Verdict
Call
18 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come62.44%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+42.44 points
Reading the verdict
Your draw is priced at 20.00% and it arrives 62.44% of the time. A lead of 42.44 points is wide enough that the call stands even if the numbers shift a little.
Counts like 18 outs often come from a mix of draws. Of 47 unseen cards, 18 help, or 38.30% on one card.
The $100 pot example
- The pot before betting$100
- Bet$33.33
- Your call$33.33
- Final pot if you call$166.67
- What a hit wins$133.33
- You lose on a miss$33.33
- How often you hit62.44%
- Expected value of a call+$70.74
- Equity the call needs20.00%
- Margin, to four decimals+42.4422 points
- Break-even count of outs4.91 outs
- Outs above the price+13.09 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 $70.74 on average: $83.26 in, $12.52 out, +2.122 per dollar called.
The same comparison in odds: the odds against hitting are 0.6 : 1, and the pot lays 4 : 1 on a call.
Watch the pot you divide by. Leaving your call out turns 20.00% into 25.00%, and the margin into +37.4422 points. Dividing by the starting pot gives 33.33% and a margin of +29.1088 points, further from the truth.
Reverse implied odds and your margin
The fewest outs that still call a third-pot bet on the flop is 5. You hold 18, so you have 13 outs to spare before the call flips to a fold.
Think of $113.28 as your safety room: the most you can give back after a hit, 3.40 times your call, with the call still level.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +42.44 points | +$70.74 | Call |
| $10 | 21.28% | +41.17 points | +$64.49 | Call |
| $25 | 23.53% | +38.91 points | +$55.13 | Call |
| $50 | 28.57% | +33.87 points | +$39.52 | Call |
| $100 | 50.00% | +12.44 points | +$8.29 | Call |
Which chance to use
You can skip the usual debate over one card versus two, because 38.30% and 62.44% both give a call against 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 62.44% | +42.4422 points | +$70.74 | Call |
| Next card only | 38.30% | +18.2979 points | +$30.50 | Call |
One out more or less
One out can change the answer, so the table lists the counts on either side of 18. Each out adds roughly 2.59 points against the 20.00% price.
The same draw against other bet sizes
Bet size sets the price, so the verdict changes as you scan the table. The third-pot bet of this page is marked in the first column.
With 62.44% to hit, no bet on the list is too big. 18 outs call all 12 sizes on the flop.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +45.78 points | Call |
| third-pot, this page | 20.00% | +42.44 points | Call |
| two-fifths-pot | 22.22% | +40.22 points | Call |
| half-pot | 25.00% | +37.44 points | Call |
| two-thirds-pot | 28.57% | +33.87 points | Call |
| three-quarter-pot | 30.00% | +32.44 points | Call |
| pot-size | 33.33% | +29.11 points | Call |
| 1.25x-pot | 35.71% | +26.73 points | Call |
| 1.5x-pot | 37.50% | +24.94 points | Call |
| 2x-pot | 40.00% | +22.44 points | Call |
| 3x-pot | 42.86% | +19.59 points | Call |
| 4x-pot | 44.44% | +18.00 points | Call |
How this is computed
Here is how 62.44% was found. Deal every pair of the 47 unseen cards: 406 of 1,081 pairs contain no out.
The model is deliberately simple: call everything, win everything on a hit, face no more bets, deal from 47 equally likely unseen cards, and ignore an opponent's holding. With the price at $33.33 / $166.67 = 20.00%, later streets and shared outs are what change the real answer.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Call or fold with 18 outs on the flop against a bet of a third of the pot?
Compare 62.44%, your chance to hit by the river, with 20.00%, the equity a third-pot bet needs. The gap is +42.44 points, so this is a call. In dollars on a $100 pot, the call averages +$70.74 when no more betting follows.
How many outs make a call correct against a third of the pot on the flop?
The fewest outs that call a third-pot bet on the flop is 5. With 5 outs you hit 20.35%, which reaches the 20.00% price, while 4 outs hit only 16.47%. You have 18, so you are 13 above that count.
Which hit chance fits a third-pot bet on the flop?
Pick the number that matches the street plan: 62.44% for seeing both cards for one bet, 38.30% for paying card by card. Both face 20.00%, and the verdict is call either way.
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