Verdict
Fold
1 out, turn, two-thirds-pot bet
- Chance to hit by the riverone card to come2.17%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-26.40 points
Reading the verdict
2.17% against 28.57%: the draw trails the price by 26.40 points. On this turn against a two-thirds-pot bet, that is an easy fold.
Holding a single out means one card in the deck helps you. Out of 46 unseen cards it arrives 2.17% of the time on one card.
Putting dollars on the call
- The pot before betting$100
- Bet$66.67
- Your call$66.67
- Pot after your call$233.33
- You can win on a hit$166.67
- Net loss when you miss$66.67
- Probability of a hit2.17%
- Expected value of a call-$61.59
- Price of the call28.57%
- Margin, to four decimals-26.3975 points
- Outs that exactly reach the price13.14 outs
- Your outs minus break-even outs-12.14 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call loses $61.59 on average. The hit side averages $3.62, the miss side $65.22, and each dollar called returns -0.924.
Written as odds, the pot lays 2.5 : 1 while the draw is 45 : 1 against.
Counting the pot without your call makes the price look like 40.00%, when the real price is 28.57%. On that mistaken price the margin would read -37.8261 points; on 66.67%, the bet over the starting pot, it would read -64.4928 points.
When later betting could rescue the call
The shortfall in dollars is $2,833.33: the amount a hit would have to win later for 2.17% to be enough. It equals 42.50 times your $66.67 call.
The smallest count that pays for a two-thirds-pot bet is 14 outs at 30.43%. You hold 1, which is 13 outs fewer.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -26.40 points | -$61.59 | Fold |
| $50 | 23.53% | -21.36 points | -$60.51 | Fold |
| $100 | 20.00% | -17.83 points | -$59.42 | Fold |
| $250 | 13.79% | -11.62 points | -$56.16 | Fold |
| $500 | 9.09% | -6.92 points | -$50.72 | Fold |
Flop and turn compared
On the turn only one card is left, so the chance by the river and the chance on the next card are the same 2.17%. Back on the flop, the same 1 out hits 4.26%, 2.08 points more, and that would have been a fold.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 4.26% | -24.3161 points | -$56.74 | Fold |
| Turn, one card to come | 2.17% | -26.3975 points | -$61.59 | Fold |
Draws around this one
One out can change the answer, so the table lists the counts just above 1. Each out moves the chance roughly 2.17 points against the 28.57% price.
How bet size moves the answer
Look down the margin column to see where the draw stops paying. Every row uses 1 out on the turn and a bet of a different size.
With 2.17% to hit, you can call a bet up to 0.02 times the pot ($2.27 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% | -14.49 points | Fold |
| third-pot | 20.00% | -17.83 points | Fold |
| two-fifths-pot | 22.22% | -20.05 points | Fold |
| half-pot | 25.00% | -22.83 points | Fold |
| two-thirds-pot, this page | 28.57% | -26.40 points | Fold |
| three-quarter-pot | 30.00% | -27.83 points | Fold |
| pot-size | 33.33% | -31.16 points | Fold |
| 1.25x-pot | 35.71% | -33.54 points | Fold |
| 1.5x-pot | 37.50% | -35.33 points | Fold |
| 2x-pot | 40.00% | -37.83 points | Fold |
| 3x-pot | 42.86% | -40.68 points | Fold |
| 4x-pot | 44.44% | -42.27 points | Fold |
Pages that use the same math
How this is computed
No sampling is involved. On the turn there are 46 unseen cards and 1 out among them, which gives 1 / 46 = 2.17%.
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 1 out on the turn worth a call against a bet of two thirds of the pot?
Math says fold. The two-thirds-pot bet of $66.67 needs 28.57% equity, 1 out on the turn gives 2.17%, and the margin is -26.40 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$61.59 on average.
What is the minimum number of outs for a two-thirds-pot bet on the turn?
The threshold is 14 outs. It gives 30.43%, clearing 28.57%, whereas 13 gives only 28.26%. Holding 1 puts you 13 below it, with a chance of 2.17%.
How many cards should you count when a two-thirds-pot bet arrives on the turn?
They are one number here. With a single card to come, 2.17% is both the next-card chance and the by-the-river chance, and it gives a fold against 28.57%, a margin of -26.40 points.
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