Flop to turn, turn to river, flop to river
Three different questions with three different denominators.
6 minute read
The chance of hitting on the next card is outs over unseen cards: on the flop that denominator is 47, on the turn 46. The chance of hitting by the river from the flop is a two-card question, best answered by counting the ways to miss twice.
| Outs | Flop → turn | Turn → river | Flop → river |
|---|---|---|---|
| 2 | 4.26% | 4.35% | 8.42% |
| 4 | 8.51% | 8.70% | 16.47% |
| 6 | 12.77% | 13.04% | 24.14% |
| 8 | 17.02% | 17.39% | 31.45% |
| 9 | 19.15% | 19.57% | 34.97% |
| 12 | 25.53% | 26.09% | 44.96% |
| 15 | 31.91% | 32.61% | 54.12% |
Notice that flop-to-river is a little less than double flop-to-turn. Hitting twice is possible but only counts once, and the second draw is from a smaller deck.
Which number applies
Use the two-card number only when you will see both cards — for example, when you are all-in on the flop. Facing a bet on the flop with more betting to come, the one-card number is the honest one; you may have to pay again on the turn.
Quick check
Nine outs. What is the chance of hitting on the turn, on the river after missing the turn, and by the river overall?
Show answer
19.15% (9/47), 19.57% (9/46), and 34.97%.