Verdict
Fold
1 out, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come4.26%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price-25.74 points
Reading the verdict
The price is 30.00% and your chance is 4.26%. You sit 25.74 points below the line, which is a wide gap, so you fold.
One out is a single card that improves you. Of the 47 unseen cards on the flop, one helps, which is 2.13% on the very next card.
The arithmetic of this call
- Pot when the bet arrives$100
- The bet$75
- Cost to call$75
- Total pot after calling$250
- Net gain when you hit$175
- Loss on a miss$75
- How often you hit4.26%
- Expected value of calling-$64.36
- Equity needed to break even30.00%
- Exact margin over the price-25.7447 points
- Outs at break-even7.59 outs
- Outs above the price-6.59 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling loses $64.36 on average. Hits bring in $7.45, misses cost $71.81, and the ratio is -0.858 per dollar called.
In odds, you face 22.5 : 1 against you and the pot pays 2.33 : 1.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 42.86% instead of 30.00% and would put your margin at -38.6018 points. Using the bet over the starting pot, 75.00%, is further off and would put it at -70.7447 points.
The extra winnings a call would need
Break-even needs $1,512.50 of future winnings on top of the $250 already in the pot, which is 20.17 times the cost of your call.
Reaching 30.00% takes 8 outs on the flop, which hit 31.45%. With 1, the distance is 7 outs.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | -25.74 points | -$64.36 | Fold |
| $50 | 25.00% | -20.74 points | -$62.23 | Fold |
| $100 | 21.43% | -17.17 points | -$60.11 | Fold |
| $250 | 15.00% | -10.74 points | -$53.72 | Fold |
| $500 | 10.00% | -5.74 points | -$43.09 | Fold |
Next card or river
Both views point the same way. By the river you hit 4.26%, on the next card 2.13%, and the price is 30.00%, so the fold holds whichever number applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 4.26% | -25.7447 points | -$64.36 | Fold |
| Next card only | 2.13% | -27.8723 points | -$69.68 | Fold |
Counts close to yours
Add a few outs and watch the verdict. Every out is worth about 4.16 points on the flop, and the price stays at 30.00%.
The same draw against other bet sizes
Your 4.26% 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.
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 | 25.00% | -20.74 points | Fold |
| two-thirds-pot | 28.57% | -24.32 points | Fold |
| three-quarter-pot, this page | 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
Everything is computed from the closed form. Pairs without an out: 1,035 of 1,081. The rest, 4.26%, hold at least one out.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $75 / $250 = 30.00%. A hit takes the whole pot, no later betting happens, and the 47 unseen cards are all equally likely, with none removed for an opponent's cards.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 1 out when a three-quarter-pot bet comes on the flop?
Compare 4.26%, your chance to hit by the river, with 30.00%, the equity a three-quarter-pot bet needs. The gap is -25.74 points, so this is a fold. In dollars on a $100 pot, the call averages -$64.36 when no more betting follows.
What count of outs clears the price of a three-quarter-pot bet on the flop?
Against 30.00%, the first count that works on the flop is 8, at 31.45%. At 7 the chance is 27.84%, too low. Compared with that threshold, your 1 out is 7 below.
Should you use the chance on the next card or by the river?
It depends on what follows, but here it does not matter. If the hand ends here, count both cards: 4.26%. If another bet is coming on the turn, count one card: 2.13%. Against 30.00%, both say fold.
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