AAKK double-suited vs JT98 double-suited	PLO	preflop	A♠A♥K♠K♥	61.5%	1,086,008
Ragged aces vs suited, connected kings	PLO	preflop	A♣A♦7♠2♥	57.2%	1,086,008
AAKK vs two rundowns, three-way	PLO	preflop	A♠A♥K♠K♥	42.6%	658,008
Four hands all in preflop	PLO	preflop	9♦8♦7♥6♥	34.7%	376,992
Top set vs a wrap	PLO	flop	Q♠J♠8♦7♣	54.4%	820
Top set vs the nut flush draw and a wrap	PLO	flop	A♥J♥T♣7♠	55.1%	820
Set over set	PLO	flop	K♠K♦Q♥5♣	90.0%	820
Nut straight vs set with the nut flush draw, on the turn	PLO	turn	T♦7♥J♣4♣	57.5%	40
5-card PLO: aces with broadways vs a suited rundown	5-card PLO	preflop	A♠A♥K♦Q♦J♣	51.4%	850,668
5-card PLO: top set vs a royal flush draw and a wrap	5-card PLO	flop	A♥K♥T♠9♥8♣	55.3%	741
6-card PLO: AAKKQJ vs a six-card rundown	6-card PLO	preflop	A♠A♥K♠K♥Q♦J♦	54.7%	658,008
6-card PLO: top set with a wrap vs the nut flush draw	6-card PLO	flop	8♥8♣7♥6♣5♦9♦	66.5%	666