A flush draw has nine outs, and by the river those nine outs produce 34.97%, not 19.15% counted twice. The two numbers belong to different questions, and the pot-odds formula is where a single figure has to be chosen between them.
Where the nine outs come from
Thirteen cards of one suit exist. Two are in the hand and two are on the board, which leaves nine unseen cards of that suit. That is the whole source of the count: it is fixed by the suit’s size and the four cards already known, so a flush draw on the flop always starts at nine outs.
The table lists 19.15% for the next card and 34.97% by the river at that count. Use 19.15% when only one card remains to be dealt and 34.97% when two do. Both come from the same nine outs; the column changes because the number of chances changes, not because the outs change.
Why two streets are not additive
Nine outs over 47 unseen cards on the flop and nine over 46 on the turn are conditional chances on two different decks. Adding them is not how a two-street probability is built. The turn card can be one of the nine, in which case the river no longer has nine left to find; it can also miss, in which case the river is drawn from a smaller deck. Either way the second fraction is not a second copy of the first.
The exact figure is built from the complement: count the ways to miss on both streets and subtract them from the whole. For nine outs that result is 34.97%, alongside 19.15% for a single card. Use the By the River column for any two-street comparison and the Next Card column for a one-street comparison; a sum of the two single-street fractions is not a row in the table and should not be carried into a calculation.
What a combination draw adds
A flush draw that is also a straight draw has more than nine outs. The table lists 12 outs for a flush draw plus a gutshot, with 25.53% on the next card and 44.96% by the river. A flush draw plus an open-ended straight draw has 15 outs, with 31.91% and 54.12%. The extra outs come from the straight draw ranks, and the two-card figure climbs well past the 34.97% of a plain flush draw.
Read those rows before treating a big draw as a slightly better nine-out hand. At 12 and 15 outs the By the River column is the number that matters, and it is far from a linear extension of the nine-out row. How the hand ranks against a made flush or straight is a separate question from how often the draw completes.
Choosing the row that matches the draw
| Draw | Outs | Next Card | By the River |
|---|---|---|---|
| Gutshot straight draw | 4 | 8.51% | 16.47% |
| Open-ended straight draw | 8 | 17.02% | 31.45% |
| Flush draw | 9 | 19.15% | 34.97% |
| Flush draw plus gutshot | 12 | 25.53% | 44.96% |
| Flush draw plus open-ended | 15 | 31.91% | 54.12% |
The table stacks the plain straight draws, the flush draw and the two combination draws on one grid. Use the row whose out count matches the hand: 4, 8, 9, 12 or 15. Then take the Next Card column for one card to come and the By the River column for two.
That keeps the comparison consistent. A nine-out flush draw and a fifteen-out combination draw are different rows, not the same row with a larger multiplier, and the table already contains the exact figure for each. The only choice left to the reader is which column the remaining number of cards calls for.