Verdict
Fold
5 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come20.35%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price-4.65 points
Your chance and the price
Against a half-pot bet the call needs 25.00%. With 5 outs you have 20.35%, which leaves you 4.65 points under it, so the fold wins out.
A count of 5 outs is usually the sum of more than one draw. Out of 47 unseen cards, one card helps 10.64% of the time.
Counting the chips on a $100 pot
- Pot when the bet arrives$100
- The bet$50
- Cost to call$50
- Final pot if you call$200
- Net gain when you hit$150
- You lose on a miss$50
- How often you hit20.35%
- Calling is worth, on average-$9.30
- Equity needed to break even25.00%
- Margin, to four decimals-4.6485 points
- Fractional outs at the price6.23 outs
- Outs above the price-1.23 outs
Assume the whole pot goes to you when you hit, the call is lost when you miss, and nothing more is bet. Calling then loses $9.30 on average: $30.53 from hits, minus $39.82 from misses, -0.186 per dollar called.
Odds say the same thing. Hitting is 3.91 : 1 against, and the pot lays 3 : 1.
Skipping your own call in the pot gives a price of 33.33% where 25.00% is correct, and a margin of -12.9818 points instead of -4.65 points. The starting pot gives 50.00% and a margin of -29.6485 points, which is wrong by even more.
Implied odds that would change the answer
Your chance is 20.35%, so a hit has to pay $245.68 in all, or $45.68 more than the pot you can see. That extra is 0.91 times what you call.
If the draw had 2 more outs, for 7 in all, the chance would be 27.84% and the call would clear 25.00%.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | -4.65 points | -$9.30 | Fold |
| $50 | 20.00% | +0.35 points | +$0.88 | Call |
| $100 | 16.67% | +3.68 points | +$11.05 | Call |
| $250 | 11.11% | +9.24 points | +$41.58 | Call |
| $500 | 7.14% | +13.21 points | +$92.46 | Call |
Next card or river
Both views point the same way. By the river you hit 20.35%, on the next card 10.64%, and the price is 25.00%, so the fold holds whichever number applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 20.35% | -4.6485 points | -$9.30 | Fold |
| Next card only | 10.64% | -14.3617 points | -$28.72 | Fold |
Nearby draws
The table shows 5 outs and the draws around it on the flop, all against the same half-pot bet. Each extra out adds about 3.79 points to the chance here.
Where the bet size flips the call
Bet size sets the price, so the verdict changes as you scan the table. The half-pot bet of this page is marked in the first column.
The ceiling for a call is a bet of 0.34 times the pot ($34.32 on a $100 pot). 2 out of 12 sizes sit under it on the flop.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +3.68 points | Call |
| third-pot | 20.00% | +0.35 points | Call |
| two-fifths-pot | 22.22% | -1.87 points | Fold |
| half-pot, this page | 25.00% | -4.65 points | Fold |
| two-thirds-pot | 28.57% | -8.22 points | Fold |
| three-quarter-pot | 30.00% | -9.65 points | Fold |
| pot-size | 33.33% | -12.98 points | Fold |
| 1.25x-pot | 35.71% | -15.36 points | Fold |
| 1.5x-pot | 37.50% | -17.15 points | Fold |
| 2x-pot | 40.00% | -19.65 points | Fold |
| 3x-pot | 42.86% | -22.51 points | Fold |
| 4x-pot | 44.44% | -24.09 points | Fold |
How this is computed
No sampling is involved. On the flop there are 1,081 pairs of unseen cards, and 861 of them contain no out, which leaves 20.35% for at least one out.
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
Is a call correct with 5 outs against a half-pot bet on the flop?
Your chance, 20.35%, set against the 25.00% price gives -4.65 points and a fold. With a $100 pot, a $50 call and no more betting, the average value of the call is -$9.30.
How many outs make a call correct against half the pot on the flop?
7 outs is the line. At 7 the chance is 27.84%, enough for 25.00%; one fewer gives 24.14%, which is not. Your 5 outs sit 2 below it on the flop, at 20.35%.
Should you use the chance on the next card or by the river?
Pick the number that matches the street plan: 20.35% for seeing both cards for one bet, 10.64% for paying card by card. Both face 25.00%, and the verdict is fold either way.
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