Verdict
Call
19 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come65.03%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+45.03 points
Chance against price
Your draw is priced at 20.00% and it arrives 65.03% of the time. A lead of 45.03 points is wide enough that the call stands even if the numbers shift a little.
No single everyday draw has exactly 19 outs, so a count like this usually combines draws. One card from the 47 unseen helps 40.43% of the time.
Worked through on a $100 pot
- Pot when the bet arrives$100
- Size of the bet$33.33
- Your call$33.33
- Pot after your call$166.67
- You can win on a hit$133.33
- You lose on a miss$33.33
- Probability of a hit65.03%
- Expected value of a call+$75.05
- Price of the call20.00%
- Your chance minus the price, unrounded+45.0324 points
- Break-even count of outs4.91 outs
- Outs above the price+14.09 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 $75.05 on average: $86.71 in, $11.66 out, +2.252 per dollar called.
Odds say the same thing. Hitting is 0.54 : 1 against, and the pot lays 4 : 1.
Skipping your own call in the pot gives a price of 25.00% where 20.00% is correct, and a margin of +40.0324 points instead of +45.03 points. The starting pot gives 33.33% and a margin of +31.6990 points, which is wrong by even more.
Reverse implied odds and your margin
The call survives losing up to 14 outs. At 5 outs the chance is 20.35%, just enough for 20.00%.
Break-even on later streets sits at $115.41 given back, or 3.46 times your call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +45.03 points | +$75.05 | Call |
| $10 | 21.28% | +43.76 points | +$68.55 | Call |
| $25 | 23.53% | +41.50 points | +$58.80 | Call |
| $50 | 28.57% | +36.46 points | +$42.54 | Call |
| $100 | 50.00% | +15.03 points | +$10.02 | Call |
By the river or next card
You can skip the usual debate over one card versus two, because 40.43% and 65.03% both give a call against 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 65.03% | +45.0324 points | +$75.05 | Call |
| Next card only | 40.43% | +20.4255 points | +$34.04 | Call |
Counts close to yours
How fast does the margin move? About 2.50 points per out on the flop. The rows below keep the third-pot bet fixed and change only the outs.
The draw across every bet size
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 19 outs on the flop.
With 65.03% to hit, no bet on the list is too big. 19 outs call all 12 sizes on the flop.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +48.37 points | Call |
| third-pot, this page | 20.00% | +45.03 points | Call |
| two-fifths-pot | 22.22% | +42.81 points | Call |
| half-pot | 25.00% | +40.03 points | Call |
| two-thirds-pot | 28.57% | +36.46 points | Call |
| three-quarter-pot | 30.00% | +35.03 points | Call |
| pot-size | 33.33% | +31.70 points | Call |
| 1.25x-pot | 35.71% | +29.32 points | Call |
| 1.5x-pot | 37.50% | +27.53 points | Call |
| 2x-pot | 40.00% | +25.03 points | Call |
| 3x-pot | 42.86% | +22.18 points | Call |
| 4x-pot | 44.44% | +20.59 points | Call |
How this is computed
Counting is exact: the pairs of unseen cards with no out number 378 out of 1,081, so hitting by the river has chance 65.03%.
Four assumptions sit behind the verdict: you call the full bet, a hit wins the entire pot, no money goes in after the call, and every one of the 47 unseen cards is equally likely. The price is $33.33 / $166.67 = 20.00%. No card is taken out for what an opponent might hold.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How should you respond to a third-pot bet on the flop when you hold 19 outs?
By the numbers it is a call. 19 outs on the flop hit 65.03% by the river, a third-pot bet needs 20.00%, and the margin is +45.03 points. That assumes you call the full $33.33 and no more betting follows, and it values the call at +$75.05 per $100 pot.
How many outs make a call correct against a third of the pot on the flop?
The threshold is 5 outs. It gives 20.35%, clearing 20.00%, whereas 4 gives only 16.47%. Holding 19 puts you 14 above it, with a chance of 65.03%.
Which chance should you compare with the price, the next card or the river?
Count two cards, 65.03%, when the bet is the last money going in, and one card, 40.43%, when the next street brings another bet. At a price of 20.00%, either number leads to a call.
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