Verdict
Call
15 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come54.12%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+34.12 points
Chance against price
With 15 outs on the flop you hit 54.12% of the time by the river, and a third-pot bet only asks for 20.00%. That 34.12-point cushion makes this a clear call.
Holding a flush draw with an open-ended straight draw gives you exactly 15 outs, out of 47 unseen cards. One card hits 31.91% of the time.
Worked through on a $100 pot
- The pot before betting$100
- Bet$33.33
- Your call$33.33
- Total pot after calling$166.67
- Net gain when you hit$133.33
- Loss on a miss$33.33
- Chance to hit by the river54.12%
- Average value of the call+$56.86
- Price of the call20.00%
- Exact margin over the price+34.1166 points
- Outs at break-even4.91 outs
- Margin measured in outs+10.09 outs
Assume the whole pot goes to you when you hit, the call is lost when you miss, and nothing more is bet. Calling then gains $56.86 on average: $72.16 from hits, minus $15.29 from misses, +1.706 per dollar called.
Odds say the same thing. Hitting is 0.85 : 1 against, and the pot lays 4 : 1.
Do not forget your own call. Dividing the bet by the pot without it gives 25.00%, not 20.00%, and would show a margin of +29.1166 points. The bet over the starting pot, 33.33%, is worse and would show +20.7832 points.
Slack in the call
If some outs turned out to be shared with a better hand, you could give up 10 outs and still call. The floor is 5, at 20.35%.
After a hit you could give back up to $105.07 on later streets, 3.15 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% | +34.12 points | +$56.86 | Call |
| $10 | 21.28% | +32.84 points | +$51.45 | Call |
| $25 | 23.53% | +30.59 points | +$43.33 | Call |
| $50 | 28.57% | +25.55 points | +$29.80 | Call |
| $100 | 50.00% | +4.12 points | +$2.74 | Call |
Next card or river
You can skip the usual debate over one card versus two, because 31.91% and 54.12% both give a call against 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 54.12% | +34.1166 points | +$56.86 | Call |
| Next card only | 31.91% | +11.9149 points | +$19.86 | Call |
How the answer moves with outs
One out can change the answer, so the table lists the counts on either side of 15. Each out adds roughly 2.87 points against the 20.00% price.
Other bet sizes for this draw
Look down the margin column to see where the draw stops paying. Every row uses 15 outs on the flop and a bet of a different size.
A draw this strong has no ceiling inside the table. 54.12% tops every price from the smallest bet to the largest.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +37.45 points | Call |
| third-pot, this page | 20.00% | +34.12 points | Call |
| two-fifths-pot | 22.22% | +31.89 points | Call |
| half-pot | 25.00% | +29.12 points | Call |
| two-thirds-pot | 28.57% | +25.55 points | Call |
| three-quarter-pot | 30.00% | +24.12 points | Call |
| pot-size | 33.33% | +20.78 points | Call |
| 1.25x-pot | 35.71% | +18.40 points | Call |
| 1.5x-pot | 37.50% | +16.62 points | Call |
| 2x-pot | 40.00% | +14.12 points | Call |
| 3x-pot | 42.86% | +11.26 points | Call |
| 4x-pot | 44.44% | +9.67 points | Call |
How this is computed
The hit chance comes straight from combinations. Out of 1,081 pairs of unseen cards, 496 miss every out, so you hit 54.12% of the time.
Four assumptions sit behind the verdict: you call the full bet, a hit wins the entire pot, no money goes in after the call, and every one of the 47 unseen cards is equally likely. The price is $33.33 / $166.67 = 20.00%. No card is taken out for what an opponent might hold.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a third-pot bet with 15 outs on the flop?
Reduce the question to a comparison of two numbers: 54.12% to hit and 20.00% to break even. The first minus the second is +34.12 points, which makes this a call, and the call averages +$56.86 on a $100 pot if no more betting follows.
How strong must a draw be to call a third-pot bet on the flop?
A call starts to work at 5 outs: 20.35% to hit versus 20.00% needed. One out fewer drops the chance to 16.47%. You hold 15, which is 10 more than the minimum.
One card or two: which number belongs next to the 20.00% price?
Both figures are right for their own situation: 54.12% with no more betting, 31.91% when the turn brings a bet. Facing 20.00%, each one gives a call.
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