Verdict
Fold
6 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come24.14%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price-0.86 points
How the verdict is reached
Folding beats calling by a hair. 24.14% misses 25.00% by 0.86 points, so the call loses a little on average.
For two overcards, 6 outs is the number to use, and one card hits 12.77% of the time out of 47 unseen.
The arithmetic of this call
- Pot when the bet arrives$100
- Bet$50
- Chips you put in$50
- Pot after your call$200
- You can win on a hit$150
- Net loss when you miss$50
- Your chance to hit24.14%
- Average value of the call-$1.71
- Break-even equity25.00%
- Your chance minus the price, unrounded-0.8557 points
- Outs that exactly reach the price6.23 outs
- Your outs minus break-even outs-0.23 outs
Expected value says the same in dollars. Win the whole pot on a hit, lose your call on a miss, add no more betting, and the call loses $1.71 on average: $36.22 in, $37.93 out, -0.034 per dollar called.
In odds, you face 3.14 : 1 against you and the pot pays 3 : 1.
The correct pot to divide by includes your call. Without it the price reads 33.33% rather than 25.00%, and the margin reads -9.1890 points. With the starting pot alone it reads 50.00% and -25.8557 points.
Closing the gap with future bets
Your chance is 24.14%, so a hit has to pay $207.09 in all, or $7.09 more than the pot you can see. That extra is 0.14 times what you call.
Count the outs the call needs: 7 reach the 25.00% price, giving 27.84%. You have 6, so you are 1 out short.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | -0.86 points | -$1.71 | Fold |
| $50 | 20.00% | +4.14 points | +$10.36 | Call |
| $100 | 16.67% | +7.48 points | +$22.43 | Call |
| $250 | 11.11% | +13.03 points | +$58.65 | Call |
| $500 | 7.14% | +17.00 points | +$119.01 | Call |
Pricing one card at a time
One card or two, the call comes out the same way. 12.77% on the next card and 24.14% by the river both sit on the fold side of 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 24.14% | -0.8557 points | -$1.71 | Fold |
| Next card only | 12.77% | -12.2340 points | -$24.47 | Fold |
How the answer moves with outs
The table shows 6 outs and the draws around it on the flop, all against the same half-pot bet. Each extra out adds about 3.70 points to the chance here.
How bet size moves the answer
Your 24.14% chance is fixed, so the only thing that moves is the price. The 12 rows below price the call at every bet size on the flop.
Break-even for this draw is a bet of 0.47 times the pot ($46.69 on a $100 pot). Sizes below it call, sizes above it fold, and 3 of the 12 sizes are calls in the table.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +7.48 points | Call |
| third-pot | 20.00% | +4.14 points | Call |
| two-fifths-pot | 22.22% | +1.92 points | Call |
| half-pot, this page | 25.00% | -0.86 points | Fold |
| two-thirds-pot | 28.57% | -4.43 points | Fold |
| three-quarter-pot | 30.00% | -5.86 points | Fold |
| pot-size | 33.33% | -9.19 points | Fold |
| 1.25x-pot | 35.71% | -11.57 points | Fold |
| 1.5x-pot | 37.50% | -13.36 points | Fold |
| 2x-pot | 40.00% | -15.86 points | Fold |
| 3x-pot | 42.86% | -18.71 points | Fold |
| 4x-pot | 44.44% | -20.30 points | Fold |
How this is computed
The chance to hit is the exact closed form, with no simulation. From the flop, 820 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 820 / 1,081, which is 24.14%.
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
How should you respond to a half-pot bet on the flop when you hold 6 outs?
The answer is a fold, with a margin of -0.86 points. 6 outs on the flop reach 24.14%; a bet of $50 into $100 needs 25.00%. Win the whole pot on a hit and lose the call on a miss, and the call is worth -$1.71 on average.
How many outs make a call correct against half the pot on the flop?
To call a half-pot bet on the flop you want 7 outs or more. 7 reach 27.84% and 6 reach 24.14%, with 25.00% as the bar. Your 6 outs are 1 under.
Which chance should you compare with the price, the next card or the river?
Count two cards, 24.14%, when the bet is the last money going in, and one card, 12.77%, when the next street brings another bet. At a price of 25.00%, either number leads to a fold.
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