Verdict
Call
12 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come44.96%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+16.39 points
Reading the verdict
44.96% against 28.57%: the draw beats the price by 16.39 points. On this flop against a two-thirds-pot bet, that is a comfortable call.
The count matches a flush draw with a gutshot, so you can read this page as that draw. The very next card completes it 25.53% of the time, 12 out of 47.
The same spot in dollars
- The pot before betting$100
- Size of the bet$66.67
- Your call$66.67
- Total pot after calling$233.33
- Gain on a hit$166.67
- Loss on a miss$66.67
- How often you hit44.96%
- Calling is worth, on average+$38.24
- Equity the call needs28.57%
- Unrounded margin+16.3869 points
- Break-even count of outs7.20 outs
- Your outs minus break-even outs+4.80 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling gains $38.24 on average. The hit side averages $74.93, the miss side $36.69, and each dollar called returns +0.574.
Odds say the same thing. Hitting is 1.22 : 1 against, and the pot lays 2.5 : 1.
Do not forget your own call. Dividing the bet by the pot without it gives 40.00%, not 28.57%, and would show a margin of +4.9584 points. The bet over the starting pot, 66.67%, is worse and would show -21.7083 points.
How much room the call has
Count how many outs the call needs: 8 reach the 28.57% price, and you have 12. That leaves 4 outs of slack.
If hitting means paying off a bigger hand later, the call survives a loss of $85.05. That is 1.28 times the $66.67 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +16.39 points | +$38.24 | Call |
| $10 | 29.85% | +15.11 points | +$33.74 | Call |
| $25 | 32.00% | +12.96 points | +$27 | Call |
| $50 | 36.36% | +8.59 points | +$15.76 | Call |
| $100 | 50.00% | -5.04 points | -$6.72 | Fold |
Which chance to use
Here the cards to come matter. Two cards reach 44.96% and point to a call; one card reaches 25.53% and points to a fold. Which one applies depends on whether the turn brings another bet.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 44.96% | +16.3869 points | +$38.24 | Call |
| Next card only | 25.53% | -3.0395 points | -$7.09 | Fold |
How the answer moves with outs
Here are the neighbors of 12 outs, priced against the same 28.57%. One more out lifts your chance by about 3.15 points.
The draw across every bet size
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 12 outs stay at 44.96%.
The call holds at every one of the 12 sizes. 44.96% is higher than the price of even the largest bet.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +28.29 points | Call |
| third-pot | 20.00% | +24.96 points | Call |
| two-fifths-pot | 22.22% | +22.74 points | Call |
| half-pot | 25.00% | +19.96 points | Call |
| two-thirds-pot, this page | 28.57% | +16.39 points | Call |
| three-quarter-pot | 30.00% | +14.96 points | Call |
| pot-size | 33.33% | +11.63 points | Call |
| 1.25x-pot | 35.71% | +9.24 points | Call |
| 1.5x-pot | 37.50% | +7.46 points | Call |
| 2x-pot | 40.00% | +4.96 points | Call |
| 3x-pot | 42.86% | +2.10 points | Call |
| 4x-pot | 44.44% | +0.51 points | Call |
How this is computed
The chance to hit is the exact closed form, with no simulation. From the flop, 595 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 595 / 1,081, which is 44.96%.
What is held fixed: the call equals the bet, so the price is $66.67 / $233.33 = 28.57%; the pot is won whole on a hit; there is no further betting; and each of the 47 unseen cards is as likely as any other. Opponent cards are not removed.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a two-thirds-pot bet with 12 outs on the flop?
Compare 44.96%, your chance to hit by the river, with 28.57%, the equity a two-thirds-pot bet needs. The gap is +16.39 points, so this is a call. In dollars on a $100 pot, the call averages +$38.24 when no more betting follows.
How many outs do you need to call a two-thirds-pot bet on the flop?
You need at least 8 outs against a two-thirds-pot bet on the flop. That count hits 31.45% against 28.57% needed, and 7 falls short at 27.84%. With 12 you are 4 past the minimum.
When is the next-card chance the better comparison?
Both figures are right for their own situation. 44.96% fits a hand with no more betting, 25.53% fits one where the turn brings a bet, and 28.57% is the price for each, giving a call and a fold.
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