Verdict
Call
9 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come34.97%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+14.97 points
How the verdict is reached
This is one of the easier spots. 9 outs on the flop reach 34.97% by the river, the third-pot bet asks for just 20.00%, and the 14.97-point margin favors the call.
9 out of 47 unseen cards is the shape of a flush draw, and a single card hits 19.15% of the time.
The arithmetic of this call
- The pot before betting$100
- Bet$33.33
- You call$33.33
- Pot after your call$166.67
- Gain on a hit$133.33
- Loss on a miss$33.33
- Your chance to hit34.97%
- Average value of the call+$24.95
- Break-even equity20.00%
- Margin, to four decimals+14.9676 points
- Outs that exactly reach the price4.91 outs
- Outs to spare, exactly+4.09 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling gains $24.95 on average. Hits bring in $46.62, misses cost $21.68, and the ratio is +0.748 per dollar called.
Written as odds, the pot lays 4 : 1 while the draw is 1.86 : 1 against.
One easy error is to use 25.00%, the bet over the pot before your call, as the price. The right price is 20.00%, and the mistaken margin would be +9.9676 points. The bet over the starting pot, 33.33%, would claim +1.6343 points.
How much room the call has
The threshold is 5 outs, a chance of 20.35%. With 9 in hand you are 4 outs clear of it.
The call keeps its edge until you lose $71.34 on later streets after hitting. That is 2.14 times the $33.33 you pay now.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +14.97 points | +$24.95 | Call |
| $10 | 21.28% | +13.69 points | +$21.45 | Call |
| $25 | 23.53% | +11.44 points | +$16.20 | Call |
| $50 | 28.57% | +6.40 points | +$7.46 | Call |
| $100 | 50.00% | -15.03 points | -$10.02 | Fold |
Which chance to use
34.97% for two cards says call, while 19.15% for one card says fold, both against 20.00%. If you will have to pay again on the turn, trust the one-card number.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 34.97% | +14.9676 points | +$24.95 | Call |
| Next card only | 19.15% | -0.8511 points | -$1.42 | Fold |
Nearby draws
Here are the neighbors of 9 outs, priced against the same 20.00%. One more out lifts your chance by about 3.42 points.
Changing the bet, keeping the draw
Bet size sets the price, so the verdict changes as you scan the table. The third-pot bet of this page is marked in the first column.
The ceiling for a call is a bet of 1.16 times the pot ($116.31 on a $100 pot). 7 out of 12 sizes sit under it on the flop.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +18.30 points | Call |
| third-pot, this page | 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 | 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 rests on counting, not on a rule of thumb. Blank pairs: 703 out of 1,081; hit chance: 34.97%.
Four assumptions sit behind the verdict: you call the full bet, a hit wins the entire pot, no money goes in after the call, and every one of the 47 unseen cards is equally likely. The price is $33.33 / $166.67 = 20.00%. No card is taken out for what an opponent might hold.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What does the math say about calling a bet of a third of the pot with 9 outs on the flop?
By the numbers it is a call. 9 outs on the flop hit 34.97% by the river, a third-pot bet needs 20.00%, and the margin is +14.97 points. That assumes you call the full $33.33 and no more betting follows, and it values the call at +$24.95 per $100 pot.
How many outs are enough to continue against a bet of a third of the pot on the flop?
To call a third-pot bet on the flop you want 5 outs or more. 5 reach 20.35% and 4 reach 16.47%, with 20.00% as the bar. Your 9 outs are 4 over.
Is the by-the-river chance the right one to use on the flop?
Use the by-the-river chance, 34.97%, when you are all-in or no more betting follows. Use the next-card chance, 19.15%, when you must pay again on the turn. Against the 20.00% price the first is a call and the second is a fold.
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