Verdict
Call
15 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come54.12%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+20.78 points
Comparing the draw with the bet
The price is 33.33% and your chance is 54.12%. You sit 20.78 points above the line, which is a wide gap, so you 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.
The $100 pot example
- Starting pot$100
- Size of the bet$100
- Your call$100
- Final pot if you call$300
- Gain on a hit$200
- You lose on a miss$100
- Chance to hit by the river54.12%
- Expected value of a call+$62.35
- Equity the call needs33.33%
- Exact margin over the price+20.7832 points
- Fractional outs at the price8.53 outs
- Outs to spare, exactly+6.47 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $62.35 on average. Hits add $108.23 on average and misses cost $45.88 on average, or +0.623 per dollar called.
Written as odds, the pot lays 2 : 1 while the draw is 0.85 : 1 against.
Watch the pot you divide by. Leaving your call out turns 33.33% into 50.00%, and the margin into +4.1166 points.
What could go wrong before the call flips
Count how many outs the call needs: 9 reach the 33.33% price, and you have 15. That leaves 6 outs of slack.
Reverse implied odds are the risk here. A hit that costs you $115.21 later, 1.15 times your call, is where the call stops being worth it.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | +20.78 points | +$62.35 | Call |
| $10 | 34.48% | +19.63 points | +$56.94 | Call |
| $25 | 36.36% | +17.75 points | +$48.82 | Call |
| $50 | 40.00% | +14.12 points | +$35.29 | Call |
| $100 | 50.00% | +4.12 points | +$8.23 | Call |
Next card or river
Watch the difference between one card and two. By the river you hold 54.12%, a call; on the next card alone you hold 31.91%, a fold. A bet on the turn tips you toward the smaller number.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 54.12% | +20.7832 points | +$62.35 | Call |
| Next card only | 31.91% | -1.4184 points | -$4.26 | Fold |
Neighbors of this draw
A few outs either way, against a pot-size bet that needs 33.33%. The chance climbs about 2.87 points with each extra out.
The same draw against other bet sizes
Bet size sets the price, so the verdict changes as you scan the table. The pot-size bet of this page is marked in the first column.
Your 54.12% chance tops every price in the table, so every bet size is a call: the largest price, 44.44%, is still below it.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +37.45 points | Call |
| third-pot | 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, this page | 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 chance rests on counting, not on a rule of thumb. Blank pairs: 496 out of 1,081; hit chance: 54.12%.
Keep the assumptions in view: a full call ($100 into $300, or 33.33%), the whole pot on a hit, no more betting, and 47 unseen cards that are equally likely. The math does not know what the other player holds.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 15 outs when a pot-size bet comes on the flop?
Reduce the question to a comparison of two numbers: 54.12% to hit and 33.33% to break even. The first minus the second is +20.78 points, which makes this a call, and the call averages +$62.35 on a $100 pot if no more betting follows.
How many outs are enough to continue against a bet of the full pot on the flop?
You need at least 9 outs against a pot-size bet on the flop. That count hits 34.97% against 33.33% needed, and 8 falls short at 31.45%. With 15 you are 6 past the minimum.
How many cards should you count when a pot-size bet arrives on the flop?
Match the number to the betting. All-in or checked down: 54.12%. Facing another bet on the turn: 31.91%. The price is 33.33%, so the verdicts are call and fold in that order.
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