Verdict
Call
15 outs, turn, third-pot bet
- Chance to hit by the riverone card to come32.61%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+12.61 points
How the verdict is reached
This is one of the easier spots. 15 outs on the turn reach 32.61% by the river, the third-pot bet asks for just 20.00%, and the 12.61-point margin favors the call.
The usual home for 15 outs is a flush draw with an open-ended straight draw. One card from the 46 unseen ones completes it 32.61% of the time.
One hand, in dollars
- Starting pot$100
- Size of the bet$33.33
- You call$33.33
- Total pot after calling$166.67
- Gain on a hit$133.33
- What a miss costs$33.33
- Probability of a hit32.61%
- Calling is worth, on average+$21.01
- Equity needed to break even20.00%
- Exact margin over the price+12.6087 points
- Break-even count of outs9.20 outs
- Margin measured in outs+5.80 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call gains $21.01 on average. The hit side averages $43.48, the miss side $22.46, and each dollar called returns +0.630.
The same comparison in odds: the odds against hitting are 2.07 : 1, and the pot lays 4 : 1 on a call.
Watch the pot you divide by. Leaving your call out turns 20.00% into 25.00%, and the margin into +7.6087 points. Dividing by the starting pot gives 33.33% and a margin of -0.7246 points, further from the truth.
Reverse implied odds and your margin
The threshold is 10 outs, a chance of 21.74%. With 15 in hand you are 5 outs clear of it.
After a hit you could give back up to $64.44 on later streets, 1.93 times your call, before the call stops paying.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +12.61 points | +$21.01 | Call |
| $10 | 21.28% | +11.33 points | +$17.75 | Call |
| $25 | 23.53% | +9.08 points | +$12.86 | Call |
| $50 | 28.57% | +4.04 points | +$4.71 | Call |
| $100 | 50.00% | -17.39 points | -$11.59 | Fold |
One card to come instead of two
One street later the draw is weaker. The same 15 outs hit 54.12% from the flop and 32.61% from the turn, a drop of 21.51 points, and the verdict on the flop would have been a call.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 54.12% | +34.1166 points | +$56.86 | Call |
| Turn, one card to come | 32.61% | +12.6087 points | +$21.01 | Call |
Counts close to yours
How fast does the margin move? About 2.17 points per out on the turn. The rows below keep the third-pot bet fixed and change only the outs.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 13 outs | 28.26% | +8.26 points | Call |
| 14 outs | 30.43% | +10.43 points | Call |
| 15 outs, this page | 32.61% | +12.61 points | Call |
| 16 outs | 34.78% | +14.78 points | Call |
| 17 outs | 36.96% | +16.96 points | Call |
How bet size moves the answer
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 15 outs stay at 32.61%.
A bet larger than 0.94 times the pot ($93.75 on a $100 pot) asks for more than 32.61%. For this draw, 6 of the 12 sizes are calls.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +15.94 points | Call |
| third-pot, this page | 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 | 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
The hit chance comes straight from combinations. With one card left and 15 outs in 46 cards, you hit 32.61% of the time.
These figures describe a clean spot. You pay the whole bet, which costs $33.33 of a $166.67 pot (20.00%), 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
Are 15 outs on the turn worth a call against a bet of a third of the pot?
Math says call. The third-pot bet of $33.33 needs 20.00% equity, 15 outs on the turn give 32.61%, and the margin is +12.61 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$21.01 on average.
How many outs are enough to continue against a bet of a third of the pot on the turn?
The threshold is 10 outs. It gives 21.74%, clearing 20.00%, whereas 9 gives only 19.57%. Holding 15 puts you 5 above it, with a chance of 32.61%.
Should you use the chance on the next card or by the river?
There is no difference on the turn, because one card remains. Use 32.61% and compare it with 20.00%: the margin is +12.61 points, a call, whichever way you phrase the question.
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