Verdict
Fold
9 outs, turn, two-thirds-pot bet
- Chance to hit by the riverone card to come19.57%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-9.01 points
How the verdict is reached
This is one of the easier spots. 9 outs on the turn reach 19.57% by the river, the two-thirds-pot bet asks for 28.57%, and the 9.01-point gap favors folding.
The usual home for 9 outs is a flush draw. One card from the 46 unseen ones completes it 19.57% of the time.
Putting dollars on the call
- The pot before betting$100
- The bet$66.67
- Chips you put in$66.67
- Pot with your call in$233.33
- Net gain when you hit$166.67
- You lose on a miss$66.67
- Chance to hit by the river19.57%
- Expected value of a call-$21.01
- Equity needed to break even28.57%
- Exact margin over the price-9.0062 points
- Break-even count of outs13.14 outs
- Your outs minus break-even outs-4.14 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling loses $21.01 on average. The hit side averages $32.61, the miss side $53.62, and each dollar called returns -0.315.
The same comparison in odds: the odds against hitting are 4.11 : 1, and the pot lays 2.5 : 1 on a call.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 40.00% instead of 28.57% and would put your margin at -20.4348 points. Using the bet over the starting pot, 66.67%, is further off and would put it at -47.1014 points.
The extra winnings a call would need
With 19.57% to hit, break-even sits $107.41 higher than the pot shows. Put another way, later bets must add 1.61 times your call.
The call starts to work at 14 outs, where the chance is 30.43%. Your 9 outs fall 5 outs below that.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -9.01 points | -$21.01 | Fold |
| $50 | 23.53% | -3.96 points | -$11.23 | Fold |
| $100 | 20.00% | -0.43 points | -$1.45 | Fold |
| $250 | 13.79% | +5.77 points | +$27.90 | Call |
| $500 | 9.09% | +10.47 points | +$76.81 | Call |
One card to come instead of two
On the turn only one card is left, so the chance by the river and the chance on the next card are the same 19.57%. Back on the flop, the same 9 outs hit 34.97%, 15.40 points more, and that would have been a call.
| Street | Chance by the river | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| Flop, two cards to come | 34.97% | +6.3962 points | +$14.92 | Call |
| Turn, one card to come | 19.57% | -9.0062 points | -$21.01 | Fold |
Counts close to yours
The table shows 9 outs and the draws around it on the turn, all against the same two-thirds-pot bet. Each extra out adds about 2.17 points to the chance here.
The same draw against other bet sizes
Look down the margin column to see where the draw stops paying. Every row uses 9 outs on the turn and a bet of a different size.
Past 0.32 times the pot ($32.14 on a $100 pot) the price outruns your chance. Of the 12 sizes, 1 is a call for 9 outs on the turn.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +2.90 points | Call |
| third-pot | 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, this page | 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
Counting is exact: one card is left, 9 of 46 unseen cards help, and the chance is 19.57%.
These figures describe a clean spot. You pay the whole bet, which costs $66.67 of a $233.33 pot (28.57%), collect the whole pot on a hit, meet no more bets, and draw from 46 equally likely cards, with no adjustment for an opponent's hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How should you respond to a two-thirds-pot bet on the turn when you hold 9 outs?
Your chance, 19.57%, set against the 28.57% price gives -9.01 points and a fold. With a $100 pot, a $66.67 call and no more betting, the average value of the call is -$21.01.
How many outs do you need to call a two-thirds-pot bet on the turn?
The threshold is 14 outs. It gives 30.43%, clearing 28.57%, whereas 13 gives only 28.26%. Holding 9 puts you 5 below it, with a chance of 19.57%.
How many cards should you count when a two-thirds-pot bet arrives on the turn?
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 28.57% price that is a fold, with a margin of -9.01 points.
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