Verdict
Call
13 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come48.10%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+28.10 points
How the verdict is reached
This is one of the easier spots. 13 outs on the flop reach 48.10% by the river, the third-pot bet asks for just 20.00%, and the 28.10-point margin favors the call.
You will reach 13 outs by adding up separate draws. With 47 cards unseen, the next card helps 27.66% of the time.
A $100 pot, step by step
- Pot before the bet$100
- Your opponent bets$33.33
- Cost to call$33.33
- Total pot after calling$166.67
- Gain on a hit$133.33
- What a miss costs$33.33
- Your chance to hit48.10%
- Average value of the call+$46.84
- Price of the call20.00%
- Your chance minus the price, unrounded+28.1036 points
- Break-even count of outs4.91 outs
- Margin measured in outs+8.09 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $64.14 in and $17.30 out, so calling gains $46.84 on average at +1.405 per dollar called.
In odds, you face 1.08 : 1 against you and the pot pays 4 : 1.
The price is 20.00% because your call goes into the pot too. Leave it out and you get 25.00%, a margin of +23.1036 points that does not exist; use the starting pot instead and 33.33% puts the margin at +14.7703 points.
Where the call would flip
The threshold is 5 outs, a chance of 20.35%. With 13 in hand you are 8 outs clear of it.
If hitting means paying off a bigger hand later, the call survives a loss of $97.37. That is 2.92 times the $33.33 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +28.10 points | +$46.84 | Call |
| $10 | 21.28% | +26.83 points | +$42.03 | Call |
| $25 | 23.53% | +24.57 points | +$34.81 | Call |
| $50 | 28.57% | +19.53 points | +$22.79 | Call |
| $100 | 50.00% | -1.90 points | -$1.26 | Fold |
Two views of the same draw
No conflict here: 48.10% for two cards and 27.66% for one both give a call against the 20.00% price, so you need not decide which view applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 48.10% | +28.1036 points | +$46.84 | Call |
| Next card only | 27.66% | +7.6596 points | +$12.77 | Call |
Nearby draws
Here are the neighbors of 13 outs, priced against the same 20.00%. One more out lifts your chance by about 3.05 points.
Other bet sizes for this draw
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.
13 outs are strong enough to call every size listed. A chance of 48.10% beats even the biggest price in the table.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +31.44 points | Call |
| third-pot, this page | 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 | 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
The hit chance comes straight from combinations. Out of 1,081 pairs of unseen cards, 561 miss every out, so you hit 48.10% 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 47 unseen cards is equally likely. The price is $33.33 / $166.67 = 20.00%. 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 third-pot bet with 13 outs on the flop?
The answer is a call, with a margin of +28.10 points. 13 outs on the flop reach 48.10%; a bet of $33.33 into $100 needs 20.00%. Win the whole pot on a hit and lose the call on a miss, and the call is worth +$46.84 on average.
How strong must a draw be to call a third-pot bet on the flop?
The threshold is 5 outs. It gives 20.35%, clearing 20.00%, whereas 4 gives only 16.47%. Holding 13 puts you 8 above it, with a chance of 48.10%.
Which hit chance fits a third-pot bet on the flop?
Count two cards, 48.10%, when the bet is the last money going in, and one card, 27.66%, when the next street brings another bet. At a price of 20.00%, either number leads to a call.
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