Verdict
Call
12 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come44.96%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+11.63 points
Chance against price
The price is 33.33% and your chance is 44.96%. You sit 11.63 points above the line, which is a wide gap, so you call.
Holding a flush draw with a gutshot gives you exactly 12 outs, out of 47 unseen cards. One card hits 25.53% of the time.
The $100 pot example
- Starting pot$100
- Your opponent bets$100
- Cost to call$100
- Total pot after calling$300
- What a hit wins$200
- Net loss when you miss$100
- How often you hit44.96%
- Calling is worth, on average+$34.88
- Equity needed to break even33.33%
- Unrounded margin+11.6250 points
- Outs at break-even8.53 outs
- Outs to spare, exactly+3.47 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 $34.88 on average: $89.92 in, $55.04 out, +0.349 per dollar called.
In odds, you face 1.22 : 1 against you and the pot pays 2 : 1.
One easy error is to use 50.00%, the bet over the pot before your call, as the price. The right price is 33.33%, and the mistaken margin would be -5.0416 points.
Reverse implied odds and your margin
Against this bet the draw needs 9 outs at the least. You have 3 outs more than that, so the call has some room.
Reverse implied odds are the risk here. A hit that costs you $77.57 later, 0.78 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% | +11.63 points | +$34.88 | Call |
| $10 | 34.48% | +10.48 points | +$30.38 | Call |
| $25 | 36.36% | +8.59 points | +$23.64 | Call |
| $50 | 40.00% | +4.96 points | +$12.40 | Call |
| $100 | 50.00% | -5.04 points | -$10.08 | Fold |
Which chance to use
The two views split. By the river 44.96% gives a call, but the next card alone is 25.53%, which gives a fold. Use the river figure when no more betting follows and the next-card figure when you face another bet on the turn.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 44.96% | +11.6250 points | +$34.88 | Call |
| Next card only | 25.53% | -7.8014 points | -$23.40 | Fold |
A few outs either way
Move up or down a few outs and watch the verdict. Every extra out is worth about 3.15 points on the flop, and the price stays at 33.33%.
The same draw against other bet sizes
Keep 12 outs and change only the bet. The price rises from the smallest size to the largest, and the pot-size 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 | 30.00% | +14.96 points | Call |
| pot-size, this page | 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
Everything is computed from the closed form. Pairs without an out: 595 of 1,081. The rest, 44.96%, hold at least one out.
What is held fixed: the call equals the bet, so the price is $100 / $300 = 33.33%; 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
Should you call a pot-size bet with 12 outs on the flop?
Your chance, 44.96%, set against the 33.33% price gives +11.63 points and a call. With a $100 pot, a $100 call and no more betting, the average value of the call is +$34.88.
What count of outs clears the price of a pot-size bet on the flop?
A call starts to work at 9 outs: 34.97% to hit versus 33.33% needed. One out fewer drops the chance to 31.45%. You hold 12, which is 3 more than the minimum.
Should you use the chance on the next card or by 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 33.33%, so the verdicts are call and fold in that order.
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