Verdict
Call
15 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come54.12%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+24.12 points
The price of the call
54.12% against 30.00%: the draw beats the price by 24.12 points. On this flop against a three-quarter-pot bet, that is a comfortable call.
The count matches a flush draw with an open-ended straight draw, so you can read this page as that draw. The very next card completes it 31.91% of the time, 15 out of 47.
The $100 pot example
- Pot before the bet$100
- Bet$75
- You call$75
- Total pot after calling$250
- Gain on a hit$175
- You lose on a miss$75
- Chance to hit by the river54.12%
- Average value of the call+$60.29
- Equity needed to break even30.00%
- Your chance minus the price, unrounded+24.1166 points
- Outs at break-even7.59 outs
- Outs to spare, exactly+7.41 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 $60.29 on average: $94.70 in, $34.41 out, +0.804 per dollar called.
Odds say the same thing. Hitting is 0.85 : 1 against, and the pot lays 2.33 : 1.
The price is 30.00% because your call goes into the pot too. Leave it out and you get 42.86%, a margin of +11.2594 points that does not exist; use the starting pot instead and 75.00% puts the margin at -20.8834 points.
Where the call would flip
The fewest outs that still call a three-quarter-pot bet on the flop is 8. You hold 15, so you have 7 outs to spare before the call flips to a fold.
Break-even on later streets sits at $111.41 given back, or 1.49 times your call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +24.12 points | +$60.29 | Call |
| $10 | 31.25% | +22.87 points | +$54.88 | Call |
| $25 | 33.33% | +20.78 points | +$46.76 | Call |
| $50 | 37.50% | +16.62 points | +$33.23 | Call |
| $100 | 50.00% | +4.12 points | +$6.17 | Call |
One card or two
The two chances agree on the verdict. 54.12% by the river and 31.91% on one card each lead to a call against 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 54.12% | +24.1166 points | +$60.29 | Call |
| Next card only | 31.91% | +1.9149 points | +$4.79 | Call |
How the answer moves with outs
The table shows 15 outs and the draws around it on the flop, all against the same three-quarter-pot bet. Each extra out adds about 2.87 points to the chance here.
Other bet sizes for this draw
Your 54.12% chance is fixed, so the only thing that moves is the price. The 12 rows below price the call at every bet size on the flop.
With 54.12% to hit, no bet on the list is too big. 15 outs call all 12 sizes on the flop.
| 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, this page | 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 number is exact rather than estimated. 496 of the 1,081 pairs that could come are blanks, which leaves 54.12% for a hit.
Keep the assumptions in view: a full call ($75 into $250, or 30.00%), 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
Does the math favor calling a three-quarter-pot bet with 15 outs on the flop?
Your chance, 54.12%, set against the 30.00% price gives +24.12 points and a call. With a $100 pot, a $75 call and no more betting, the average value of the call is +$60.29.
What count of outs clears the price of a three-quarter-pot bet on the flop?
8 outs is the line. At 8 the chance is 31.45%, enough for 30.00%; one fewer gives 27.84%, which is not. Your 15 outs sit 7 above it on the flop, at 54.12%.
Should you use the chance on the next card or by the river?
Match the number to the betting: 54.12% if all-in or checked down, 31.91% if you face another bet on the turn. The price is 30.00%, and both numbers agree on call.
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