Verdict
Fold
13 outs, turn, two-thirds-pot bet
- Chance to hit by the riverone card to come28.26%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-0.31 points
Chance against price
By the numbers this is a fold, but only barely. 0.31 points is all that separates your 28.26% from the 28.57% you need.
Few single draws land on exactly 13 outs, so add up each way to improve and check the total. One card hits 28.26% of the time here.
One hand, in dollars
- Starting pot$100
- Size of the bet$66.67
- Your call$66.67
- Pot with your call in$233.33
- What a hit wins$166.67
- What a miss costs$66.67
- Chance to hit by the river28.26%
- Calling is worth, on average-$0.72
- Price of the call28.57%
- Your chance minus the price, unrounded-0.3106 points
- Fractional outs at the price13.14 outs
- Outs to spare, exactly-0.14 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling loses $0.72 on average. The hit side averages $47.10, the miss side $47.83, and each dollar called returns -0.011.
Odds say the same thing. Hitting is 2.54 : 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 -11.7391 points. Using the bet over the starting pot, 66.67%, is further off and would put it at -38.4058 points.
Closing the gap with future bets
Implied odds are the way to close the gap. You need $2.56 more on later streets after hitting, which is 0.04 times the call you make.
Count the outs the call needs: 14 reach the 28.57% price, giving 30.43%. You have 13, so you are 1 out short.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -0.31 points | -$0.72 | Fold |
| $50 | 23.53% | +4.73 points | +$13.41 | Call |
| $100 | 20.00% | +8.26 points | +$27.54 | Call |
| $250 | 13.79% | +14.47 points | +$69.93 | Call |
| $500 | 9.09% | +19.17 points | +$140.58 | Call |
The cost of waiting a street
Waiting a street costs 19.84 points. The flop gives 13 outs two chances to hit, 48.10%, and a call against 28.57%; the turn gives one, 28.26%.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 48.10% | +19.5322 points | +$45.58 | Call |
| Turn, one card to come | 28.26% | -0.3106 points | -$0.72 | Fold |
A few outs either way
A few outs either way, against a two-thirds-pot bet that needs 28.57%. The chance climbs about 2.17 points with each extra out.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 11 outs | 23.91% | -4.66 points | Fold |
| 12 outs | 26.09% | -2.48 points | Fold |
| 13 outs, this page | 28.26% | -0.31 points | Fold |
| 14 outs | 30.43% | +1.86 points | Call |
| 15 outs | 32.61% | +4.04 points | Call |
The same draw against other bet sizes
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.
Your draw can face a bet of up to 0.65 times the pot ($65 on a $100 pot) and still break even. 4 of the 12 sizes fall at or under that line.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +11.59 points | Call |
| third-pot | 20.00% | +8.26 points | Call |
| two-fifths-pot | 22.22% | +6.04 points | Call |
| half-pot | 25.00% | +3.26 points | Call |
| two-thirds-pot, this page | 28.57% | -0.31 points | Fold |
| three-quarter-pot | 30.00% | -1.74 points | Fold |
| pot-size | 33.33% | -5.07 points | Fold |
| 1.25x-pot | 35.71% | -7.45 points | Fold |
| 1.5x-pot | 37.50% | -9.24 points | Fold |
| 2x-pot | 40.00% | -11.74 points | Fold |
| 3x-pot | 42.86% | -14.60 points | Fold |
| 4x-pot | 44.44% | -16.18 points | Fold |
How this is computed
Counting is exact: one card is left, 13 of 46 unseen cards help, and the chance is 28.26%.
The price is call / (pot + bet + call), here $66.67 / $233.33 = 28.57%, and the margin is your chance minus it. The page assumes you call the whole bet, win the whole pot whenever you hit, and see no more betting. All 46 unseen cards are equally likely and none is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against one hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a two-thirds-pot bet with 13 outs on the turn?
Reduce the question to a comparison of two numbers: 28.26% to hit and 28.57% to break even. The first minus the second is -0.31 points, which makes this a fold, and the call averages -$0.72 on a $100 pot if no more betting follows.
What count of outs clears the price of a two-thirds-pot bet on the turn?
A call starts to work at 14 outs: 30.43% to hit versus 28.57% needed. One out fewer drops the chance to 28.26%. You hold 13, which is 1 fewer than the minimum.
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, 28.26% is both the next-card chance and the by-the-river chance, and it gives a fold against 28.57%, a margin of -0.31 points.
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