Verdict
Call
9 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come34.97%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+4.97 points
Comparing the draw with the bet
Against a three-quarter-pot bet the call needs 30.00%. With 9 outs you have 34.97%, so you clear it by 4.97 points and the call wins out.
Count a flush draw and you land on 9 outs. With 47 cards unseen, the next card helps 19.15% of the time.
One hand, in dollars
- The pot before betting$100
- The bet$75
- You call$75
- Pot after your call$250
- Net gain when you hit$175
- Net loss when you miss$75
- Probability of a hit34.97%
- Expected value of a call+$12.42
- Break-even equity30.00%
- Margin, to four decimals+4.9676 points
- Outs at break-even7.59 outs
- Outs above the price+1.41 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling gains $12.42 on average. The hit side averages $61.19, the miss side $48.77, and each dollar called returns +0.166.
Written as odds, the pot lays 2.33 : 1 while the draw is 1.86 : 1 against.
Counting the pot without your call makes the price look like 42.86%, when the real price is 30.00%. On that mistaken price the margin would read -7.8895 points; on 75.00%, the bet over the starting pot, it would read -40.0324 points.
Your cushion over the price
The fewest outs that still call a three-quarter-pot bet on the flop is 8. You hold 9, so you have 1 out to spare before the call flips to a fold.
Your margin is worth $35.52 in later losses. Past that, 0.47 times your call, folding would have been better.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +4.97 points | +$12.42 | Call |
| $10 | 31.25% | +3.72 points | +$8.92 | Call |
| $25 | 33.33% | +1.63 points | +$3.68 | Call |
| $50 | 37.50% | -2.53 points | -$5.06 | Fold |
| $100 | 50.00% | -15.03 points | -$22.55 | Fold |
Two cards to come, or just one
The two views split. By the river 34.97% gives a call, but the next card alone is 19.15%, which gives a fold. Use the river figure when no more betting follows and the next-card figure when you face another bet on the turn.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 34.97% | +4.9676 points | +$12.42 | Call |
| Next card only | 19.15% | -10.8511 points | -$27.13 | Fold |
Counts close to yours
Move up or down a few outs and watch the verdict. Every extra out is worth about 3.42 points on the flop, and the price stays at 30.00%.
How bet size moves the answer
Keep 9 outs and change only the bet. The price rises from the smallest size to the largest, and the three-quarter-pot row is marked as this page.
Past 1.16 times the pot ($116.31 on a $100 pot) the price outruns your chance. Of the 12 sizes, 7 are calls for 9 outs on the flop.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +18.30 points | Call |
| third-pot | 20.00% | +14.97 points | Call |
| two-fifths-pot | 22.22% | +12.75 points | Call |
| half-pot | 25.00% | +9.97 points | Call |
| two-thirds-pot | 28.57% | +6.40 points | Call |
| three-quarter-pot, this page | 30.00% | +4.97 points | Call |
| pot-size | 33.33% | +1.63 points | Call |
| 1.25x-pot | 35.71% | -0.75 points | Fold |
| 1.5x-pot | 37.50% | -2.53 points | Fold |
| 2x-pot | 40.00% | -5.03 points | Fold |
| 3x-pot | 42.86% | -7.89 points | Fold |
| 4x-pot | 44.44% | -9.48 points | Fold |
Pages that use the same math
How this is computed
The hit chance comes straight from combinations. Out of 1,081 pairs of unseen cards, 703 miss every out, so you hit 34.97% of the time.
The model is deliberately simple: call everything, win everything on a hit, face no more bets, deal from 47 equally likely unseen cards, and ignore an opponent's holding. With the price at $75 / $250 = 30.00%, later streets and shared outs are what change the real answer.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a three-quarter-pot bet with 9 outs on the flop?
The answer is a call, with a margin of +4.97 points. 9 outs on the flop reach 34.97%; a bet of $75 into $100 needs 30.00%. Win the whole pot on a hit and lose the call on a miss, and the call is worth +$12.42 on average.
How strong must a draw be to call a three-quarter-pot bet on the flop?
Look for 8 outs. That is the smallest count whose chance, 31.45%, reaches the 30.00% price; 7 manages 27.84%. You have 9, so you are 1 ahead of the minimum.
Which hit chance fits a three-quarter-pot bet on the flop?
Pick the number that matches the street plan: 34.97% for seeing both cards for one bet, 19.15% for paying card by card. Both face 30.00%, and they lead to call and fold in that order.
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