Chance to hit on the river
23.91%
11 outs, one card to come
- Odds against3.18 : 1
- Rule of 2 estimate-1.91 points from the exact chance22%
- Unseen cards46
The count behind 11 outs on the turn
A 23.91% chance gives the draw real weight. You will miss 76.09% of the time, yet a bet of up to 45.83% of the pot still costs less than your chance.
- Unseen cards46
- Your outs11
- Cards that miss35
- Chance on the river23.91%
- Chance on the next card (the river)23.91%
- Odds against hitting3.18 : 1
- Estimate from the rule of 222%
- Error of the rule of 2-1.91 points
Chance on the river = k / u, with u = 46 unseen cardsFor 11 outs: 11 / 46 = 23.91%
One card is left to come out of 46 unseen. 11 of them are outs and 35 miss, so the chance is 11 divided by 46, which is 23.91%.
The true chance is 23.91%, which beats the 22% that the rule of 2 reports by 1.91 points.
Leave the adjusted rule for bigger flop draws. With 11 outs on the turn, the plain rule of 2 figure is 22%.
Which holding has 11 outs?
This count has no one textbook draw behind it. It is the total you get after adding up several draws and checking for overlap.
A shared out has a price: 2.17 points for the first, and 6.52 points in all with 3 shared. Subtract any shared outs before you compare with a bet.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 11 | 23.91% | 0.00 points |
| 1 | 10 | 21.74% | 2.17 points |
| 2 | 9 | 19.57% | 4.35 points |
| 3 | 8 | 17.39% | 6.52 points |
The bets 11 outs can call on the turn
Bet sizes run from 1/4 pot to 4x pot. Against 23.91% on the river, 3 of the 12 bet sizes are calls.
Past 45.83% of the pot, the price beats your 23.91%. On a $100 pot that line is $45.83.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +7.25 points | Call |
| 1/3 pot | 20.00% | +3.91 points | Call |
| 2/5 pot | 22.22% | +1.69 points | Call |
| 1/2 pot | 25.00% | -1.09 points | Fold |
| 2/3 pot | 28.57% | -4.66 points | Fold |
| 3/4 pot | 30.00% | -6.09 points | Fold |
| full pot | 33.33% | -9.42 points | Fold |
| 1.25x pot | 35.71% | -11.80 points | Fold |
| 1.5x pot | 37.50% | -13.59 points | Fold |
| 2x pot | 40.00% | -16.09 points | Fold |
| 3x pot | 42.86% | -18.94 points | Fold |
| 4x pot | 44.44% | -20.53 points | Fold |
Nearby counts on both streets
Not sure whether to count one more out? It changes the chance by about 2.17 points. The table shows both streets for the counts around 11.
- 11 outs on the flop: 41.72% by the river.
- 10 outs on the turn: 21.74% on the river.
- 12 outs on the turn: 26.09% on the river.
The river is the last card
On the turn there is nothing left to separate: the river is the last card, so the by-the-river chance and the next-card chance are the same 23.91%.
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 11 outs that is 11 / 46 = 23.91%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 22%, and its error is that figure minus the exact chance in percentage points, here -1.91 points.
The chance counts only the 46 cards you cannot see, each equally likely. It ignores what an opponent may hold and any money still to be won. Verdicts compare your chance with the bet over the pot plus two bets, on a $100 pot.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the chance to hit with 11 outs on the turn?
With 11 outs on the turn you hit on the river 23.91% of the time, about 24 of every 100 hands, because 11 of the 46 unseen cards are outs. The odds against are 3.18 : 1.
What is the error of the rule of 2 at 11 outs?
The rule of 2 gives 22% for 11 outs against an exact 23.91%, an error of -1.91 points. The shortcut sits below the true chance, so the exact figure is better for you.
Do 11 outs on the turn justify a call, and against which bets?
At 23.91% on the river, you can call 3 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -1.09 points, so against half the pot the verdict is Fold. The largest bet you can call is 45.83% of the pot, or $45.83 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 23.91% to 21.74%, and with 3 shared it falls to 17.39%, a loss of 6.52 points. The effective count is then 8 outs.
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