// equity calculator · 3-way · preflop
AKo vs AQo vs KQo
All in preflop: AsKd owns 72.0%, AhQc owns 20.9%, and KhQd owns 7.1% of the pot. Exact: the engine dealt all 1,370,754 possible run-outs.
Three broadway hands that all share cards. Each one is dominated by one of the others, and the shared ranks mean pairing a card often helps two hands at once.
Board
preflop| Hand | Equity | Wins | Splits | Equity bar |
|---|---|---|---|---|
| A♠K♦ | 71.97% | 69.08% | 5.96% | |
| A♥Q♣ | 20.89% | 18.02% | 5.94% | |
| K♥Q♦ | 7.13% | 6.42% | 1.62% |
The working
- Cards out of the deck. 3 hands × 2 = 6, which leaves 46 unseen.
- Run-outs. 5 board cards to come from 46: C(46, 5) = 1,370,754 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 A♠K♦: (946,965 wins + 39586.33 from 81,709 splits) ÷ 1,370,754 = 71.971%.
- Check. Every board's pot goes somewhere, so the equities add to 100.000%. Win percentages do not, because a split board counts as a split for every hand in it.
What each hand wins with
Share of all 1,370,754 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 | AsKd | AhQc | KhQd |
|---|---|---|---|
| Straight flush | 0.01% | 0.01% | 0.01% |
| Full house | 0.25% | 0.24% | 0.23% |
| Flush | 2.15% | 2.14% | · |
| Straight | 1.35% | 1.35% | 3.62% |
| Three of a kind | 2.68% | 0.51% | · |
| Two pair | 12.57% | 7.43% | 2.56% |
| Pair | 34.60% | 6.34% | · |
| High card | 15.48% | · | · |
// settle the thread
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 →// what is computed, and what is assumed
- 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 |
| 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 |
| Set vs flush draw vs straight draw | flop | 2♣2♦ | 56.8% | 903 |
| 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 |