// PLO equity · 2-way · preflop

Ragged aces vs suited, connected kings

All in preflop: AcAd7s2h owns 57.2%, and KsKhQsJh owns 42.8% of the pot. Exact: the engine dealt all 1,086,008 possible run-outs.

Aces with two side cards that do nothing, against kings with two suits and two connecting broadway cards. Hold’em players expect aces to crush kings. In Omaha the side cards decide how much the pair is worth.

Board
preflop
HandEquityWinsSplitsEquity bar
A♣A♦7♠2♥57.20%57.20%0.00%
K♠K♥Q♠J♥42.80%42.80%0.00%

The working

  1. Cards out of the deck. 2 hands × 4 = 8, which leaves 44 unseen.
  2. Run-outs. 5 board cards to come from 44: C(44, 5) = 1,086,008 boards, every one of them dealt.
  3. 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 130,320,960 five-card hands, each one scored the way the engine scores it.
  4. 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♦7♠2♥: (621,222 wins + 0 from 0 splits) ÷ 1,086,008 = 57.202%.
  5. Check. Every board's pot goes somewhere, so the equities add to 100.000%.

What each hand wins with

Share of all 1,086,008 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 handAcAd7s2hKsKhQsJh
Straight flush·0.29%
Four of a kind1.20%1.20%
Full house9.58%7.24%
Flush·11.29%
Straight3.05%8.86%
Three of a kind10.49%10.93%
Two pair21.30%2.98%
Pair11.58%·
// settle the thread

The link carries every card. Anyone who opens it gets the same counts, dealt again in their own browser.

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

SpotGameStreetFavouriteEquityBoards dealt
AAKK double-suited vs JT98 double-suitedPLOpreflopA♠A♥K♠K♥61.5%1,086,008
AAKK vs two rundowns, three-wayPLOpreflopA♠A♥K♠K♥42.6%658,008
Four hands all in preflopPLOpreflop9♦8♦7♥6♥34.7%376,992
Top set vs a wrapPLOflopQ♠J♠8♦7♣54.4%820
Top set vs the nut flush draw and a wrapPLOflopA♥J♥T♣7♠55.1%820
Set over setPLOflopK♠K♦Q♥5♣90.0%820
Nut straight vs set with the nut flush draw, on the turnPLOturnT♦7♥J♣4♣57.5%40
One heart is not a flushPLOriver3♥2♥T♠9♠100.0%1
5-card PLO: aces with broadways vs a suited rundown5-card PLOpreflopA♠A♥K♦Q♦J♣51.4%850,668
5-card PLO: top set vs a royal flush draw and a wrap5-card PLOflopA♥K♥T♠9♥8♣55.3%741
6-card PLO: AAKKQJ vs a six-card rundown6-card PLOpreflopA♠A♥K♠K♥Q♦J♦54.7%658,008
6-card PLO: top set with a wrap vs the nut flush draw6-card PLOflop8♥8♣7♥6♣5♦9♦66.5%666