Set vs flush draw vs straight draw
All in on the flop on Th9h2s: 2c2d owns 56.8%, AhKh owns 25.9%, and QsJs owns 17.3% of the pot. Exact: the engine dealt all 903 possible run-outs.
Bottom set against the nut flush draw with two overcards and an open-ended straight draw, all in on the flop. The set is ahead now, and the table below shows which turn cards change that.
| Hand | Equity | Wins | Splits | Equity bar |
|---|---|---|---|---|
| 2♣2♦ | 56.81% | 56.81% | 0.00% | |
| A♥K♥ | 25.91% | 25.91% | 0.00% | |
| Q♠J♠ | 17.28% | 17.28% | 0.00% |
The working
- Cards out of the deck. 3 hands × 2 + 3 on the board = 9, which leaves 43 unseen.
- Run-outs. 2 board cards to come from 43: C(43, 2) = 903 boards. The engine dealt every one of them and scored every hand on each, so nothing below is sampled.
- Equity. A board a hand wins outright is worth 1 pot; a split is worth 1 ÷ the number of hands sharing it. For 2♣2♦: (513 wins + 0 from 0 splits) ÷ 903 = 56.811%.
- Check. Every board's pot goes somewhere, so the equities add to 100.000%. No board is split, so win percentages and equities are the same thing here.
Card by card: the turn
Each of the 43 possible turns, and who leads once it lands. Each turn's equity is the average over the 42 rivers that can follow it, so these rows average back to the totals above.
Every turn, with each hand's equity after it
| Turn | 2c2d | AhKh | QsJs |
|---|---|---|---|
| A♠ | 54.8% | 19.0% | 26.2% |
| A♦ | 66.7% | 19.0% | 14.3% |
| A♣ | 66.7% | 19.0% | 14.3% |
| K♠ | 21.4% | 19.0% | 59.5% |
| K♦ | 21.4% | 19.0% | 59.5% |
| K♣ | 21.4% | 19.0% | 59.5% |
| Q♥ | 21.4% | 78.6% | 0.0% |
| Q♦ | 64.3% | 21.4% | 14.3% |
| Q♣ | 64.3% | 21.4% | 14.3% |
| J♥ | 21.4% | 78.6% | 0.0% |
| J♦ | 64.3% | 21.4% | 14.3% |
| J♣ | 64.3% | 21.4% | 14.3% |
| T♠ | 100.0% | 0.0% | 0.0% |
| T♦ | 100.0% | 0.0% | 0.0% |
| T♣ | 100.0% | 0.0% | 0.0% |
| 9♠ | 100.0% | 0.0% | 0.0% |
| 9♦ | 100.0% | 0.0% | 0.0% |
| 9♣ | 100.0% | 0.0% | 0.0% |
| 8♠ | 23.8% | 16.7% | 59.5% |
| 8♥ | 23.8% | 76.2% | 0.0% |
| 8♦ | 23.8% | 16.7% | 59.5% |
| 8♣ | 23.8% | 16.7% | 59.5% |
| 7♠ | 57.1% | 16.7% | 26.2% |
| 7♥ | 23.8% | 76.2% | 0.0% |
| 7♦ | 69.0% | 16.7% | 14.3% |
| 7♣ | 69.0% | 16.7% | 14.3% |
| 6♠ | 57.1% | 16.7% | 26.2% |
| 6♥ | 23.8% | 76.2% | 0.0% |
| 6♦ | 69.0% | 16.7% | 14.3% |
| 6♣ | 69.0% | 16.7% | 14.3% |
| 5♠ | 57.1% | 16.7% | 26.2% |
| 5♥ | 23.8% | 76.2% | 0.0% |
| 5♦ | 69.0% | 16.7% | 14.3% |
| 5♣ | 69.0% | 16.7% | 14.3% |
| 4♠ | 57.1% | 16.7% | 26.2% |
| 4♥ | 23.8% | 76.2% | 0.0% |
| 4♦ | 69.0% | 16.7% | 14.3% |
| 4♣ | 69.0% | 16.7% | 14.3% |
| 3♠ | 57.1% | 16.7% | 26.2% |
| 3♥ | 23.8% | 76.2% | 0.0% |
| 3♦ | 69.0% | 16.7% | 14.3% |
| 3♣ | 69.0% | 16.7% | 14.3% |
| 2♥ | 100.0% | 0.0% | 0.0% |
What each hand wins with
Share of all 903 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 | 2c2d | AhKh | QsJs |
|---|---|---|---|
| Straight flush | · | 0.11% | · |
| Four of a kind | 4.65% | · | · |
| Full house | 30.90% | · | · |
| Flush | · | 25.36% | 3.10% |
| Straight | · | 0.44% | 14.17% |
| Three of a kind | 21.26% | · | · |
The link carries every card. Anyone who opens it gets the same counts, dealt again in their own browser.
Suits, a dead card, a different board: any change 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, and every hand scored on each by the same engine that runs the trainer. Splits are shared equally among the hands in them. No sampling, so no error bars.
- Assumed: everyone sees the showdown. Equity is each hand's share of the pot if nobody folds and no more money goes in. That is exact when everyone is all-in; with chips behind it is a starting point, not a verdict, because folds, bets and implied odds are not in it.
- Specific hands only. Multi-way equity against ranges multiplies the work by the number of combos per player, so it is not here. For one hand against a range, with the bet priced in big blinds, use the spot check.
- Input: cards as rank then suit, spaces optional: Ah Kd, Tc 9c, or AhKd. Dead cards are any cards you know are gone, such as a folded hand.
More multi-way spots
| Spot | Street | Favourite | Equity | Boards dealt |
|---|---|---|---|---|
| AA vs KK vs QQ | preflop | A♥A♦ | 66.9% | 1,370,754 |
| AA vs KK vs QQ vs JJ | preflop | A♥A♦ | 54.6% | 1,086,008 |
| AKo vs QQ vs JJ | preflop | Q♥Q♣ | 46.5% | 1,370,754 |
| AA vs KK vs AK | preflop | A♥A♦ | 84.9% | 1,370,754 |
| AKo vs AQo vs KQo | preflop | A♠K♦ | 72.0% | 1,370,754 |
| JTs vs AA vs KK | preflop | A♠A♦ | 64.3% | 1,370,754 |
| 22 vs AKo vs KQs | preflop | 2♠2♣ | 40.3% | 1,370,754 |
| Overpair vs top two pair vs flush draw | flop | K♦Q♦ | 51.9% | 903 |
| Top pair vs flush draw vs gutshot, on the turn | turn | A♠J♦ | 66.7% | 42 |
| KK vs top pair vs flush draw | flop | A♥Q♣ | 55.7% | 903 |
| Six hands all in preflop | preflop | A♥A♦ | 41.7% | 658,008 |