// PLO equity · 3-way · preflop

AAKK vs two rundowns, three-way

All in preflop: AsAhKsKh owns 42.6%, QdJdTc9c owns 33.9%, and 8h7h6d5d owns 23.5% of the pot. Exact: the engine dealt all 658,008 possible run-outs.

Double-suited aces and kings against a high rundown and a low one. Three hands, ten different ranks between them, and every board scored for all three.

Board

preflop

Hand	Equity	Wins	Splits
A♠A♥K♠K♥	42.63%	42.62%	0.01%
Q♦J♦T♣9♣	33.87%	33.87%	0.01%
8♥7♥6♦5♦	23.50%	23.50%	0.00%

The working

Cards out of the deck. 3 hands × 4 = 12, which leaves 40 unseen.
Run-outs. 5 board cards to come from 40: C(40, 5) = 658,008 boards, every one of them dealt.
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 118,441,440 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 A♠A♥K♠K♥: (280,467 wins + 35 from 70 splits) ÷ 658,008 = 42.629%.
Check. Every board's pot goes somewhere, so the equities add to 100.000%.

What each hand wins with

Share of all 658,008 boards that each hand wins outright, by the made hand it shows down. Splits are left out, so each column adds to that hand's win rate, not its equity.

Made hand	AsAhKsKh	QdJdTc9c	8h7h6d5d
Straight flush	0.20%	0.68%	0.77%
Four of a kind	2.53%	0.40%	0.40%
Full house	14.52%	5.86%	5.87%
Flush	13.70%	12.20%	·
Straight	1.11%	10.80%	13.86%
Three of a kind	6.25%	1.60%	1.50%
Two pair	4.30%	2.33%	1.11%

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
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
One heart is not a flush	PLO	river	3♥2♥T♠9♠	100.0%	1
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