Verdict
Call
12 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come44.96%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+14.96 points
Your chance and the price
This is one of the easier spots. 12 outs on the flop reach 44.96% by the river, the three-quarter-pot bet asks for just 30.00%, and the 14.96-point margin favors the call.
For a flush draw with a gutshot, 12 outs is the number to use, and one card hits 25.53% of the time out of 47 unseen.
Counting the chips on a $100 pot
- Pot before the bet$100
- Your opponent bets$75
- Chips you put in$75
- Final pot if you call$250
- You can win on a hit$175
- You lose on a miss$75
- Chance to hit by the river44.96%
- Expected value of calling+$37.40
- Equity the call needs30.00%
- Your chance minus the price, unrounded+14.9584 points
- Fractional outs at the price7.59 outs
- Outs above the price+4.41 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 $37.40 on average. The hit side averages $78.68, the miss side $41.28, and each dollar called returns +0.499.
Odds say the same thing. Hitting is 1.22 : 1 against, and the pot lays 2.33 : 1.
Skipping your own call in the pot gives a price of 42.86% where 30.00% is correct, and a margin of +2.1012 points instead of +14.96 points. The starting pot gives 75.00% and a margin of -30.0416 points, which is wrong by even more.
Slack in the call
If some outs turned out to be shared with a better hand, you could give up 4 outs and still call. The floor is 8, at 31.45%.
Think of $83.18 as your safety room: the most you can give back after a hit, 1.11 times your call, with the call still level.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +14.96 points | +$37.40 | Call |
| $10 | 31.25% | +13.71 points | +$32.90 | Call |
| $25 | 33.33% | +11.63 points | +$26.16 | Call |
| $50 | 37.50% | +7.46 points | +$14.92 | Call |
| $100 | 50.00% | -5.04 points | -$7.56 | Fold |
Next card or river
The two figures land on opposite sides, or on the line. 44.96% gives a call and 25.53% gives a fold against 30.00%, so check whether more betting is likely before you rely on the river number.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 44.96% | +14.9584 points | +$37.40 | Call |
| Next card only | 25.53% | -4.4681 points | -$11.17 | Fold |
The call as outs change
The table shows 12 outs and the draws around it on the flop, all against the same three-quarter-pot bet. Each extra out adds about 3.15 points to the chance here.
Other bet sizes for this draw
Keep 12 outs and change only the bet. The price rises from the smallest size to the largest, and the three-quarter-pot row is marked as this page.
Nothing in the list is too big to call: 12 outs reach 44.96% on the flop, above every price on the page.
| 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 | 28.57% | +16.39 points | Call |
| three-quarter-pot, this page | 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 hit chance comes straight from combinations. Out of 1,081 pairs of unseen cards, 595 miss every out, so you hit 44.96% of the time.
What is held fixed: the call equals the bet, so the price is $75 / $250 = 30.00%; 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
What is the right play with 12 outs when a three-quarter-pot bet comes on the flop?
Reduce the question to a comparison of two numbers: 44.96% to hit and 30.00% to break even. The first minus the second is +14.96 points, which makes this a call, and the call averages +$37.40 on a $100 pot if no more betting follows.
How strong must a draw be to call 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 12 outs sit 4 above it on the flop, at 44.96%.
Which chance should you compare with the price, the next card or the river?
Match the number to the betting. All-in or checked down: 44.96%. Facing another bet on the turn: 25.53%. The price is 30.00%, so the verdicts are call and fold in that order.
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