What is a draw?
A draw is an incomplete hand that may reach a target combination with a later card. Four available cards of one suit may become a flush with a fifth. Completing the combination and winning the pot are separate questions.
Why a flush draw often has nine nominal outs
Each suit has thirteen cards. If four of your two hole cards plus the three-card flop are spades, nine spades remain among 47 unseen cards. The next-card proportion is 9/47, about 19.1%, assuming no additional card information.
Open-ended and gutshot draws
Available ranks 5-6-7-8 can make a straight with a 4 or 9: eight nominal cards. Ranks 5-6-8-9 need a 7: four nominal cards. In standard high poker an ace can sit at the low or high end, but cannot wrap through K-A-2.
Completing your draw may still leave you behind
A card may improve your hand while giving an opponent a higher flush, full house or straight; it may also produce a tie. Clean outs depend on the board and possible opposing hands. Not every improving card is a winning card.
Two-card probabilities are not a simple sum
In that nine-out example, if both turn and river will be seen, the chance of at least one spade is 1 − (38/47 × 37/46), about 35.0%. This does not account for opposing hands, later action or pot eligibility, and is not a winning probability or a recommendation.
Worked example: remove overlapping outs before counting the next card
In this Hold’em example, your hole cards are J♥ 10♥ and the flop is Q♥ 9♥ 2♣. Only these 5 cards are known, with no information about opponents’ cards or any other cards. There are 52 − 5 = 47 unknown cards. We count only the nominal chance that the next turn card completes a straight or flush pattern, not the chance of eventually winning the pot.
One card can complete both a straight and a flush. Here K♥ and 8♥ make straight flushes, but each is still just one unknown card and must be counted once. List both groups, then subtract the overlap.
- There are 9 flush-completing cards: A♥, K♥, 8♥, 7♥, 6♥, 5♥, 4♥, 3♥ and 2♥. The known Q♥, J♥, 10♥ and 9♥ are excluded.
- There are 8 open-ended straight-completing cards: K♠, K♥, K♦, K♣, 8♠, 8♥, 8♦ and 8♣. Any K makes 9-10-J-Q-K; any 8 makes 8-9-10-J-Q.
- Only K♥ and 8♥ overlap. Each was counted twice, so there are 9 + 8 − 2 = 15 distinct nominal outs, not 17.
- For the next card only: 15 / 47 ≈ 31.9%. This is a one-card calculation with five known cards and no additional card information, not the combined chance across both turn and river.
- Completing the draw does not guarantee a win. An opponent may still have a stronger hand, and later board cards can change the result or create a tie. This is not winning equity, a calling recommendation or a profit forecast; 31.9% is not an actual win probability.
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Keep exploring
This guide was independently compiled in Chinese. The following sources let you verify the rules.
MIT OpenCourseWare: Poker Probability Exercises(new window)