Verdict
Call
19 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come65.03%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+36.46 points
The price of the call
Your draw is priced at 28.57% and it arrives 65.03% of the time. A lead of 36.46 points is wide enough that the call stands even if the numbers shift a little.
A count of 19 outs is usually the sum of more than one draw. Out of 47 unseen cards, one card helps 40.43% of the time.
The $100 pot example
- Pot when the bet arrives$100
- Your opponent bets$66.67
- You call$66.67
- Pot with your call in$233.33
- What a hit wins$166.67
- Net loss when you miss$66.67
- Chance to hit by the river65.03%
- Calling is worth, on average+$85.08
- Equity needed to break even28.57%
- Margin, to four decimals+36.4609 points
- Outs that exactly reach the price7.20 outs
- Outs to spare, exactly+11.80 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 $85.08 on average. The hit side averages $108.39, the miss side $23.31, and each dollar called returns +1.276.
The same comparison in odds: the odds against hitting are 0.54 : 1, and the pot lays 2.5 : 1 on a call.
Skipping your own call in the pot gives a price of 40.00% where 28.57% is correct, and a margin of +25.0324 points instead of +36.46 points. The starting pot gives 66.67% and a margin of -1.6343 points, which is wrong by even more.
What could go wrong before the call flips
Count how many outs the call needs: 8 reach the 28.57% price, and you have 19. That leaves 11 outs of slack.
If hitting means paying off a bigger hand later, the call survives a loss of $130.82. That is 1.96 times the $66.67 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +36.46 points | +$85.08 | Call |
| $10 | 29.85% | +35.18 points | +$78.57 | Call |
| $25 | 32.00% | +33.03 points | +$68.82 | Call |
| $50 | 36.36% | +28.67 points | +$52.56 | Call |
| $100 | 50.00% | +15.03 points | +$20.04 | Call |
By the river or next card
Whether you count one card or two, the answer is a call. The river figure is 65.03%, the next-card figure is 40.43%, and both are measured against 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 65.03% | +36.4609 points | +$85.08 | Call |
| Next card only | 40.43% | +11.8541 points | +$27.66 | Call |
Counts close to yours
One out can change the answer, so the table lists the counts on either side of 19. Each out adds roughly 2.50 points against the 28.57% price.
The same draw against other bet sizes
Keep 19 outs and change only the bet. The price rises from the smallest size to the largest, and the two-thirds-pot row is marked as this page.
No bet size here outprices a 65.03% 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% | +48.37 points | Call |
| third-pot | 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, this page | 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%.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $66.67 / $233.33 = 28.57%. A hit takes the whole pot, no later betting happens, and the 47 unseen cards are all equally likely, with none removed for an opponent's cards.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Is a call correct with 19 outs against a two-thirds-pot bet on the flop?
The answer is a call, with a margin of +36.46 points. 19 outs on the flop reach 65.03%; a bet of $66.67 into $100 needs 28.57%. Win the whole pot on a hit and lose the call on a miss, and the call is worth +$85.08 on average.
How many outs make a call correct against two thirds of the pot on the flop?
8 outs is the line. At 8 the chance is 31.45%, enough for 28.57%; one fewer gives 27.84%, which is not. Your 19 outs sit 11 above it on the flop, at 65.03%.
One card or two: which number belongs next to the 28.57% price?
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 28.57%, either number leads to a call.
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