Chance to hit on the river
19.57%
9 outs, one card to come
- Odds against4.11 : 1
- Rule of 2 estimate-1.57 points from the exact chance18%
- Unseen cards46
The count behind 9 outs on the turn
This count leaves you empty-handed 80.43% of the time. A 19.57% chance can still be worth chasing, but only when the bet you face is a small fraction of the pot.
- Unseen cards46
- Your outs9
- Cards that miss37
- Chance on the river19.57%
- Chance on the next card (the river)19.57%
- Odds against hitting4.11 : 1
- Estimate from the rule of 218%
- Error of the rule of 2-1.57 points
Chance on the river = k / u, with u = 46 unseen cardsFor 9 outs: 9 / 46 = 19.57%
One card is left to come out of 46 unseen. 9 of them are outs and 37 miss, so the chance is 9 divided by 46, which is 19.57%.
Multiplying 9 by 2 gives 18%, short of the exact 19.57% by 1.57 points. The shortcut under-reads the draw a little more with each extra out.
Leave the adjusted rule for bigger flop draws. With 9 outs on the turn, the plain rule of 2 figure is 18%.
Which holding has 9 outs?
One standard source of this count is a flush draw. Count the cards carefully at the table, because outs that also help a rival do not count in full.
Not every out is clean. Here is the chance once shared outs are removed: from 19.57% down to 13.04% when 3 are shared.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 9 | 19.57% | 0.00 points |
| 1 | 8 | 17.39% | 2.17 points |
| 2 | 7 | 15.22% | 4.35 points |
| 3 | 6 | 13.04% | 6.52 points |
The bets 9 outs can call on the turn
A call is right when your chance beats what the bet asks of you. At 19.57%, that holds for 1 of the 12 bet sizes in the table.
The biggest bet you can call is 32.14% of the pot, which is $32.14 on a $100 pot.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +2.90 points | Call |
| 1/3 pot | 20.00% | -0.43 points | Fold |
| 2/5 pot | 22.22% | -2.66 points | Fold |
| 1/2 pot | 25.00% | -5.43 points | Fold |
| 2/3 pot | 28.57% | -9.01 points | Fold |
| 3/4 pot | 30.00% | -10.43 points | Fold |
| full pot | 33.33% | -13.77 points | Fold |
| 1.25x pot | 35.71% | -16.15 points | Fold |
| 1.5x pot | 37.50% | -17.93 points | Fold |
| 2x pot | 40.00% | -20.43 points | Fold |
| 3x pot | 42.86% | -23.29 points | Fold |
| 4x pot | 44.44% | -24.88 points | Fold |
Nearby counts on both streets
A single out is worth about 2.17 points here. The table lists the counts around 9 on both streets so you can see how the other street compares.
- 9 outs on the flop: 34.97% by the river.
- 8 outs on the turn: 17.39% on the river.
- 10 outs on the turn: 21.74% on the river.
The river is the last card
You do not need a second view on the turn. The 19.57% chance is final, and against a half-pot price of 25.00% it leaves -5.43 points: Fold.
How this is computed
The chance to hit on the river from the turn is k / 46, where 46 is the number of unseen cards and k is your effective outs. For 9 outs that is 9 / 46 = 19.57%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 18%, and its error is that figure minus the exact chance in percentage points, here -1.57 points.
Read the figures as a card count. All 46 unseen cards stay in, including any your opponent holds, so the figures describe your outs, not a matchup. Bets are called in full against a $100 pot with no extra money assumed.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What percent chance does a count of 9 give you on the turn?
With 9 outs on the turn you hit on the river 19.57% of the time, about 20 of every 100 hands, because 9 of the 46 unseen cards are outs. The odds against are 4.11 : 1.
Can I trust the shortcut for 9 outs on the turn?
The rule of 2 gives 18% for 9 outs against an exact 19.57%, an error of -1.57 points. The shortcut sits below the true chance, so the exact figure is better for you.
What is the largest bet worth calling with a count of 9 on the turn?
At 19.57% on the river, you can call 1 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -5.43 points, so against half the pot the verdict is Fold. The largest bet you can call is 32.14% of the pot, or $32.14 on a $100 pot.
How many points do I lose if outs are shared with a better hand?
Take them off the count first. With one shared out the chance on the river falls from 19.57% to 17.39%, and with 3 shared it falls to 13.04%, a loss of 6.52 points. The effective count is then 6 outs.
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