Verdict
Fold
5 outs, turn, three-quarter-pot bet
- Chance to hit by the riverone card to come10.87%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price-19.13 points
The call in numbers
The price is 30.00% and your chance is 10.87%. You sit 19.13 points below the line, which is a wide gap, so you fold.
You will reach 5 outs by adding up separate draws. With 46 cards unseen, the next card helps 10.87% of the time.
One hand, in dollars
- Starting pot$100
- Your opponent bets$75
- You call$75
- Final pot if you call$250
- What a hit wins$175
- Net loss when you miss$75
- How often you hit10.87%
- Average value of the call-$47.83
- Equity needed to break even30.00%
- Exact margin over the price-19.1304 points
- Fractional outs at the price13.80 outs
- Margin measured in outs-8.80 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $19.02 in and $66.85 out, so calling loses $47.83 on average at -0.638 per dollar called.
Read as odds: 8.2 : 1 against you, 2.33 : 1 from the pot.
One easy error is to use 42.86%, the bet over the pot before your call, as the price. The right price is 30.00%, and the mistaken margin would be -31.9876 points. The bet over the starting pot, 75.00%, would claim -64.1304 points.
When later betting could rescue the call
To make the call break even you would need to win another $440 after you hit, which is 5.87 times your call. Anything above that makes the call a good one.
Count the outs the call needs: 14 reach the 30.00% price, giving 30.43%. You have 5, so you are 9 outs short.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | -19.13 points | -$47.83 | Fold |
| $50 | 25.00% | -14.13 points | -$42.39 | Fold |
| $100 | 21.43% | -10.56 points | -$36.96 | Fold |
| $250 | 15.00% | -4.13 points | -$20.65 | Fold |
| $500 | 10.00% | +0.87 points | +$6.52 | Call |
Flop and turn compared
One street later the draw is weaker. The same 5 outs hit 20.35% from the flop and 10.87% from the turn, a drop of 9.48 points, and the verdict on the flop would have been a fold.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 20.35% | -9.6485 points | -$24.12 | Fold |
| Turn, one card to come | 10.87% | -19.1304 points | -$47.83 | Fold |
Draws around this one
One out can change the answer, so the table lists the counts on either side of 5. Each out adds roughly 2.17 points against the 30.00% price.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 3 outs | 6.52% | -23.48 points | Fold |
| 4 outs | 8.70% | -21.30 points | Fold |
| 5 outs, this page | 10.87% | -19.13 points | Fold |
| 6 outs | 13.04% | -16.96 points | Fold |
| 7 outs | 15.22% | -14.78 points | Fold |
The same draw against other bet sizes
Your 10.87% chance is fixed, so the only thing that moves is the price. The 12 rows below price the call at every bet size on the turn.
With 10.87% to hit, you can call a bet up to 0.14 times the pot ($13.89 on a $100 pot) and no more, which is smaller than every size listed. All 12 rows are folds.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -5.80 points | Fold |
| third-pot | 20.00% | -9.13 points | Fold |
| two-fifths-pot | 22.22% | -11.35 points | Fold |
| half-pot | 25.00% | -14.13 points | Fold |
| two-thirds-pot | 28.57% | -17.70 points | Fold |
| three-quarter-pot, this page | 30.00% | -19.13 points | Fold |
| pot-size | 33.33% | -22.46 points | Fold |
| 1.25x-pot | 35.71% | -24.84 points | Fold |
| 1.5x-pot | 37.50% | -26.63 points | Fold |
| 2x-pot | 40.00% | -29.13 points | Fold |
| 3x-pot | 42.86% | -31.99 points | Fold |
| 4x-pot | 44.44% | -33.57 points | Fold |
How this is computed
Everything is computed from the closed form. The river chance is 5 outs over 46 unseen cards, 10.87%.
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 46 unseen cards is equally likely. The price is $75 / $250 = 30.00%. No card is taken out for what an opponent might hold.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Are 5 outs on the turn worth a call against a bet of three quarters of the pot?
Compare 10.87%, your chance to hit by the river, with 30.00%, the equity a three-quarter-pot bet needs. The gap is -19.13 points, so this is a fold. In dollars on a $100 pot, the call averages -$47.83 when no more betting follows.
How strong must a draw be to call a three-quarter-pot bet on the turn?
Against 30.00%, the first count that works on the turn is 14, at 30.43%. At 13 the chance is 28.26%, too low. Compared with that threshold, your 5 outs are 9 below.
How many cards should you count when a three-quarter-pot bet arrives on the turn?
One card left means one chance: 10.87%. Set it beside the 30.00% price and you get -19.13 points, which is a fold. There is no second figure to weigh against it.
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