Poker Equity & OddsRunner-runner odds: what a backdoor draw is worth
Short answer
A runner-runner flush, three of your suit on the flop and two more on the turn and river, comes in 4.2% of the time: 45 of 1,081 runouts. Against top pair it is worth about one out. A♥ J♥ on K♥ 7♣ 2♠ has 17.5% against K♦ Q♣, and the same ranks without the hearts have 13.0%. Two backdoors do more: on that board 9♥ 8♥ has 7 times the equity of 9♣ 4♦. Every runout is counted by the Poker Equity & Odds engine.
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Same hand, with and without the backdoor
Top pair. Good luck.
Both hands face K♦ Q♣ on K♥ 7♣ 2♠, with 990 turn and river pairs left once all four hole cards are out. Ace-jack wins the same ways in both, mostly by pairing the ace. The only difference is the hearts, and they add 4.5 points. One clean out is worth 4.3% by the river, so "a backdoor flush draw is about one out" holds up here.
How the backdoors add up
| Your hand | Straight | Flush | Equity |
|---|---|---|---|
| 9♣ 4♦ | 0.0% | 0.0% | 1.5% |
| 9♣ 8♦ | 4.4% | 0.0% | 6.4% |
| 9♥ 8♥ | 4.2% | 4.2% | 10.6% |
Nine-four has only 1.5%: a nine or a four just makes a pair that loses to kings, so it needs two pair or trips. Swap the four for an eight and the runner-runner straights (ten-jack, ten-six, six-five) take it to 6.4%. Make it two hearts and it is 10.6%, about 7 times where it started. None of these is a call against a real bet, but most of what the suited nine-eight has comes from its backdoors.
The turn is where it pays
turn brings a heart
10 hearts among the 47 cards you can't see.
then the river
Now a plain flush draw, 9 outs from 46 cards.
Multiply the two and you are back at the runner-runner 4.2%. About one turn in 5 brings a heart and gives you a real flush draw, and that is the turn you keep playing. The flush draw guide takes it from there, and should I call with a draw puts a price on it.
Count every out, the backdoor too
Outs & Odds lists the cards that improve you and the exact chance they come. After a drill, Show me why lays out your outs card by card and how the runouts end.
Questions
What are the odds of a runner-runner flush?
With three of a suit on the flop, 45 of the 1,081 possible turn and river pairs bring two more: 4.2%, about one time in 24.
How much equity is a backdoor flush draw worth?
In the hand above, 4.5 points against top pair: A♥ J♥ has 17.5% on K♥ 7♣ 2♠, the same hand without the hearts 13.0%. That is close to one clean out, 4.3% by the river.
What is a backdoor straight draw?
Three cards to a straight that need both the turn and the river. 9♣ 8♦ on K♥ 7♣ 2♠ makes a straight on 48 of the 1,081 possible turn and river pairs, 4.4%.
Should I call because of a backdoor draw?
Rarely on its own. A backdoor adds a few points, and its real use is the turn: one time in 5 the turn gives you a real flush draw. It can tip a close spot toward a call.
Where the numbers come from. Every figure on this page comes from the app's own engine, the code that runs on your phone. Outs come from the Outs & Odds tool, hit chances are exact counts, and equities count every runout with no sampling. Engine build 482550e8. More worked numbers: flush draw odds and the pot odds cheat sheet.