How often does a flush draw get there?
A flush draw has nine outs. Here is how often it hits on the next card, the last card and by the river, with the rule of 4 checked against exact counts.
You hold two hearts and the flop brings two more. You need one of the nine hearts left in the deck. How often does it come? Here are exact numbers, with no simulation: every figure is a count of the cards still to come.
The outs table
An out is a card that completes your hand. Each row shows how many outs the draw has, and the chance it gets there. This is from your point of view with five cards seen (your two and the three on the flop), so 47 cards are unseen. "Next card" is the turn. "Last card" is the river after the turn missed. "Both cards" is the flop all the way to the river.
| Draw | Outs | Next card | Last card, after a miss | Both cards | Rule of 4 |
|---|---|---|---|---|---|
| Gutshot straight draw | 4 | 8.5% | 8.7% | 16.5% | 16% |
| Two overcards | 6 | 12.8% | 13.0% | 24.1% | 24% |
| Open-ended straight draw | 8 | 17.0% | 17.4% | 31.5% | 32% |
| Flush draw | 9 | 19.1% | 19.6% | 35.0% | 36% |
| Flush draw + gutshot | 12 | 25.5% | 26.1% | 45.0% | 48% |
| Flush draw + open-ended straight draw | 15 | 31.9% | 32.6% | 54.1% | 60% |
For a flush draw, the answer is 35.0% by the river from the flop, and 19.1% on the next card alone.
How we counted
- Next card: outs divided by 47.
- Last card, after a miss: outs divided by 46, because the turn is now seen and wasn't an out.
- Both cards: one minus the chance both cards miss. With n outs that's 1 − C(47−n, 2) / C(47, 2), where C(a, 2) is the number of ways to choose two cards from a.
We recounted every cell a second way too, by listing all 1,081 possible turn and river pairs and counting the ones that contain an out. Both methods agree on every number above.
How good is the rule of 4?
The rule of 4 says to multiply your outs by 4 to estimate the chance of hitting by the river from the flop. For nine outs that gives 36% against an exact 35.0%, close enough for use at the table. It gets worse as the outs pile up: with 12 outs the rule says 48% against an exact 45.0%, and with 15 outs it says 60% against 54.1%. For one card to come, the rule of 2 says 18% for nine outs, against an exact 19.6% for the last card.
When the outs aren't clean
The table assumes every out is live, and that you don't know your opponent's cards. Neither is always true. Here are two spots from our calculator, which counts every possible runout (990 of them on the flop).
A pair against a combo draw. A♠︎A♣︎ against 9♥︎8♥︎ on 7♥︎6♥︎2♣︎. The second hand has a flush draw and an open-ended straight draw: nine hearts, plus three fives and three tens, for 15 outs. The aces win 43.7% and the draw wins 56.3%. The pair is the underdog.
A flush draw against an overpair. A♥︎5♥︎ against K♠︎K♦︎ on Q♥︎8♥︎3♣︎. The ace-high flush draw wins 46.3% and the kings win 53.7%. A big draw against a made hand is often close to a coin flip.
These numbers ignore betting. Equity is not advice about how to play a hand.
Run it yourself
Every number here comes from our calculator, which counts every possible deal. Open the spot and check it.
What changed
- Published. Every cell in the outs table was recounted exactly.
The Thursday email
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