// PLO equity · 2-way · turn
Nut straight vs set with the nut flush draw, on the turn
All in on the turn on 9s8c6s2d: Td7hJc4c owns 57.5%, and 8h8dAsKs owns 42.5% of the pot. Exact: the engine dealt all 40 possible run-outs.
One card to come. The straight is ahead, the set has the full house and the nut flush to draw to, and the river table lists every card that changes hands.
Board
9♠8♣6♠2♦| Hand | Equity | Wins | Splits | Equity bar |
|---|---|---|---|---|
| T♦7♥J♣4♣ | 57.50% | 57.50% | 0.00% | |
| 8♥8♦A♠K♠ | 42.50% | 42.50% | 0.00% |
The working
- Cards out of the deck. 2 hands × 4 + 4 on the board = 12, which leaves 40 unseen.
- Run-outs. 1 board card to come from 40: C(40, 1) = 40 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 4,800 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 T♦7♥J♣4♣: (23 wins + 0 from 0 splits) ÷ 40 = 57.500%.
- Check. Every board's pot goes somewhere, so the equities add to 100.000%.
Card by card: the river
Each of the 40 possible rivers, and who it gives the pot to.
T♦7♥J♣4♣wins on 23 rivers
A♥A♦A♣K♥K♦K♣Q♥Q♦Q♣J♥J♦T♥T♣7♦7♣5♥5♦5♣4♥4♦3♥3♦3♣
8♥8♦A♠K♠wins on 17 rivers
Q♠J♠T♠9♥9♦9♣8♠7♠6♥6♦6♣5♠4♠3♠2♠2♥2♣
Every river, with each hand's equity after it
| River | Td7hJc4c | 8h8dAsKs |
|---|---|---|
| A♥ | 100.0% | 0.0% |
| A♦ | 100.0% | 0.0% |
| A♣ | 100.0% | 0.0% |
| K♥ | 100.0% | 0.0% |
| K♦ | 100.0% | 0.0% |
| K♣ | 100.0% | 0.0% |
| Q♠ | 0.0% | 100.0% |
| Q♥ | 100.0% | 0.0% |
| Q♦ | 100.0% | 0.0% |
| Q♣ | 100.0% | 0.0% |
| J♠ | 0.0% | 100.0% |
| J♥ | 100.0% | 0.0% |
| J♦ | 100.0% | 0.0% |
| T♠ | 0.0% | 100.0% |
| T♥ | 100.0% | 0.0% |
| T♣ | 100.0% | 0.0% |
| 9♥ | 0.0% | 100.0% |
| 9♦ | 0.0% | 100.0% |
| 9♣ | 0.0% | 100.0% |
| 8♠ | 0.0% | 100.0% |
| 7♠ | 0.0% | 100.0% |
| 7♦ | 100.0% | 0.0% |
| 7♣ | 100.0% | 0.0% |
| 6♥ | 0.0% | 100.0% |
| 6♦ | 0.0% | 100.0% |
| 6♣ | 0.0% | 100.0% |
| 5♠ | 0.0% | 100.0% |
| 5♥ | 100.0% | 0.0% |
| 5♦ | 100.0% | 0.0% |
| 5♣ | 100.0% | 0.0% |
| 4♠ | 0.0% | 100.0% |
| 4♥ | 100.0% | 0.0% |
| 4♦ | 100.0% | 0.0% |
| 3♠ | 0.0% | 100.0% |
| 3♥ | 100.0% | 0.0% |
| 3♦ | 100.0% | 0.0% |
| 3♣ | 100.0% | 0.0% |
| 2♠ | 0.0% | 100.0% |
| 2♥ | 0.0% | 100.0% |
| 2♣ | 0.0% | 100.0% |
What each hand wins with
Share of all 40 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 | Td7hJc4c | 8h8dAsKs |
|---|---|---|
| Four of a kind | · | 2.50% |
| Full house | · | 22.50% |
| Flush | · | 17.50% |
| Straight | 57.50% | · |
// 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
| 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 |
| 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 |