Verdict
Call
13 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come48.10%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+14.77 points
The call in numbers
This is one of the easier spots. 13 outs on the flop reach 48.10% by the river, the pot-size bet asks for just 33.33%, and the 14.77-point margin favors the call.
A count of 13 outs is usually the sum of more than one draw. Out of 47 unseen cards, one card helps 27.66% of the time.
The same spot in dollars
- Pot when the bet arrives$100
- Size of the bet$100
- Chips you put in$100
- Pot with your call in$300
- You can win on a hit$200
- What a miss costs$100
- Your chance to hit48.10%
- Average value of the call+$44.31
- Equity the call needs33.33%
- Your chance minus the price, unrounded+14.7703 points
- Fractional outs at the price8.53 outs
- Outs to spare, exactly+4.47 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 $44.31 on average. Hits bring in $96.21, misses cost $51.90, and the ratio is +0.443 per dollar called.
The same comparison in odds: the odds against hitting are 1.08 : 1, and the pot lays 2 : 1 on a call.
Skipping your own call in the pot gives a price of 50.00% where 33.33% is correct, and a margin of -1.8964 points instead of +14.77 points.
Reverse implied odds and your margin
The call survives losing up to 4 outs. At 9 outs the chance is 34.97%, just enough for 33.33%.
Reverse implied odds are the risk here. A hit that costs you $92.12 later, 0.92 times your call, is where the call stops being worth it.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | +14.77 points | +$44.31 | Call |
| $10 | 34.48% | +13.62 points | +$39.50 | Call |
| $25 | 36.36% | +11.74 points | +$32.28 | Call |
| $50 | 40.00% | +8.10 points | +$20.26 | Call |
| $100 | 50.00% | -1.90 points | -$3.79 | Fold |
Next card or river
Do not mix up the two chances. 48.10% is for seeing both cards and supports a call; 27.66% is for one card and supports a fold. A second bet makes the one-card view the right one.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 48.10% | +14.7703 points | +$44.31 | Call |
| Next card only | 27.66% | -5.6738 points | -$17.02 | Fold |
How the answer moves with outs
A few outs either way, against a pot-size bet that needs 33.33%. The chance climbs about 3.05 points with each extra out.
How bet size moves the answer
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 13 outs on the flop.
With 48.10% to hit, no bet on the list is too big. 13 outs call all 12 sizes on the flop.
| 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 | 28.57% | +19.53 points | Call |
| three-quarter-pot | 30.00% | +18.10 points | Call |
| pot-size, this page | 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
Everything is computed from the closed form. Pairs without an out: 561 of 1,081. The rest, 48.10%, hold at least one out.
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 $100 / $300 = 33.33%. No card is taken out for what an opponent might hold.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Are 13 outs on the flop worth a call against a bet of the full pot?
Verdict: call. A pot-size bet asks for 33.33% and you have 48.10%, a margin of +14.77 points. For a $100 call into a $100 pot, with no later bets and the whole pot won on a hit, the average is +$44.31.
What is the fewest outs that can call a pot-size bet on the flop?
9 outs is the line. At 9 the chance is 34.97%, enough for 33.33%; one fewer gives 31.45%, which is not. Your 13 outs sit 4 above it on the flop, at 48.10%.
Is the by-the-river chance the right one to use on the flop?
Match the number to the betting. All-in or checked down: 48.10%. Facing another bet on the turn: 27.66%. The price is 33.33%, so the verdicts are call and fold in that order.
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