Verdict
Fold
7 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come27.84%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price-2.16 points
The price of the call
Against a three-quarter-pot bet the call needs 30.00%. With 7 outs you have 27.84%, which leaves you 2.16 points under it, so the fold wins out.
A total of 7 outs tends to come from stacking several ways to improve. The next card is an out 14.89% of the time, 7 in 47.
A $100 pot, step by step
- The pot before betting$100
- The bet$75
- Chips you put in$75
- Total pot after calling$250
- Gain on a hit$175
- Net loss when you miss$75
- Chance to hit by the river27.84%
- Calling is worth, on average-$5.39
- Equity needed to break even30.00%
- Unrounded margin-2.1554 points
- Fractional outs at the price7.59 outs
- Margin measured in outs-0.59 outs
Expected value says the same in dollars. Win the whole pot on a hit, lose your call on a miss, add no more betting, and the call loses $5.39 on average: $48.73 in, $54.12 out, -0.072 per dollar called.
The same comparison in odds: the odds against hitting are 2.59 : 1, and the pot lays 2.33 : 1 on a call.
The correct pot to divide by includes your call. Without it the price reads 42.86% rather than 30.00%, and the margin reads -15.0126 points. With the starting pot alone it reads 75.00% and -47.1554 points.
Implied odds that would change the answer
The call becomes fair only if a hit brings in $19.35 more after the draw arrives. Measured against the $75 you pay, that is 0.26 times your call.
Reaching 30.00% takes 8 outs on the flop, which hit 31.45%. With 7, the distance is 1 out.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | -2.16 points | -$5.39 | Fold |
| $50 | 25.00% | +2.84 points | +$8.53 | Call |
| $100 | 21.43% | +6.42 points | +$22.46 | Call |
| $250 | 15.00% | +12.84 points | +$64.22 | Call |
| $500 | 10.00% | +17.84 points | +$133.83 | Call |
The next card against the whole runout
One card or two, the call comes out the same way. 14.89% on the next card and 27.84% by the river both sit on the fold side of 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 27.84% | -2.1554 points | -$5.39 | Fold |
| Next card only | 14.89% | -15.1064 points | -$37.77 | Fold |
The call as outs change
The table shows 7 outs and the draws around it on the flop, all against the same three-quarter-pot bet. Each extra out adds about 3.61 points to the chance here.
Bigger and smaller bets
Look down the margin column to see where the draw stops paying. Every row uses 7 outs on the flop and a bet of a different size.
7 outs stop paying at 0.63 times the pot ($62.84 on a $100 pot). The call holds up against 4 of the 12 bet sizes.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +11.18 points | Call |
| third-pot | 20.00% | +7.84 points | Call |
| two-fifths-pot | 22.22% | +5.62 points | Call |
| half-pot | 25.00% | +2.84 points | Call |
| two-thirds-pot | 28.57% | -0.73 points | Fold |
| three-quarter-pot, this page | 30.00% | -2.16 points | Fold |
| pot-size | 33.33% | -5.49 points | Fold |
| 1.25x-pot | 35.71% | -7.87 points | Fold |
| 1.5x-pot | 37.50% | -9.66 points | Fold |
| 2x-pot | 40.00% | -12.16 points | Fold |
| 3x-pot | 42.86% | -15.01 points | Fold |
| 4x-pot | 44.44% | -16.60 points | Fold |
How this is computed
Here is how 27.84% was found. Deal every pair of the 47 unseen cards: 780 of 1,081 pairs contain no out.
The price is call / (pot + bet + call), here $75 / $250 = 30.00%, and the margin is your chance minus it. The page assumes you call the whole bet, win the whole pot whenever you hit, and see no more betting. All 47 unseen cards are equally likely and none is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against one hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a three-quarter-pot bet with 7 outs on the flop?
Math says fold. The three-quarter-pot bet of $75 needs 30.00% equity, 7 outs on the flop give 27.84%, and the margin is -2.16 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$5.39 on average.
How strong must a draw be to call a three-quarter-pot bet on the flop?
To call a three-quarter-pot bet on the flop you want 8 outs or more. 8 reach 31.45% and 7 reach 27.84%, with 30.00% as the bar. Your 7 outs are 1 under.
How many cards should you count when a three-quarter-pot bet arrives on the flop?
Count two cards, 27.84%, when the bet is the last money going in, and one card, 14.89%, when the next street brings another bet. At a price of 30.00%, either number leads to a fold.
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