Verdict
Fold
1 out, flop, half-pot bet
- Chance to hit by the rivertwo cards to come4.26%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price-20.74 points
The price of the call
4.26% against 25.00%: the draw trails the price by 20.74 points. On this flop against a half-pot bet, that is an easy fold.
Holding a single out means one card in the deck helps you. Out of 47 unseen cards it arrives 2.13% of the time on one card.
The arithmetic of this call
- Starting pot$100
- Bet$50
- Cost to call$50
- Pot after your call$200
- What a hit wins$150
- Net loss when you miss$50
- How often you hit4.26%
- Calling is worth, on average-$41.49
- Break-even equity25.00%
- Your chance minus the price, unrounded-20.7447 points
- Fractional outs at the price6.23 outs
- Margin measured in outs-5.23 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 $41.49 on average: $6.38 from hits, minus $47.87 from misses, -0.830 per dollar called.
The same comparison in odds: the odds against hitting are 22.5 : 1, and the pot lays 3 : 1 on a call.
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 -29.0780 points. The bet over the starting pot, 50.00%, would claim -45.7447 points.
Closing the gap with future bets
The call becomes fair only if a hit brings in $975 more after the draw arrives. Measured against the $50 you pay, that is 19.50 times your call.
Another way to close the gap is more outs. The fewest outs that call a half-pot bet on the flop is 7; with 7 outs you would hit 27.84%. That is 6 more outs than the 1 you hold.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | -20.74 points | -$41.49 | Fold |
| $50 | 20.00% | -15.74 points | -$39.36 | Fold |
| $100 | 16.67% | -12.41 points | -$37.23 | Fold |
| $250 | 11.11% | -6.86 points | -$30.85 | Fold |
| $500 | 7.14% | -2.89 points | -$20.21 | Fold |
One card or two
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 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 4.26% | -20.7447 points | -$41.49 | Fold |
| Next card only | 2.13% | -22.8723 points | -$45.74 | Fold |
Draws around this one
How fast does the margin move? About 4.16 points per out on the flop. The rows below keep the half-pot bet fixed and change only the outs.
Bigger and smaller bets
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 1 out on the flop.
With 4.26% to hit, you can call a bet up to 0.05 times the pot ($4.65 on a $100 pot) and no more, which is smaller than every size listed. All 12 rows are folds.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -12.41 points | Fold |
| third-pot | 20.00% | -15.74 points | Fold |
| two-fifths-pot | 22.22% | -17.97 points | Fold |
| half-pot, this page | 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
Here is how 4.26% was found. Deal every pair of the 47 unseen cards: 1,035 of 1,081 pairs contain no out.
These figures describe a clean spot. You pay the whole bet, which costs $50 of a $200 pot (25.00%), 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
Call or fold with 1 out on the flop against a bet of half the pot?
Math says fold. The half-pot bet of $50 needs 25.00% equity, 1 out on the flop gives 4.26%, and the margin is -20.74 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$41.49 on average.
What is the fewest outs that can call a half-pot bet 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 1 out sits 6 below it on the flop, at 4.26%.
Is the by-the-river chance the right one to use on the flop?
Use the by-the-river chance, 4.26%, when no more betting follows, and the next-card chance, 2.13%, when you must pay again on the turn. Against the 25.00% price both give a fold, so the choice does not change the play here.
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