Verdict
Fold
1 out, flop, third-pot bet
- Chance to hit by the rivertwo cards to come4.26%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-15.74 points
Reading the verdict
The price is 20.00% and your chance is 4.26%. You sit 15.74 points below the line, which is a wide gap, so you fold.
With one out, exactly one of the 47 unseen cards improves your hand, and one card hits 2.13% of the time.
Worked through on a $100 pot
- Pot when the bet arrives$100
- The bet$33.33
- Chips you put in$33.33
- Pot after your call$166.67
- Net gain when you hit$133.33
- Loss on a miss$33.33
- How often you hit4.26%
- Expected value of calling-$26.24
- Equity needed to break even20.00%
- Unrounded margin-15.7447 points
- Fractional outs at the price4.91 outs
- Margin measured in outs-3.91 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling loses $26.24 on average. The hit side averages $5.67, the miss side $31.91, and each dollar called returns -0.787.
As odds, 22.5 : 1 against hitting meets pot odds of 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 -20.7447 points that does not exist; use the starting pot instead and 33.33% puts the margin at -29.0780 points.
What implied odds would have to do
Think of it as a missing $616.67. When the draw hits you must collect that much beyond the pot for the $33.33 call to pay for itself, 18.50 times your call.
The smallest count that pays for a third-pot bet is 5 outs at 20.35%. You hold 1, which is 4 outs fewer.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -15.74 points | -$26.24 | Fold |
| $50 | 15.38% | -11.13 points | -$24.11 | Fold |
| $100 | 12.50% | -8.24 points | -$21.99 | Fold |
| $250 | 8.00% | -3.74 points | -$15.60 | Fold |
| $500 | 5.00% | -0.74 points | -$4.96 | Fold |
Which chance to use
One card or two, the call comes out the same way. 2.13% on the next card and 4.26% by the river both sit on the fold side of 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 4.26% | -15.7447 points | -$26.24 | Fold |
| Next card only | 2.13% | -17.8723 points | -$29.79 | Fold |
Counts close to yours
Here are the closest counts to 1 out, priced against the same 20.00%. One more out moves your chance by about 4.16 points.
How bet size moves the answer
Bigger bets ask for more equity while your chance stays at 4.26%. Here is every bet size against the same draw, with the row for this page marked.
1 out stops paying at 0.05 times the pot ($4.65 on a $100 pot), below the smallest size listed. The call fails at all 12 bet sizes.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -12.41 points | Fold |
| third-pot, this page | 20.00% | -15.74 points | Fold |
| two-fifths-pot | 22.22% | -17.97 points | Fold |
| half-pot | 25.00% | -20.74 points | Fold |
| two-thirds-pot | 28.57% | -24.32 points | Fold |
| three-quarter-pot | 30.00% | -25.74 points | Fold |
| pot-size | 33.33% | -29.08 points | Fold |
| 1.25x-pot | 35.71% | -31.46 points | Fold |
| 1.5x-pot | 37.50% | -33.24 points | Fold |
| 2x-pot | 40.00% | -35.74 points | Fold |
| 3x-pot | 42.86% | -38.60 points | Fold |
| 4x-pot | 44.44% | -40.19 points | Fold |
How this is computed
The hit chance comes straight from combinations. Out of 1,081 pairs of unseen cards, 1,035 miss every out, so you hit 4.26% of the time.
These figures describe a clean spot. You pay the whole bet, which costs $33.33 of a $166.67 pot (20.00%), collect the whole pot on a hit, meet no more bets, and draw from 47 equally likely cards, with no adjustment for an opponent's hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Is a call correct with 1 out against a third-pot bet on the flop?
By the numbers it is a fold. 1 out on the flop hits 4.26% by the river, a third-pot bet needs 20.00%, and the margin is -15.74 points. That assumes you call the full $33.33 and no more betting follows, and it values the call at -$26.24 per $100 pot.
How strong must a draw be to call a third-pot bet on the flop?
5 outs is the line. At 5 the chance is 20.35%, enough for 20.00%; one fewer gives 16.47%, which is not. Your 1 out sits 4 below it on the flop, at 4.26%.
When is the next-card chance the better comparison?
Count two cards, 4.26%, when the bet is the last money going in, and one card, 2.13%, when the next street brings another bet. At a price of 20.00%, either number leads to a fold.
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