Verdict
Call
9 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come34.97%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+6.40 points
Reading the verdict
The odds you are given are better than the odds you need: 28.57% needed, 34.97% held, 6.40 points to spare.
The count matches a flush draw, so you can read this page as that draw. The very next card completes it 19.15% of the time, 9 out of 47.
Counting the chips on a $100 pot
- Pot when the bet arrives$100
- The bet$66.67
- Cost to call$66.67
- Pot with your call in$233.33
- Gain on a hit$166.67
- Loss on a miss$66.67
- Your chance to hit34.97%
- Calling is worth, on average+$14.92
- Equity needed to break even28.57%
- Exact margin over the price+6.3962 points
- Break-even count of outs7.20 outs
- Outs above the price+1.80 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 $14.92 on average. Hits bring in $58.28, misses cost $43.35, and the ratio is +0.224 per dollar called.
As odds, 1.86 : 1 against hitting meets pot odds of 2.5 : 1.
Do not forget your own call. Dividing the bet by the pot without it gives 40.00%, not 28.57%, and would show a margin of -5.0324 points. The bet over the starting pot, 66.67%, is worse and would show -31.6990 points.
What could go wrong before the call flips
With 9 outs you sit 1 out above the minimum of 8 that a two-thirds-pot bet requires on the flop.
If hitting means paying off a bigger hand later, the call survives a loss of $42.68. That is 0.64 times the $66.67 call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +6.40 points | +$14.92 | Call |
| $10 | 29.85% | +5.12 points | +$11.43 | Call |
| $25 | 32.00% | +2.97 points | +$6.18 | Call |
| $50 | 36.36% | -1.40 points | -$2.56 | Fold |
| $100 | 50.00% | -15.03 points | -$20.04 | Fold |
Two cards to come, or just one
The verdict depends on how many cards you get to see. The runout figure is 34.97% (call), the next-card figure is 19.15% (fold), and the price is 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 34.97% | +6.3962 points | +$14.92 | Call |
| Next card only | 19.15% | -9.4225 points | -$21.99 | Fold |
A few outs either way
One out can change the answer, so the table lists the counts on either side of 9. Each out adds roughly 3.42 points against the 28.57% price.
Every bet size, one draw
Look down the margin column to see where the draw stops paying. Every row uses 9 outs on the flop and a bet of a different size.
The largest bet this draw can call on the flop is 1.16 times the pot ($116.31 on a $100 pot). 9 outs call 7 of the 12 bet sizes listed.
| 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, this page | 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.
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 47 equally likely cards, with no adjustment for an opponent's hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 9 outs when a two-thirds-pot bet comes on the flop?
By the numbers it is a call. 9 outs on the flop hit 34.97% by the river, a two-thirds-pot bet needs 28.57%, and the margin is +6.40 points. That assumes you call the full $66.67 and no more betting follows, and it values the call at +$14.92 per $100 pot.
How many outs make a call correct against two thirds of the pot on the flop?
The threshold is 8 outs. It gives 31.45%, clearing 28.57%, whereas 7 gives only 27.84%. Holding 9 puts you 1 above it, with a chance of 34.97%.
One card or two: which number belongs next to the 28.57% price?
Two cards cost one bet only if the hand really ends here. In that case use 34.97%. If you will face the turn bet as well, use 19.15%. Versus 28.57%, the first is a call and the second is a fold.
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