Poker Equity & OddsDoes running it twice change your equity?
Short answer
No. Running it twice gives you the same share of the pot on average as running it once. What changes is how often you walk away with nothing. AA against KK all in on 7♥ 8♥ 2♣: in one run the kings take the whole pot 8.4% of the time. In two runs they take both 0.4% of the time and the pot is split 16.0%. The aces' average share is 91.6% both ways. Every pair of runs below is counted exactly in the Poker Equity & Odds engine.
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AA vs KK, on the flop and the turn
| Street | Board | One run: win | One run: lose | Two runs: win both | Split | Lose both | Average share |
|---|---|---|---|---|---|---|---|
| Flop | 7♥ 8♥ 2♣ | 91.6% | 8.4% | 83.6% | 16.0% | 0.4% | 91.6% |
| Turn | 7♥ 8♥ 2♣ 4♦ | 95.5% | 4.5% | 91.0% | 8.9% | 0.1% | 95.5% |
Run once from the flop, the aces win the whole pot 91.6% of the time and lose all of it 8.4%. Run twice, the kings win both runs only 0.4% of the time, and one of the two 16.0%. The price is that the aces also scoop less often, 83.6% instead of 91.6%. Add it up and the aces' share is 91.6%, the same as their equity.
A flush draw against top pair
| Street | Board | One run: win | One run: lose | Two runs: win both | Split | Lose both | Average share |
|---|---|---|---|---|---|---|---|
| Flop | K♥ 9♥ 2♣ | 38.9% | 61.1% | 14.3% | 49.2% | 36.5% | 38.9% |
| Turn | K♥ 9♥ 2♣ 7♣ | 20.5% | 79.5% | 3.8% | 33.3% | 62.9% | 20.5% |
From the draw's side it looks different. In one run from the flop it loses everything 61.1% of the time. In two runs that drops to 36.5%, and it gets one of the two runs 49.2% of the time. But it wins both only 14.3%, against 38.9% in one run. On the turn, with one card per run, the draw wins both runs 3.8% of the time. Either way the average share is 38.9% from the flop and 20.5% from the turn, the draw's equity.
A flush draw plus an open-ender on 10♥ 7♥ 2♣ is the favourite against top pair, 56.8%. Two runs give it 31.4% to win both, 50.8% to split and 17.8% to lose both, against 56.8% and 43.2% in one run.
Why the average does not move
Each run is half the pot. Before anything is dealt, the second run is just as likely to be any runout as the first one is, so each run on its own goes to you as often as your equity says. Two halves, each worth your equity on average, add up to your equity. The engine checks this on every spot above: the average share over all pairs of runs matches the one-run equity to within a billionth of the pot.
Same pot, cut in two. Same equity.
What changes is the spread. One way to measure it is the standard deviation of your share of the pot. For AA against KK on the flop it is 27.7 points of the pot for one run and 19.2 points for two. For the flush draw it is 48.7 points against 33.8 points. Smaller swings, same average.
The second run is not a fresh deck
The cards from the first run are gone, so the second run is not quite independent. If the first run brings a heart, the flush draw has one heart fewer for the second. That pulls the two extremes in a little. With a fresh deck for each run, the flush draw would win both runs 15.1% of the time; the real figure is 14.3%. It would lose both 37.3%; the real figure is 36.5%. Every spot on this page moves the same direction, and none of it changes the average.
When it matters
Running it twice is about how much the result swings, not about how much you win on average. If a big loss would hurt your stack or your mood, two runs make it less likely. If you don't care, the equity is the same. Either way, the number to know is the one-run equity, and that is what the calculator gives you.
Your equity is the same either way
Tap in both hands and the board, and the calculator counts every runout. That equity is your average share whether you run it once or twice.
Questions
Does running it twice change your equity?
No. Your average share of the pot is the same whether you run it once or twice. AA against KK on 7♥ 8♥ 2♣ gets 91.6% either way, and the flush draw against top pair gets 38.9% either way. Only the spread of results changes.
Does running it twice help the underdog?
It doesn't give the underdog any equity. It makes losing the whole pot less likely and winning the whole pot less likely too. The flush draw on K♥ 9♥ 2♣ loses everything 61.1% of the time in one run and 36.5% in two, but wins everything 38.9% in one run and only 14.3% in two.
What are the odds of losing both runs?
It depends on the spot. Kings against aces on 7♥ 8♥ 2♣ win both runs 0.4% of the time. A flush draw with one card to come against top pair loses both 62.9%.
Are the two runs independent?
Not quite. The second run is dealt from the cards the first run left, so a heart on run one is one heart fewer for run two. In every spot here that makes winning both and losing both a little rarer than with a fresh deck, and the split a little more common. The average stays the same.
Where the numbers come from. Every figure on this page is an exact count in the Poker Equity & Odds engine. For each spot it deals every possible first run, then every possible second run from the cards that are left, and scores both boards: 893,970 pairs of runs from the flop, 1,892 from the turn. The script that writes these numbers stops if the average share over two runs differs from the one-run equity by more than a billionth of the pot. None of these spots can end in a tie, so every pot is won, lost or split one run each. Engine build 482550e8. More worked numbers: the flop equity cheat sheet and the preflop all-in chart.
