Verdict
Call
9 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come34.97%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+1.63 points
What the numbers say
The call just clears the price. You hold 34.97%, the pot-size bet asks for 33.33%, and the margin is 1.63 points.
Holding a flush draw gives you exactly 9 outs, out of 47 unseen cards. One card hits 19.15% of the time.
Worked through on a $100 pot
- Pot when the bet arrives$100
- Bet$100
- You call$100
- Final pot if you call$300
- Gain on a hit$200
- You lose on a miss$100
- Your chance to hit34.97%
- Expected value of calling+$4.90
- Equity the call needs33.33%
- Your chance minus the price, unrounded+1.6343 points
- Outs that exactly reach the price8.53 outs
- Your outs minus break-even outs+0.47 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $4.90 on average. Hits add $69.94 on average and misses cost $65.03 on average, or +0.049 per dollar called.
Odds say the same thing. Hitting is 1.86 : 1 against, and the pot lays 2 : 1.
Do not forget your own call. Dividing the bet by the pot without it gives 50.00%, not 33.33%, and would show a margin of -15.0324 points.
How much room the call has
The call does not survive losing even one out. At 9 outs the chance is 34.97%, just enough for 33.33%, and that is the count you hold.
Reverse implied odds are the risk here. A hit that costs you $14.02 later, 0.14 times your call, is where the call stops being worth it.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | +1.63 points | +$4.90 | Call |
| $10 | 34.48% | +0.48 points | +$1.41 | Call |
| $25 | 36.36% | -1.40 points | -$3.84 | Fold |
| $50 | 40.00% | -5.03 points | -$12.58 | Fold |
| $100 | 50.00% | -15.03 points | -$30.06 | Fold |
Next card or river
Watch the difference between one card and two. By the river you hold 34.97%, a call; on the next card alone you hold 19.15%, a fold. A bet on the turn tips you toward the smaller number.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 34.97% | +1.6343 points | +$4.90 | Call |
| Next card only | 19.15% | -14.1844 points | -$42.55 | Fold |
A few outs either way
Here are the neighbors of 9 outs, priced against the same 33.33%. One more out lifts your chance by about 3.42 points.
Changing the bet, keeping the draw
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 9 outs on the flop.
Your draw can face a bet of up to 1.16 times the pot ($116.31 on a $100 pot) and still break even. 7 of the 12 sizes fall at or under that line.
| 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 | 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, this page | 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 |
Pages that use the same math
How this is computed
The chance to hit is the exact closed form, with no simulation. From the flop, 703 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 703 / 1,081, which is 34.97%.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $100 / $300 = 33.33%. A hit takes the whole pot, no later betting happens, and the 47 unseen cards are all equally likely, with none removed for an opponent's cards.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a pot-size bet with 9 outs on the flop?
Math says call. The pot-size bet of $100 needs 33.33% equity, 9 outs on the flop give 34.97%, and the margin is +1.63 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$4.90 on average.
What count of outs clears the price of a pot-size bet on the flop?
To call a pot-size bet on the flop you want 9 outs or more. 9 reach 34.97% and 8 reach 31.45%, with 33.33% as the bar. Your 9 outs are right on the line.
Is the by-the-river chance the right one to use on the flop?
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 33.33%, and they lead to call and fold in that order.
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