Verdict
Call
13 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come48.10%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+19.53 points
What the numbers say
Your draw is priced at 28.57% and it arrives 48.10% of the time. A lead of 19.53 points is wide enough that the call stands even if the numbers shift a little.
13 out of 47 unseen cards is a combined count rather than one named draw, and one card hits 27.66% of the time.
A $100 pot, step by step
- Starting pot$100
- Bet$66.67
- You call$66.67
- Total pot after calling$233.33
- Gain on a hit$166.67
- Loss on a miss$66.67
- Chance to hit by the river48.10%
- Expected value of calling+$45.58
- Price of the call28.57%
- Your chance minus the price, unrounded+19.5322 points
- Outs that exactly reach the price7.20 outs
- Margin measured in outs+5.80 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling gains $45.58 on average. Hits bring in $80.17, misses cost $34.60, and the ratio is +0.684 per dollar called.
Read as odds: 1.08 : 1 against you, 2.5 : 1 from the pot.
Do not forget your own call. Dividing the bet by the pot without it gives 40.00%, not 28.57%, and would show a margin of +8.1036 points. The bet over the starting pot, 66.67%, is worse and would show -18.5631 points.
Where the call would flip
The fewest outs that still call a two-thirds-pot bet on the flop is 8. You hold 13, so you have 5 outs to spare before the call flips to a fold.
Your margin is worth $94.74 in later losses. Past that, 1.42 times your call, folding would have been better.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +19.53 points | +$45.58 | Call |
| $10 | 29.85% | +18.25 points | +$40.76 | Call |
| $25 | 32.00% | +16.10 points | +$33.55 | Call |
| $50 | 36.36% | +11.74 points | +$21.52 | Call |
| $100 | 50.00% | -1.90 points | -$2.53 | Fold |
Two views of the same draw
Here the cards to come matter. Two cards reach 48.10% and point to a call; one card reaches 27.66% and points to a fold. Which one applies depends on whether the turn brings another bet.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 48.10% | +19.5322 points | +$45.58 | Call |
| Next card only | 27.66% | -0.9119 points | -$2.13 | Fold |
Counts close to yours
One out can change the answer, so the table lists the counts on either side of 13. Each out adds roughly 3.05 points against the 28.57% price.
How bet size moves the answer
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 13 outs stay at 48.10%.
Your 48.10% chance tops every price in the table, so every bet size is a call: the largest price, 44.44%, is still below it.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +31.44 points | Call |
| third-pot | 20.00% | +28.10 points | Call |
| two-fifths-pot | 22.22% | +25.88 points | Call |
| half-pot | 25.00% | +23.10 points | Call |
| two-thirds-pot, this page | 28.57% | +19.53 points | Call |
| three-quarter-pot | 30.00% | +18.10 points | Call |
| pot-size | 33.33% | +14.77 points | Call |
| 1.25x-pot | 35.71% | +12.39 points | Call |
| 1.5x-pot | 37.50% | +10.60 points | Call |
| 2x-pot | 40.00% | +8.10 points | Call |
| 3x-pot | 42.86% | +5.25 points | Call |
| 4x-pot | 44.44% | +3.66 points | Call |
How this is computed
Counting is exact: the pairs of unseen cards with no out number 561 out of 1,081, so hitting by the river has chance 48.10%.
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 47 unseen cards is equally likely. The price is $66.67 / $233.33 = 28.57%. No card is taken out for what an opponent might hold.
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 flop?
The answer is a call, with a margin of +19.53 points. 13 outs on the flop reach 48.10%; a bet of $66.67 into $100 needs 28.57%. Win the whole pot on a hit and lose the call on a miss, and the call is worth +$45.58 on average.
How many outs are enough to continue against a bet of two thirds of the pot on the flop?
A call starts to work at 8 outs: 31.45% to hit versus 28.57% needed. One out fewer drops the chance to 27.84%. You hold 13, which is 5 more than the minimum.
Which hit chance fits a two-thirds-pot bet on the flop?
Both figures are right for their own situation. 48.10% fits a hand with no more betting, 27.66% fits one where the turn brings a bet, and 28.57% is the price for each, giving a call and a fold.
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