Verdict
Call
15 outs, turn, two-thirds-pot bet
- Chance to hit by the riverone card to come32.61%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+4.04 points
Your chance and the price
Against a two-thirds-pot bet the call needs 28.57%. With 15 outs you have 32.61%, so you clear it by 4.04 points and the call wins out.
Holding a flush draw with an open-ended straight draw gives you exactly 15 outs, out of 46 unseen cards. One card hits 32.61% of the time.
A $100 pot, step by step
- Pot before the bet$100
- Size of the bet$66.67
- Your call$66.67
- Final pot if you call$233.33
- Gain on a hit$166.67
- What a miss costs$66.67
- Your chance to hit32.61%
- Calling is worth, on average+$9.42
- Equity needed to break even28.57%
- Margin, to four decimals+4.0373 points
- Fractional outs at the price13.14 outs
- Outs above the price+1.86 outs
Expected value says the same in dollars. Win the whole pot on a hit, lose your call on a miss, add no more betting, and the call gains $9.42 on average: $54.35 in, $44.93 out, +0.141 per dollar called.
In odds, you face 2.07 : 1 against you and the pot pays 2.5 : 1.
Skipping your own call in the pot gives a price of 40.00% where 28.57% is correct, and a margin of -7.3913 points instead of +4.04 points. The starting pot gives 66.67% and a margin of -34.0580 points, which is wrong by even more.
Reverse implied odds and your margin
If some outs turned out to be shared with a better hand, you could give up 1 out and still call. The floor is 14, at 30.43%.
The call keeps its edge until you lose $28.89 on later streets after hitting. That is 0.43 times the $66.67 you pay now.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +4.04 points | +$9.42 | Call |
| $10 | 29.85% | +2.76 points | +$6.16 | Call |
| $25 | 32.00% | +0.61 points | +$1.27 | Call |
| $50 | 36.36% | -3.75 points | -$6.88 | Fold |
| $100 | 50.00% | -17.39 points | -$23.19 | Fold |
Losing a card to come
Compare the streets. With two cards left, 15 outs hit 54.12% (a call); with one card left they hit 32.61% (a call). The difference is 21.51 points.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 54.12% | +25.5451 points | +$59.61 | Call |
| Turn, one card to come | 32.61% | +4.0373 points | +$9.42 | Call |
Nearby draws
Same bet, same street, different draws. The row for 15 outs is marked, and every out is worth about 2.17 points.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 13 outs | 28.26% | -0.31 points | Fold |
| 14 outs | 30.43% | +1.86 points | Call |
| 15 outs, this page | 32.61% | +4.04 points | Call |
| 16 outs | 34.78% | +6.21 points | Call |
| 17 outs | 36.96% | +8.39 points | Call |
The draw across every bet size
Bigger bets ask for more equity while your chance stays at 32.61%. Here is every bet size against the same draw, with the row for this page marked.
Past 0.94 times the pot ($93.75 on a $100 pot) the price outruns your chance. Of the 12 sizes, 6 are calls for 15 outs on the turn.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +15.94 points | Call |
| third-pot | 20.00% | +12.61 points | Call |
| two-fifths-pot | 22.22% | +10.39 points | Call |
| half-pot | 25.00% | +7.61 points | Call |
| two-thirds-pot, this page | 28.57% | +4.04 points | Call |
| three-quarter-pot | 30.00% | +2.61 points | Call |
| pot-size | 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 |
How this is computed
Counting is exact: one card is left, 15 of 46 unseen cards help, and the chance is 32.61%.
These figures describe a clean spot. You pay the whole bet, which costs $66.67 of a $233.33 pot (28.57%), collect the whole pot on a hit, meet no more bets, and draw from 46 equally likely cards, with no adjustment for an opponent's hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Is a call correct with 15 outs against a two-thirds-pot bet on the turn?
Your chance, 32.61%, set against the 28.57% price gives +4.04 points and a call. With a $100 pot, a $66.67 call and no more betting, the average value of the call is +$9.42.
How strong must a draw be to call a two-thirds-pot bet on the turn?
You need at least 14 outs against a two-thirds-pot bet on the turn. That count hits 30.43% against 28.57% needed, and 13 falls short at 28.26%. With 15 you are 1 past the minimum.
One card or two: which number belongs next to the 28.57% price?
One card left means one chance: 32.61%. Set it beside the 28.57% price and you get +4.04 points, which is a call. There is no second figure to weigh against it.
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