Verdict
Fold
13 outs, turn, three-quarter-pot bet
- Chance to hit by the riverone card to come28.26%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price-1.74 points
Your chance and the price
You sit 1.74 points below break-even: 28.26% to hit, 30.00% to call. A small amount of implied value would be enough to change the answer.
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.
The $100 pot example
- Starting pot$100
- Size of the bet$75
- Cost to call$75
- Pot after your call$250
- Net gain when you hit$175
- What a miss costs$75
- Your chance to hit28.26%
- Calling is worth, on average-$4.35
- Equity the call needs30.00%
- Exact margin over the price-1.7391 points
- Outs that exactly reach the price13.80 outs
- Outs above the price-0.80 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling loses $4.35 on average. Hits add $49.46 on average and misses cost $53.80 on average, or -0.058 per dollar called.
The same comparison in odds: the odds against hitting are 2.54 : 1, and the pot lays 2.33 : 1 on a call.
Counting the pot without your call makes the price look like 42.86%, when the real price is 30.00%. On that mistaken price the margin would read -14.5963 points; on 75.00%, the bet over the starting pot, it would read -46.7391 points.
Closing the gap with future bets
To make the call break even you would need to win another $15.38 after you hit, which is 0.21 times your call. Anything above that makes the call a good one.
Reaching 30.00% takes 14 outs on the turn, which hit 30.43%. With 13, the distance is 1 out.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | -1.74 points | -$4.35 | Fold |
| $50 | 25.00% | +3.26 points | +$9.78 | Call |
| $100 | 21.43% | +6.83 points | +$23.91 | Call |
| $250 | 15.00% | +13.26 points | +$66.30 | Call |
| $500 | 10.00% | +18.26 points | +$136.96 | Call |
One card to come instead of two
Compare the streets. With two cards left, 13 outs hit 48.10% (a call); with one card left they hit 28.26% (a fold). The difference is 19.84 points.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 48.10% | +18.1036 points | +$45.26 | Call |
| Turn, one card to come | 28.26% | -1.7391 points | -$4.35 | Fold |
How the answer moves with outs
Here are the neighbors of 13 outs, priced against the same 30.00%. One more out lifts your chance by about 2.17 points.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 11 outs | 23.91% | -6.09 points | Fold |
| 12 outs | 26.09% | -3.91 points | Fold |
| 13 outs, this page | 28.26% | -1.74 points | Fold |
| 14 outs | 30.43% | +0.43 points | Call |
| 15 outs | 32.61% | +2.61 points | Call |
The same draw against other bet sizes
The same 13 outs on the turn meet a different price at each bet size. The table runs from the smallest bet to the largest, and the row for this page is marked.
The ceiling for a call is a bet of 0.65 times the pot ($65 on a $100 pot). 4 out of 12 sizes sit under it on the turn.
| 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 | 28.57% | -0.31 points | Fold |
| three-quarter-pot, this page | 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
The hit chance comes straight from combinations. With one card left and 13 outs in 46 cards, you hit 28.26% of the time.
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
Call or fold with 13 outs on the turn against a bet of three quarters of the pot?
The verdict is fold. Your chance is 28.26% and the price is 30.00%, which leaves -1.74 points. On a $100 pot with a $75 bet, calling is worth -$4.35 on average if the whole pot is won on a hit and nothing more is bet.
How many outs do you need to call a three-quarter-pot bet on the turn?
14 outs is the line. At 14 the chance is 30.43%, enough for 30.00%; one fewer gives 28.26%, which is not. Your 13 outs sit 1 below it on the turn, at 28.26%.
Does it matter whether you count one card or two against a three-quarter-pot bet?
There is no difference on the turn, because one card remains. Use 28.26% and compare it with 30.00%: the margin is -1.74 points, a fold, whichever way you phrase the question.
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