Verdict
Call
18 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come62.44%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+29.11 points
What the numbers say
Pay the pot-size bet and you get a better deal than the draw needs. You need 33.33%, you have 62.44%, and the 29.11-point difference is large.
You will reach 18 outs by adding up separate draws. With 47 cards unseen, the next card helps 38.30% of the time.
The same spot in dollars
- The pot before betting$100
- The bet$100
- Your call$100
- Total pot after calling$300
- Net gain when you hit$200
- You lose on a miss$100
- Your chance to hit62.44%
- Average value of the call+$87.33
- Equity needed to break even33.33%
- Unrounded margin+29.1088 points
- Outs at break-even8.53 outs
- Outs to spare, exactly+9.47 outs
Assume the whole pot goes to you when you hit, the call is lost when you miss, and nothing more is bet. Calling then gains $87.33 on average: $124.88 from hits, minus $37.56 from misses, +0.873 per dollar called.
Written as odds, the pot lays 2 : 1 while the draw is 0.6 : 1 against.
Watch the pot you divide by. Leaving your call out turns 33.33% into 50.00%, and the margin into +12.4422 points.
What could go wrong before the call flips
Against this bet the draw needs 9 outs at the least. You have 9 outs more than that, so the call has some room.
Think of $139.85 as your safety room: the most you can give back after a hit, 1.40 times your call, with the call still level.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | +29.11 points | +$87.33 | Call |
| $10 | 34.48% | +27.96 points | +$81.08 | Call |
| $25 | 36.36% | +26.08 points | +$71.72 | Call |
| $50 | 40.00% | +22.44 points | +$56.11 | Call |
| $100 | 50.00% | +12.44 points | +$24.88 | Call |
Which chance to use
One card or two, the call comes out the same way. 38.30% on the next card and 62.44% by the river both sit on the call side of 33.33%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 62.44% | +29.1088 points | +$87.33 | Call |
| Next card only | 38.30% | +4.9645 points | +$14.89 | Call |
Nearby draws
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 33.33% price.
How bet size moves the answer
Keep 18 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.
No bet size here outprices a 62.44% chance. The call works at all 12 sizes, since the highest price is 44.44%.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +45.78 points | Call |
| third-pot | 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, this page | 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
Everything is computed from the closed form. Pairs without an out: 406 of 1,081. The rest, 62.44%, 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
What is the right play with 18 outs when a pot-size bet comes on the flop?
Reduce the question to a comparison of two numbers: 62.44% to hit and 33.33% to break even. The first minus the second is +29.11 points, which makes this a call, and the call averages +$87.33 on a $100 pot if no more betting follows.
How strong must a draw be to call a pot-size bet on the flop?
Against 33.33%, the first count that works on the flop is 9, at 34.97%. At 8 the chance is 31.45%, too low. Compared with that threshold, your 18 outs are 9 above.
Which chance should you compare with the price, the next card or the river?
Use the by-the-river chance, 62.44%, when no more betting follows, and the next-card chance, 38.30%, when you must pay again on the turn. Against the 33.33% price both give a call, so the choice does not change the play here.
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