Verdict
Fold
15 outs, turn, pot-size bet
- Chance to hit by the riverone card to come32.61%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price-0.72 points
Comparing the draw with the bet
Folding beats calling by a hair. 32.61% misses 33.33% by 0.72 points, so the call loses a little on average.
15 out of 46 unseen cards is the shape of a flush draw with an open-ended straight draw, and a single card hits 32.61% of the time.
Worked through on a $100 pot
- Starting pot$100
- Size of the bet$100
- You call$100
- Total pot after calling$300
- You can win on a hit$200
- You lose on a miss$100
- Your chance to hit32.61%
- Expected value of calling-$2.17
- Equity needed to break even33.33%
- Exact margin over the price-0.7246 points
- Break-even count of outs15.33 outs
- Margin measured in outs-0.33 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling loses $2.17 on average. Hits add $65.22 on average and misses cost $67.39 on average, or -0.022 per dollar called.
Odds say the same thing. Hitting is 2.07 : 1 against, and the pot lays 2 : 1.
The price is 33.33% because your call goes into the pot too. Leave it out and you get 50.00%, a margin of -17.3913 points that does not exist.
Implied odds that would change the answer
The shortfall in dollars is $6.67: the amount a hit would have to win later for 32.61% to be enough. It equals 0.07 times your $100 call.
The call starts to work at 16 outs, where the chance is 34.78%. Your 15 outs fall 1 out below that.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | -0.72 points | -$2.17 | Fold |
| $50 | 28.57% | +4.04 points | +$14.13 | Call |
| $100 | 25.00% | +7.61 points | +$30.43 | Call |
| $250 | 18.18% | +14.43 points | +$79.35 | Call |
| $500 | 12.50% | +20.11 points | +$160.87 | Call |
Flop and turn compared
Compare the streets. With two cards left, 15 outs hit 54.12% (a call); with one card left they hit 32.61% (a fold). 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% | +20.7832 points | +$62.35 | Call |
| Turn, one card to come | 32.61% | -0.7246 points | -$2.17 | Fold |
Draws around this one
Here are the neighbors of 15 outs, priced against the same 33.33%. One more out lifts your chance by about 2.17 points.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 13 outs | 28.26% | -5.07 points | Fold |
| 14 outs | 30.43% | -2.90 points | Fold |
| 15 outs, this page | 32.61% | -0.72 points | Fold |
| 16 outs | 34.78% | +1.45 points | Call |
| 17 outs | 36.96% | +3.62 points | Call |
Changing the bet, keeping the draw
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%.
The largest bet this draw can call on the turn is 0.94 times the pot ($93.75 on a $100 pot). 15 outs call 6 of the 12 bet sizes listed.
| 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 | 28.57% | +4.04 points | Call |
| three-quarter-pot | 30.00% | +2.61 points | Call |
| pot-size, this page | 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
Here is how 32.61% was found. There is one card to come, so the chance is read directly from 15 outs among 46 unseen cards.
The model is deliberately simple: call everything, win everything on a hit, face no more bets, deal from 46 equally likely unseen cards, and ignore an opponent's holding. With the price at $100 / $300 = 33.33%, later streets and shared outs are what change the real answer.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Should you call a pot-size bet with 15 outs on the turn?
Reduce the question to a comparison of two numbers: 32.61% to hit and 33.33% to break even. The first minus the second is -0.72 points, which makes this a fold, and the call averages -$2.17 on a $100 pot if no more betting follows.
How many outs do you need to call a pot-size bet on the turn?
Look for 16 outs. That is the smallest count whose chance, 34.78%, reaches the 33.33% price; 15 manages 32.61%. You have 15, so you are 1 behind the minimum.
Which hit chance fits a pot-size bet on the turn?
Both views collapse into 32.61%. Against the 33.33% price of a pot-size bet, that leaves -0.72 points and a fold, and the choice between one card and two no longer applies.
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