Verdict
Call
8 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come31.45%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+1.45 points
The call in numbers
The call just clears the price. You hold 31.45%, the three-quarter-pot bet asks for 30.00%, and the margin is 1.45 points.
8 outs is the standard count for an open-ended straight draw. Of the 47 unseen cards on the flop, 8 complete it, which is 17.02% on the very next card.
The $100 pot example
- Pot before the bet$100
- The bet$75
- Your call$75
- Pot with your call in$250
- Gain on a hit$175
- Net loss when you miss$75
- Your chance to hit31.45%
- Expected value of a call+$3.63
- Equity needed to break even30.00%
- Margin, to four decimals+1.4524 points
- Fractional outs at the price7.59 outs
- Outs above the price+0.41 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call gains $3.63 on average. The hit side averages $55.04, the miss side $51.41, and each dollar called returns +0.048.
Odds say the same thing. Hitting is 2.18 : 1 against, and the pot lays 2.33 : 1.
One easy error is to use 42.86%, the bet over the pot before your call, as the price. The right price is 30.00%, and the mistaken margin would be -11.4048 points. The bet over the starting pot, 75.00%, would claim -43.5476 points.
How safe the call is
The call does not survive losing even one out. At 8 outs the chance is 31.45%, just enough for 30.00%, and that is the count you hold.
After a hit you could give back up to $11.54 on later streets, 0.15 times your call, before the call stops paying.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +1.45 points | +$3.63 | Call |
| $10 | 31.25% | +0.20 points | +$0.49 | Call |
| $25 | 33.33% | -1.88 points | -$4.23 | Fold |
| $50 | 37.50% | -6.05 points | -$12.10 | Fold |
| $100 | 50.00% | -18.55 points | -$27.82 | Fold |
Which chance to use
The verdict depends on how many cards you get to see. The runout figure is 31.45% (call), the next-card figure is 17.02% (fold), and the price is 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 31.45% | +1.4524 points | +$3.63 | Call |
| Next card only | 17.02% | -12.9787 points | -$32.45 | Fold |
How the answer moves with outs
A few outs either way, against a three-quarter-pot bet that needs 30.00%. The chance climbs about 3.52 points with each extra out.
Bigger and smaller bets
Look down the margin column to see where the draw stops paying. Every row uses 8 outs on the flop and a bet of a different size.
Past 0.85 times the pot ($84.79 on a $100 pot) the price outruns your chance. Of the 12 sizes, 6 are calls for 8 outs on the flop.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +14.79 points | Call |
| third-pot | 20.00% | +11.45 points | Call |
| two-fifths-pot | 22.22% | +9.23 points | Call |
| half-pot | 25.00% | +6.45 points | Call |
| two-thirds-pot | 28.57% | +2.88 points | Call |
| three-quarter-pot, this page | 30.00% | +1.45 points | Call |
| pot-size | 33.33% | -1.88 points | Fold |
| 1.25x-pot | 35.71% | -4.26 points | Fold |
| 1.5x-pot | 37.50% | -6.05 points | Fold |
| 2x-pot | 40.00% | -8.55 points | Fold |
| 3x-pot | 42.86% | -11.40 points | Fold |
| 4x-pot | 44.44% | -12.99 points | Fold |
How this is computed
No sampling is involved. On the flop there are 1,081 pairs of unseen cards, and 741 of them contain no out, which leaves 31.45% for at least one out.
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
Call or fold with 8 outs on the flop against a bet of three quarters of the pot?
Verdict: call. A three-quarter-pot bet asks for 30.00% and you have 31.45%, a margin of +1.45 points. For a $75 call into a $100 pot, with no later bets and the whole pot won on a hit, the average is +$3.63.
What is the minimum number of outs for a three-quarter-pot bet on the flop?
You need at least 8 outs against a three-quarter-pot bet on the flop. That count hits 31.45% against 30.00% needed, and 7 falls short at 27.84%. With 8 you are exactly at the minimum.
Does it matter whether you count one card or two against a three-quarter-pot bet?
It depends on what follows. If the hand ends here, count both cards: 31.45%. If another bet is coming on the turn, count one card: 17.02%. Compared with 30.00%, that is a call in the first case and a fold in the second.
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