Verdict
Call
13 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come48.10%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+23.10 points
Reading the verdict
With 13 outs on the flop you hit 48.10% of the time by the river, and a half-pot bet only asks for 25.00%. That 23.10-point cushion makes this a clear call.
Think of 13 outs as a running total of every card that improves you. 13 of the 47 unseen cards qualify, which is 27.66% on one card.
Putting dollars on the call
- Pot when the bet arrives$100
- The bet$50
- Your call$50
- Pot after your call$200
- You can win on a hit$150
- You lose on a miss$50
- Probability of a hit48.10%
- Expected value of a call+$46.21
- Break-even equity25.00%
- Margin, to four decimals+23.1036 points
- Outs that exactly reach the price6.23 outs
- Outs above the price+6.77 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $72.16, the average loss is $25.95, and calling gains $46.21 on average, or +0.924 per dollar called.
Odds say the same thing. Hitting is 1.08 : 1 against, and the pot lays 3 : 1.
One easy error is to use 33.33%, the bet over the pot before your call, as the price. The right price is 25.00%, and the mistaken margin would be +14.7703 points. The bet over the starting pot, 50.00%, would claim -1.8964 points.
Reverse implied odds and your margin
The fewest outs that still call a half-pot bet on the flop is 7. You hold 13, so you have 6 outs to spare before the call flips to a fold.
If hitting means paying off a bigger hand later, the call survives a loss of $96.06. That is 1.92 times the $50 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | +23.10 points | +$46.21 | Call |
| $10 | 26.32% | +21.79 points | +$41.40 | Call |
| $25 | 28.57% | +19.53 points | +$34.18 | Call |
| $50 | 33.33% | +14.77 points | +$22.16 | Call |
| $100 | 50.00% | -1.90 points | -$1.90 | Fold |
One card or two
No conflict here: 48.10% for two cards and 27.66% for one both give a call against the 25.00% 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% | +23.1036 points | +$46.21 | Call |
| Next card only | 27.66% | +2.6596 points | +$5.32 | Call |
Counts close to yours
Draws close to yours, on the same street and against the same bet: the price is fixed at 25.00%, and each out moves the chance about 3.05 points.
Changing the bet, keeping the draw
Look down the margin column to see where the draw stops paying. Every row uses 13 outs on the flop and a bet of a different size.
The call holds at every one of the 12 sizes. 48.10% is higher than the price of even the largest bet.
| 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, this page | 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.
The numbers are a baseline rather than a prediction for one hand. The price is 25.00%, from $50 into $200, and the chance assumes a whole pot won on a hit, no more betting, 47 equally likely unseen cards, and no cards removed for the other player.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a half-pot bet with 13 outs on the flop?
The verdict is call. Your chance is 48.10% and the price is 25.00%, which leaves +23.10 points. On a $100 pot with a $50 bet, calling is worth +$46.21 on average if the whole pot is won on a hit and nothing more is bet.
What is the minimum number of outs for a half-pot bet on the flop?
Against 25.00%, the first count that works on the flop is 7, at 27.84%. At 6 the chance is 24.14%, too low. Compared with that threshold, your 13 outs are 6 above.
Which chance should you compare with the price, the next card or the river?
Match the number to the betting: 48.10% if all-in or checked down, 27.66% if you face another bet on the turn. The price is 25.00%, and both numbers agree on call.
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