Verdict
Fold
9 outs, turn, third-pot bet
- Chance to hit by the riverone card to come19.57%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-0.43 points
The price of the call
Folding beats calling by a hair. 19.57% misses 20.00% by 0.43 points, so the call loses a little on average.
9 outs is the standard count for a flush draw. Of the 46 unseen cards on the turn, 9 complete it, which is 19.57% on the very next card.
The $100 pot example
- The pot before betting$100
- Bet$33.33
- Your call$33.33
- Pot with your call in$166.67
- Gain on a hit$133.33
- Net loss when you miss$33.33
- How often you hit19.57%
- Calling is worth, on average-$0.72
- Break-even equity20.00%
- Margin, to four decimals-0.4348 points
- Outs at break-even9.20 outs
- Your outs minus break-even outs-0.20 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call loses $0.72 on average. The hit side averages $26.09, the miss side $26.81, and each dollar called returns -0.022.
Stated as odds, you are 4.11 : 1 against hitting and the call gets 4 : 1 from the pot.
Counting the pot without your call makes the price look like 25.00%, when the real price is 20.00%. On that mistaken price the margin would read -5.4348 points; on 33.33%, the bet over the starting pot, it would read -13.7681 points.
What it would take to call
The shortfall in dollars is $3.70: the amount a hit would have to win later for 19.57% to be enough. It equals 0.11 times your $33.33 call.
Reaching 20.00% takes 10 outs on the turn, which hit 21.74%. With 9, the distance is 1 out.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -0.43 points | -$0.72 | Fold |
| $50 | 15.38% | +4.18 points | +$9.06 | Call |
| $100 | 12.50% | +7.07 points | +$18.84 | Call |
| $250 | 8.00% | +11.57 points | +$48.19 | Call |
| $500 | 5.00% | +14.57 points | +$97.10 | Call |
What the flop would have given you
Waiting a street costs 15.40 points. The flop gives 9 outs two chances to hit, 34.97%, and a call against 20.00%; the turn gives one, 19.57%.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 34.97% | +14.9676 points | +$24.95 | Call |
| Turn, one card to come | 19.57% | -0.4348 points | -$0.72 | Fold |
The call as outs change
A few outs either way, against a third-pot bet that needs 20.00%. The chance climbs about 2.17 points with each extra out.
| Outs | By the river | Margin | Verdict |
|---|---|---|---|
| 7 outs | 15.22% | -4.78 points | Fold |
| 8 outs | 17.39% | -2.61 points | Fold |
| 9 outs, this page | 19.57% | -0.43 points | Fold |
| 10 outs | 21.74% | +1.74 points | Call |
| 11 outs | 23.91% | +3.91 points | Call |
The same draw against other bet sizes
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 9 outs on the turn.
The largest bet this draw can call on the turn is 0.32 times the pot ($32.14 on a $100 pot). 9 outs call 1 of the 12 bet sizes listed.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +2.90 points | Call |
| third-pot, this page | 20.00% | -0.43 points | Fold |
| two-fifths-pot | 22.22% | -2.66 points | Fold |
| half-pot | 25.00% | -5.43 points | Fold |
| two-thirds-pot | 28.57% | -9.01 points | Fold |
| three-quarter-pot | 30.00% | -10.43 points | Fold |
| pot-size | 33.33% | -13.77 points | Fold |
| 1.25x-pot | 35.71% | -16.15 points | Fold |
| 1.5x-pot | 37.50% | -17.93 points | Fold |
| 2x-pot | 40.00% | -20.43 points | Fold |
| 3x-pot | 42.86% | -23.29 points | Fold |
| 4x-pot | 44.44% | -24.88 points | Fold |
How this is computed
The number is exact rather than estimated. 9 of the 46 cards that could come are outs, which is 19.57%.
Keep the assumptions in view: a full call ($33.33 into $166.67, or 20.00%), the whole pot on a hit, no more betting, and 46 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
Should you call a third-pot bet with 9 outs on the turn?
Math says fold. The third-pot bet of $33.33 needs 20.00% equity, 9 outs on the turn give 19.57%, and the margin is -0.43 points. Assuming a whole pot won on a hit and no further bets, the call is worth -$0.72 on average.
At what count of outs does a third-pot bet on the turn become a call?
To call a third-pot bet on the turn you want 10 outs or more. 10 reach 21.74% and 9 reach 19.57%, with 20.00% as the bar. Your 9 outs are 1 under.
Does it matter whether you count one card or two against a third-pot bet?
On the turn only one card is left, so the by-the-river chance and the next-card chance are the same, 19.57%. Against the 20.00% price that is a fold, with a margin of -0.43 points.
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