Verdict
Fold
4 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come16.47%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price-13.53 points
Comparing the draw with the bet
The price is 30.00% and your chance is 16.47%. You sit 13.53 points below the line, which is a wide gap, so you fold.
Holding a gutshot straight draw gives you exactly 4 outs, out of 47 unseen cards. One card hits 8.51% of the time.
The arithmetic of this call
- Pot before the bet$100
- The bet$75
- Cost to call$75
- Final pot if you call$250
- Net gain when you hit$175
- Net loss when you miss$75
- Your chance to hit16.47%
- Expected value of calling-$33.83
- Equity needed to break even30.00%
- Unrounded margin-13.5338 points
- Break-even count of outs7.59 outs
- Your outs minus break-even outs-3.59 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 $33.83 on average: $28.82 from hits, minus $62.65 from misses, -0.451 per dollar called.
Stated as odds, you are 5.07 : 1 against hitting and the call gets 2.33 : 1 from the pot.
Do not forget your own call. Dividing the bet by the pot without it gives 42.86%, not 30.00%, and would show a margin of -26.3909 points. The bet over the starting pot, 75.00%, is worse and would show -58.5338 points.
When later betting could rescue the call
The call becomes fair only if a hit brings in $205.48 more after the draw arrives. Measured against the $75 you pay, that is 2.74 times your call.
Count the outs the call needs: 8 reach the 30.00% price, giving 31.45%. You have 4, so you are 4 outs short.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | -13.53 points | -$33.83 | Fold |
| $50 | 25.00% | -8.53 points | -$25.60 | Fold |
| $100 | 21.43% | -4.96 points | -$17.37 | Fold |
| $250 | 15.00% | +1.47 points | +$7.33 | Call |
| $500 | 10.00% | +6.47 points | +$48.50 | Call |
By the river or next card
Whether you count one card or two, the answer is a fold. The river figure is 16.47%, the next-card figure is 8.51%, and both are measured against 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 16.47% | -13.5338 points | -$33.83 | Fold |
| Next card only | 8.51% | -21.4894 points | -$53.72 | Fold |
One out more or less
The table shows 4 outs and the draws around it on the flop, all against the same three-quarter-pot bet. Each extra out adds about 3.89 points to the chance here.
Other bet sizes for this draw
Look down the margin column to see where the draw stops paying. Every row uses 4 outs on the flop and a bet of a different size.
With 16.47% to hit, you can call a bet up to 0.25 times the pot ($24.55 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% | -0.20 points | Fold |
| third-pot | 20.00% | -3.53 points | Fold |
| two-fifths-pot | 22.22% | -5.76 points | Fold |
| half-pot | 25.00% | -8.53 points | Fold |
| two-thirds-pot | 28.57% | -12.11 points | Fold |
| three-quarter-pot, this page | 30.00% | -13.53 points | Fold |
| pot-size | 33.33% | -16.87 points | Fold |
| 1.25x-pot | 35.71% | -19.25 points | Fold |
| 1.5x-pot | 37.50% | -21.03 points | Fold |
| 2x-pot | 40.00% | -23.53 points | Fold |
| 3x-pot | 42.86% | -26.39 points | Fold |
| 4x-pot | 44.44% | -27.98 points | Fold |
How this is computed
Here is how 16.47% was found. Deal every pair of the 47 unseen cards: 903 of 1,081 pairs contain no out.
The numbers are a baseline rather than a prediction for one hand. The price is 30.00%, from $75 into $250, 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
What is the right play with 4 outs when a three-quarter-pot bet comes on the flop?
Compare 16.47%, your chance to hit by the river, with 30.00%, the equity a three-quarter-pot bet needs. The gap is -13.53 points, so this is a fold. In dollars on a $100 pot, the call averages -$33.83 when no more betting follows.
At what count of outs does a three-quarter-pot bet on the flop become a call?
The threshold is 8 outs. It gives 31.45%, clearing 30.00%, whereas 7 gives only 27.84%. Holding 4 puts you 4 below it, with a chance of 16.47%.
When is the next-card chance the better comparison?
The river figure of 16.47% assumes no further betting; the next-card figure of 8.51% assumes you pay again on the turn. Against 30.00%, both say fold, so you can use either.
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