Verdict
Call
19 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come65.03%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+40.03 points
Your chance and the price
This is one of the easier spots. 19 outs on the flop reach 65.03% by the river, the half-pot bet asks for just 25.00%, and the 40.03-point margin favors the call.
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.
Putting dollars on the call
- Starting pot$100
- Size of the bet$50
- Cost to call$50
- Final pot if you call$200
- Gain on a hit$150
- What a miss costs$50
- Probability of a hit65.03%
- Expected value of a call+$80.06
- Break-even equity25.00%
- Unrounded margin+40.0324 points
- Outs that exactly reach the price6.23 outs
- Outs to spare, exactly+12.77 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 $80.06 on average: $97.55 from hits, minus $17.48 from misses, +1.601 per dollar called.
Odds say the same thing. Hitting is 0.54 : 1 against, and the pot lays 3 : 1.
Do not forget your own call. Dividing the bet by the pot without it gives 33.33%, not 25.00%, and would show a margin of +31.6990 points. The bet over the starting pot, 50.00%, is worse and would show +15.0324 points.
What could go wrong before the call flips
The call survives losing up to 12 outs. At 7 outs the chance is 27.84%, just enough for 25.00%.
Your margin is worth $123.12 in later losses. Past that, 2.46 times your call, folding would have been better.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | +40.03 points | +$80.06 | Call |
| $10 | 26.32% | +38.72 points | +$73.56 | Call |
| $25 | 28.57% | +36.46 points | +$63.81 | Call |
| $50 | 33.33% | +31.70 points | +$47.55 | Call |
| $100 | 50.00% | +15.03 points | +$15.03 | Call |
Two views of the same draw
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 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 65.03% | +40.0324 points | +$80.06 | Call |
| Next card only | 40.43% | +15.4255 points | +$30.85 | Call |
One out more or less
A few outs either way, against a half-pot bet that needs 25.00%. The chance climbs about 2.50 points with each extra out.
Bigger and smaller bets
Keep 19 outs and change only the bet. The price rises from the smallest size to the largest, and the half-pot row is marked as this page.
A draw this strong has no ceiling inside the table. 65.03% tops every price from the smallest bet to the largest.
| 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, this page | 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%.
What is held fixed: the call equals the bet, so the price is $50 / $200 = 25.00%; 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 19 outs when a half-pot bet comes on the flop?
Math says call. The half-pot bet of $50 needs 25.00% equity, 19 outs on the flop give 65.03%, and the margin is +40.03 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$80.06 on average.
How strong must a draw be to call a half-pot bet on the flop?
To call a half-pot bet on the flop you want 7 outs or more. 7 reach 27.84% and 6 reach 24.14%, with 25.00% as the bar. Your 19 outs are 12 over.
Which hit chance fits a half-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 25.00%, and both numbers agree on call.
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