Chance to hit on the river
32.61%
15 outs, one card to come
- Odds against2.07 : 1
- Rule of 2 estimate-2.61 points from the exact chance30%
- Unseen cards46
The count behind 15 outs on the turn
With 32.61% on the river, the draw fails 67.39% of the time and lands the rest. That is enough to call a bet of up to 93.75% of the pot.
- Unseen cards46
- Your outs15
- Cards that miss31
- Chance on the river32.61%
- Chance on the next card (the river)32.61%
- Odds against hitting2.07 : 1
- Estimate from the rule of 230%
- Error of the rule of 2-2.61 points
Chance on the river = k / u, with u = 46 unseen cardsFor 15 outs: 15 / 46 = 32.61%
The river is the last card, so the by-the-river chance and the next-card chance are the same number. For 15 outs it is 15 / 46, or 32.61%.
Being 2.61 points low, 30% still points the right way, but the exact 32.61% is the number to put against a bet.
Leave the adjusted rule for bigger flop draws. With 15 outs on the turn, the plain rule of 2 figure is 30%.
Which holding has 15 outs?
Common holding with this count: a flush draw with an open-ended straight draw. This page tells you how often it gets there.
The table removes shared outs one at a time. The first costs 2.17 points; with 3 shared you are at 26.09%, 6.52 points lower than the clean count.
| Shared outs | Effective outs | Chance on the river | Chance given up |
|---|---|---|---|
| 0 | 15 | 32.61% | 0.00 points |
| 1 | 14 | 30.43% | 2.17 points |
| 2 | 13 | 28.26% | 4.35 points |
| 3 | 12 | 26.09% | 6.52 points |
The bets 15 outs can call on the turn
Bet sizes run from 1/4 pot to 4x pot. Against 32.61% on the river, 6 of the 12 bet sizes are calls.
Your 32.61% stretches to a bet of 93.75% of the pot. Put in dollars, that is $93.75 when the pot holds $100.
| Bet size | Equity a call needs | Margin over it | Verdict |
|---|---|---|---|
| 1/4 pot | 16.67% | +15.94 points | Call |
| 1/3 pot | 20.00% | +12.61 points | Call |
| 2/5 pot | 22.22% | +10.39 points | Call |
| 1/2 pot | 25.00% | +7.61 points | Call |
| 2/3 pot | 28.57% | +4.04 points | Call |
| 3/4 pot | 30.00% | +2.61 points | Call |
| full pot | 33.33% | -0.72 points | Fold |
| 1.25x pot | 35.71% | -3.11 points | Fold |
| 1.5x pot | 37.50% | -4.89 points | Fold |
| 2x pot | 40.00% | -7.39 points | Fold |
| 3x pot | 42.86% | -10.25 points | Fold |
| 4x pot | 44.44% | -11.84 points | Fold |
Nearby counts on both streets
Use the rows below to see what the count next door looks like. A step of one out is about 2.17 points on the turn.
- 15 outs on the flop: 54.12% by the river.
- 14 outs on the turn: 30.43% on the river.
- 16 outs on the turn: 34.78% 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 32.61%.
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 15 outs that is 15 / 46 = 32.61%. The next card is the river, so both chances are the same.
The rule of 2 figure is 2 x k, here 30%, and its error is that figure minus the exact chance in percentage points, here -2.61 points.
Seen as a pure card count, the 46 unseen cards are all equally likely and an opponent's hand removes none of them. Prices use a $100 pot and a call equal to the bet, so the equity needed is the bet over the pot plus two bets.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How should I read the hit chance for 15 outs on the turn?
With 15 outs on the turn you hit on the river 32.61% of the time, about 33 of every 100 hands, because 15 of the 46 unseen cards are outs. The odds against are 2.07 : 1.
Can I trust the shortcut for 15 outs on the turn?
The rule of 2 gives 30% for 15 outs against an exact 32.61%, an error of -2.61 points. The shortcut sits below the true chance, so the exact figure is better for you.
When should I call or fold with 15 outs on the turn?
At 32.61% on the river, you can call 6 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of +7.61 points, so against half the pot the verdict is Call. The largest bet you can call is 93.75% of the pot, or $93.75 on a $100 pot.
Does every one of the 15 outs count in full on the turn?
Take them off the count first. With one shared out the chance on the river falls from 32.61% to 30.43%, and with 3 shared it falls to 26.09%, a loss of 6.52 points. The effective count is then 12 outs.
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