Verdict
Call
8 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come31.45%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+6.45 points
The price of the call
A call fits the numbers. The half-pot bet is priced at 25.00%, 8 outs on the flop reach 31.45%, and that leaves 6.45 points in your favor.
Count an open-ended straight draw and you land on 8 outs. With 47 cards unseen, the next card helps 17.02% of the time.
One hand, in dollars
- Pot before the bet$100
- The bet$50
- Cost to call$50
- Final pot if you call$200
- Net gain when you hit$150
- Loss on a miss$50
- Your chance to hit31.45%
- Expected value of a call+$12.90
- Break-even equity25.00%
- Exact margin over the price+6.4524 points
- Outs at break-even6.23 outs
- Outs to spare, exactly+1.77 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $47.18, the average loss is $34.27, and calling gains $12.90 on average, or +0.258 per dollar called.
The same comparison in odds: the odds against hitting are 2.18 : 1, and the pot lays 3 : 1 on a call.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 33.33% instead of 25.00% and would put your margin at -1.8810 points. Using the bet over the starting pot, 50.00%, is further off and would put it at -18.5476 points.
Where the call would flip
The threshold is 7 outs, a chance of 27.84%. With 8 in hand you are 1 out clear of it.
Think of $41.03 as your safety room: the most you can give back after a hit, 0.82 times your call, with the call still level.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | +6.45 points | +$12.90 | Call |
| $10 | 26.32% | +5.14 points | +$9.76 | Call |
| $25 | 28.57% | +2.88 points | +$5.04 | Call |
| $50 | 33.33% | -1.88 points | -$2.82 | Fold |
| $100 | 50.00% | -18.55 points | -$18.55 | Fold |
By the river or next card
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% | +6.4524 points | +$12.90 | Call |
| Next card only | 17.02% | -7.9787 points | -$15.96 | Fold |
Counts close to yours
One out can change the answer, so the table lists the counts on either side of 8. Each out adds roughly 3.52 points against the 25.00% price.
How bet size moves the answer
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 8 outs on the flop.
The largest bet this draw can call on the flop is 0.85 times the pot ($84.79 on a $100 pot). 8 outs call 6 of the 12 bet sizes listed.
| 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, this page | 25.00% | +6.45 points | Call |
| two-thirds-pot | 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
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.
Keep the assumptions in view: a full call ($50 into $200, or 25.00%), the whole pot on a hit, no more betting, and 47 unseen cards that are equally likely. The math does not know what the other player holds.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Is a call correct with 8 outs against a half-pot bet on the flop?
Math says call. The half-pot bet of $50 needs 25.00% equity, 8 outs on the flop give 31.45%, and the margin is +6.45 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$12.90 on average.
What is the minimum number of outs for a half-pot bet on the flop?
You need at least 7 outs against a half-pot bet on the flop. That count hits 27.84% against 25.00% needed, and 6 falls short at 24.14%. With 8 you are 1 past the minimum.
How many cards should you count when a half-pot bet arrives on the flop?
Pick the number that matches the street plan: 31.45% for seeing both cards for one bet, 17.02% for paying card by card. Both face 25.00%, and they lead to call and fold in that order.
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