Verdict
Call
9 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come34.97%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+9.97 points
Reading the verdict
34.97% against 25.00%: the draw beats the price by 9.97 points. On this flop against a half-pot bet, that is a comfortable call.
9 outs is the standard count for a flush draw. Of the 47 unseen cards on the flop, 9 complete it, which is 19.15% on the very next card.
Worked through on a $100 pot
- The pot before betting$100
- The bet$50
- You call$50
- Pot after your call$200
- What a hit wins$150
- Net loss when you miss$50
- How often you hit34.97%
- Expected value of calling+$19.94
- Equity needed to break even25.00%
- Exact margin over the price+9.9676 points
- Outs at break-even6.23 outs
- Your outs minus break-even outs+2.77 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 gains $19.94 on average: $52.45 in, $32.52 out, +0.399 per dollar called.
As odds, 1.86 : 1 against hitting meets pot odds of 3 : 1.
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 +1.6343 points. Using the bet over the starting pot, 50.00%, is further off and would put it at -15.0324 points.
Your cushion over the price
Against this bet the draw needs 7 outs at the least. You have 2 outs more than that, so the call has some room.
Break-even on later streets sits at $57.01 given back, or 1.14 times your call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | +9.97 points | +$19.94 | Call |
| $10 | 26.32% | +8.65 points | +$16.44 | Call |
| $25 | 28.57% | +6.40 points | +$11.19 | Call |
| $50 | 33.33% | +1.63 points | +$2.45 | Call |
| $100 | 50.00% | -15.03 points | -$15.03 | Fold |
Two views of the same draw
Here the cards to come matter. Two cards reach 34.97% and point to a call; one card reaches 19.15% 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 | 34.97% | +9.9676 points | +$19.94 | Call |
| Next card only | 19.15% | -5.8511 points | -$11.70 | Fold |
Neighbors of this draw
A few outs either way, against a half-pot bet that needs 25.00%. The chance climbs about 3.42 points with each extra out.
Changing the bet, keeping the draw
The same 9 outs on the flop meet a different price at each bet size. The table runs from the smallest bet to the largest, and the row for this page is marked.
A bet larger than 1.16 times the pot ($116.31 on a $100 pot) asks for more than 34.97%. For this draw, 7 of the 12 sizes are calls.
| 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, this page | 25.00% | +9.97 points | Call |
| two-thirds-pot | 28.57% | +6.40 points | Call |
| three-quarter-pot | 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 |
How this is computed
Everything is computed from the closed form. Pairs without an out: 703 of 1,081. The rest, 34.97%, hold at least one out.
What is held fixed: the call equals the bet, so the price is $50 / $200 = 25.00%; the pot is won whole on a hit; there is no further betting; and each of the 47 unseen cards is as likely as any other. Opponent cards are not removed.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Are 9 outs on the flop worth a call against a bet of half the pot?
Math says call. The half-pot bet of $50 needs 25.00% equity, 9 outs on the flop give 34.97%, and the margin is +9.97 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$19.94 on average.
How many outs are enough to continue against a bet of half the pot 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 9 you are 2 past the minimum.
Which chance should you compare with the price, the next card or the river?
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 25.00%, and they lead to call and fold in that order.
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