Verdict
Call
19 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come65.03%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+35.03 points
How the verdict is reached
The price is 30.00% and your chance is 65.03%. You sit 35.03 points above the line, which is a wide gap, so you call.
Think of 19 outs as a running total of every card that improves you. 19 of the 47 unseen cards qualify, which is 40.43% on one card.
A $100 pot, step by step
- The pot before betting$100
- The bet$75
- Your call$75
- Pot after your call$250
- Net gain when you hit$175
- What a miss costs$75
- Your chance to hit65.03%
- Expected value of a call+$87.58
- Equity the call needs30.00%
- Unrounded margin+35.0324 points
- Outs that exactly reach the price7.59 outs
- Outs to spare, exactly+11.41 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $113.81, the average loss is $26.23, and calling gains $87.58 on average, or +1.168 per dollar called.
Read as odds: 0.54 : 1 against you, 2.33 : 1 from the pot.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 42.86% instead of 30.00% and would put your margin at +22.1752 points. Using the bet over the starting pot, 75.00%, is further off and would put it at -9.9676 points.
Slack in the call
If some outs turned out to be shared with a better hand, you could give up 11 outs and still call. The floor is 8, at 31.45%.
Break-even on later streets sits at $134.67 given back, or 1.80 times your call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +35.03 points | +$87.58 | Call |
| $10 | 31.25% | +33.78 points | +$81.08 | Call |
| $25 | 33.33% | +31.70 points | +$71.32 | Call |
| $50 | 37.50% | +27.53 points | +$55.06 | Call |
| $100 | 50.00% | +15.03 points | +$22.55 | Call |
One card or two
Both views point the same way. By the river you hit 65.03%, on the next card 40.43%, and the price is 30.00%, so the call holds whichever number applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 65.03% | +35.0324 points | +$87.58 | Call |
| Next card only | 40.43% | +10.4255 points | +$26.06 | Call |
Neighbors of this draw
The table shows 19 outs and the draws around it on the flop, all against the same three-quarter-pot bet. Each extra out adds about 2.50 points to the chance here.
Other bet sizes for this draw
Bet size sets the price, so the verdict changes as you scan the table. The three-quarter-pot bet of this page is marked in the first column.
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 | 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, this page | 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
Everything is computed from the closed form. Pairs without an out: 378 of 1,081. The rest, 65.03%, hold at least one out.
The numbers are a baseline rather than a prediction for one hand. The price is 30.00%, from $75 into $250, and the chance assumes a whole pot won on a hit, no more betting, 47 equally likely unseen cards, and no cards removed for the other player.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Are 19 outs on the flop worth a call against a bet of three quarters of the pot?
Compare 65.03%, your chance to hit by the river, with 30.00%, the equity a three-quarter-pot bet needs. The gap is +35.03 points, so this is a call. In dollars on a $100 pot, the call averages +$87.58 when no more betting follows.
What is the fewest outs that can call a three-quarter-pot bet on the flop?
You need at least 8 outs against a three-quarter-pot bet on the flop. That count hits 31.45% against 30.00% needed, and 7 falls short at 27.84%. With 19 you are 11 past the minimum.
Which hit chance fits a three-quarter-pot bet on the flop?
Match the number to the betting: 65.03% if all-in or checked down, 40.43% if you face another bet on the turn. The price is 30.00%, and both numbers agree on call.
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