Verdict
Fold
4 outs, turn, two-thirds-pot bet
- Chance to hit by the riverone card to come8.70%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-19.88 points
Chance against price
Pay the two-thirds-pot bet and you pay more than the draw is worth. You need 28.57%, you have 8.70%, and the 19.88-point shortfall is large.
For a gutshot straight draw, 4 outs is the number to use, and one card hits 8.70% of the time out of 46 unseen.
The arithmetic of this call
- The pot before betting$100
- The bet$66.67
- You call$66.67
- Final pot if you call$233.33
- Gain on a hit$166.67
- What a miss costs$66.67
- Your chance to hit8.70%
- Expected value of a call-$46.38
- Break-even equity28.57%
- Your chance minus the price, unrounded-19.8758 points
- Outs at break-even13.14 outs
- Margin measured in outs-9.14 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call loses $46.38 on average. The hit side averages $14.49, the miss side $60.87, and each dollar called returns -0.696.
Odds say the same thing. Hitting is 10.5 : 1 against, and the pot lays 2.5 : 1.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 40.00% instead of 28.57% and would put your margin at -31.3043 points. Using the bet over the starting pot, 66.67%, is further off and would put it at -57.9710 points.
The extra winnings a call would need
With 8.70% to hit, break-even sits $533.33 higher than the pot shows. Put another way, later bets must add 8.00 times your call.
14 outs is the threshold against a two-thirds-pot bet on the turn, a chance of 30.43%. That is 10 more than your 4.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -19.88 points | -$46.38 | Fold |
| $50 | 23.53% | -14.83 points | -$42.03 | Fold |
| $100 | 20.00% | -11.30 points | -$37.68 | Fold |
| $250 | 13.79% | -5.10 points | -$24.64 | Fold |
| $500 | 9.09% | -0.40 points | -$2.90 | Fold |
The cost of waiting a street
Compare the streets. With two cards left, 4 outs hit 16.47% (a fold); with one card left they hit 8.70% (a fold). The difference is 7.77 points.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 16.47% | -12.1052 points | -$28.25 | Fold |
| Turn, one card to come | 8.70% | -19.8758 points | -$46.38 | Fold |
A few outs either way
Same bet, same street, different draws. The row for 4 outs is marked, and every out is worth about 2.17 points.
Bigger and smaller bets
Bet size sets the price, so the verdict changes as you scan the table. The two-thirds-pot bet of this page is marked in the first column.
Even the smallest bet on the list outprices 4 outs on the turn. The break-even bet is 0.11 times the pot ($10.53 on a $100 pot), and every one of the 12 sizes is above it.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -7.97 points | Fold |
| third-pot | 20.00% | -11.30 points | Fold |
| two-fifths-pot | 22.22% | -13.53 points | Fold |
| half-pot | 25.00% | -16.30 points | Fold |
| two-thirds-pot, this page | 28.57% | -19.88 points | Fold |
| three-quarter-pot | 30.00% | -21.30 points | Fold |
| pot-size | 33.33% | -24.64 points | Fold |
| 1.25x-pot | 35.71% | -27.02 points | Fold |
| 1.5x-pot | 37.50% | -28.80 points | Fold |
| 2x-pot | 40.00% | -31.30 points | Fold |
| 3x-pot | 42.86% | -34.16 points | Fold |
| 4x-pot | 44.44% | -35.75 points | Fold |
How this is computed
The hit chance comes straight from combinations. With one card left and 4 outs in 46 cards, you hit 8.70% of the time.
What is held fixed: the call equals the bet, so the price is $66.67 / $233.33 = 28.57%; the pot is won whole on a hit; there is no further betting; and each of the 46 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
Is a call correct with 4 outs against a two-thirds-pot bet on the turn?
Compare 8.70%, your chance to hit by the river, with 28.57%, the equity a two-thirds-pot bet needs. The gap is -19.88 points, so this is a fold. In dollars on a $100 pot, the call averages -$46.38 when no more betting follows.
How strong must a draw be to call a two-thirds-pot bet on the turn?
The fewest outs that call a two-thirds-pot bet on the turn is 14. With 14 outs you hit 30.43%, which reaches the 28.57% price, while 13 outs hit only 28.26%. You have 4, so you are 10 below that count.
One card or two: which number belongs next to the 28.57% price?
Count the river card only. 8.70% is the full chance and the price is 28.57%, so the verdict is fold with a gap of 19.88 points. Nothing else is left to come.
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