Verdict
Call
8 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come31.45%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+2.88 points
Chance against price
8 outs on the flop hit 31.45% by the river, and the two-thirds-pot bet needs 28.57%. You are 2.88 points above the price, a real edge, so calling is right.
Holding an open-ended straight draw gives you exactly 8 outs, out of 47 unseen cards. One card hits 17.02% of the time.
Worked through on a $100 pot
- The pot before betting$100
- Your opponent bets$66.67
- Your call$66.67
- Pot after your call$233.33
- What a hit wins$166.67
- You lose on a miss$66.67
- Chance to hit by the river31.45%
- Average value of the call+$6.72
- Price of the call28.57%
- Your chance minus the price, unrounded+2.8809 points
- Outs at break-even7.20 outs
- Margin measured in outs+0.80 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $6.72 on average. Hits add $52.42 on average and misses cost $45.70 on average, or +0.101 per dollar called.
Written as odds, the pot lays 2.5 : 1 while the draw is 2.18 : 1 against.
One easy error is to use 40.00%, the bet over the pot before your call, as the price. The right price is 28.57%, and the mistaken margin would be -8.5476 points. The bet over the starting pot, 66.67%, would claim -35.2143 points.
Reverse implied odds and your margin
The call does not survive losing even one out. At 8 outs the chance is 31.45%, just enough for 28.57%, and that is the count you hold.
The call keeps its edge until you lose $21.37 on later streets after hitting. That is 0.32 times the $66.67 you pay now.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +2.88 points | +$6.72 | Call |
| $10 | 29.85% | +1.60 points | +$3.58 | Call |
| $25 | 32.00% | -0.55 points | -$1.14 | Fold |
| $50 | 36.36% | -4.91 points | -$9 | Fold |
| $100 | 50.00% | -18.55 points | -$24.73 | Fold |
The next card against the whole runout
Here the cards to come matter. Two cards reach 31.45% and point to a call; one card reaches 17.02% and points to a fold. Which one applies depends on whether the turn brings another bet.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 31.45% | +2.8809 points | +$6.72 | Call |
| Next card only | 17.02% | -11.5502 points | -$26.95 | Fold |
Neighbors of this draw
Draws close to yours, on the same street and against the same bet: the price is fixed at 28.57%, and each out moves the chance about 3.52 points.
Where the bet size flips the call
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, this page | 28.57% | +2.88 points | Call |
| three-quarter-pot | 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
The chance rests on counting, not on a rule of thumb. Blank pairs: 741 out of 1,081; hit chance: 31.45%.
The numbers are a baseline rather than a prediction for one hand. The price is 28.57%, from $66.67 into $233.33, 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
Does the math favor calling a two-thirds-pot bet with 8 outs on the flop?
Reduce the question to a comparison of two numbers: 31.45% to hit and 28.57% to break even. The first minus the second is +2.88 points, which makes this a call, and the call averages +$6.72 on a $100 pot if no more betting follows.
How many outs are enough to continue against a bet of two thirds of the pot on the flop?
8 outs is the line. At 8 the chance is 31.45%, enough for 28.57%; one fewer gives 27.84%, which is not. Your 8 outs sit right on it on the flop, at 31.45%.
Is the by-the-river chance the right one to use on the flop?
Match the number to the betting. All-in or checked down: 31.45%. Facing another bet on the turn: 17.02%. The price is 28.57%, so the verdicts are call and fold in that order.
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