5-card PLO: top set vs a royal flush draw and a wrap
All in on the flop on QhJh5c: AhKhTs9h8c owns 55.3%, and QsQd9c4d2s owns 44.7% of the pot. Exact: the engine dealt all 741 possible run-outs.
Ace-king of hearts on a queen-jack-heart flop is a draw to the royal flush, and the other hole cards add a wrap. It is not a made straight: Omaha takes exactly two hole cards, so ace-king-ten in the hand cannot combine with queen-jack on the board. The draw is the favourite anyway.
| Hand | Equity | Wins | Splits | Equity bar |
|---|---|---|---|---|
| Q♠Q♦9♣4♦2♠ | 44.67% | 44.67% | 0.00% | |
| A♥K♥T♠9♥8♣ | 55.33% | 55.33% | 0.00% |
The working
- Cards out of the deck. 2 hands × 5 + 3 on the board = 13, which leaves 39 unseen.
- Run-outs. 2 board cards to come from 39: C(39, 2) = 741 boards, every one of them dealt.
- Exactly two plus three. On each board a hand plays exactly two of its 5 hole cards with exactly three of the five board cards: C(5, 2) × C(5, 3) = 100 five-card hands, and the best of them is its score. Across the deal that is 148,200 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♥K♥T♠9♥8♣: (410 wins + 0 from 0 splits) ÷ 741 = 55.331%.
- Check. Every board's pot goes somewhere, so the equities add to 100.000%.
Card by card: the turn
Each of the 39 possible turns, and who leads once it lands. Each turn's equity is the average over the 38 rivers that can follow it, so these rows average back to the totals above.
Every turn, with each hand's equity after it
| Turn | QsQd9c4d2s | AhKhTs9h8c |
|---|---|---|
| A♠ | 23.7% | 76.3% |
| A♦ | 23.7% | 76.3% |
| A♣ | 23.7% | 76.3% |
| K♠ | 23.7% | 76.3% |
| K♦ | 23.7% | 76.3% |
| K♣ | 23.7% | 76.3% |
| Q♣ | 97.4% | 2.6% |
| J♠ | 97.4% | 2.6% |
| J♦ | 97.4% | 2.6% |
| J♣ | 97.4% | 2.6% |
| T♥ | 0.0% | 100.0% |
| T♦ | 21.1% | 78.9% |
| T♣ | 21.1% | 78.9% |
| 9♠ | 21.1% | 78.9% |
| 9♦ | 21.1% | 78.9% |
| 8♠ | 23.7% | 76.3% |
| 8♥ | 23.7% | 76.3% |
| 8♦ | 23.7% | 76.3% |
| 7♠ | 44.7% | 55.3% |
| 7♥ | 26.3% | 73.7% |
| 7♦ | 44.7% | 55.3% |
| 7♣ | 44.7% | 55.3% |
| 6♠ | 44.7% | 55.3% |
| 6♥ | 26.3% | 73.7% |
| 6♦ | 44.7% | 55.3% |
| 6♣ | 44.7% | 55.3% |
| 5♠ | 97.4% | 2.6% |
| 5♥ | 97.4% | 2.6% |
| 5♦ | 97.4% | 2.6% |
| 4♠ | 52.6% | 47.4% |
| 4♥ | 23.7% | 76.3% |
| 4♣ | 52.6% | 47.4% |
| 3♠ | 52.6% | 47.4% |
| 3♥ | 26.3% | 73.7% |
| 3♦ | 52.6% | 47.4% |
| 3♣ | 52.6% | 47.4% |
| 2♥ | 23.7% | 76.3% |
| 2♦ | 52.6% | 47.4% |
| 2♣ | 52.6% | 47.4% |
What each hand wins with
Share of all 741 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 | QsQd9c4d2s | AhKhTs9h8c |
|---|---|---|
| Straight flush | · | 5.13% |
| Four of a kind | 4.99% | · |
| Full house | 31.85% | · |
| Flush | · | 20.24% |
| Straight | 1.21% | 29.96% |
| Three of a kind | 6.61% | · |
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 →- 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 |
| 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 |
| 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 |