Verdict
Call
11 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come41.72%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+13.15 points
Your chance and the price
41.72% against 28.57%: the draw beats the price by 13.15 points. On this flop against a two-thirds-pot bet, that is a comfortable call.
Counts like 11 outs often come from a mix of draws. Of 47 unseen cards, 11 help, or 23.40% on one card.
The $100 pot example
- The pot before betting$100
- Bet$66.67
- Chips you put in$66.67
- Final pot if you call$233.33
- Gain on a hit$166.67
- Net loss when you miss$66.67
- Your chance to hit41.72%
- Expected value of a call+$30.68
- Equity the call needs28.57%
- Margin, to four decimals+13.1492 points
- Break-even count of outs7.20 outs
- Your outs minus break-even outs+3.80 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $30.68 on average. Hits add $69.53 on average and misses cost $38.85 on average, or +0.460 per dollar called.
Put as odds, the draw is 1.4 : 1 against, and the pot offers 2.5 : 1 for the 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 +1.7206 points. Using the bet over the starting pot, 66.67%, is further off and would put it at -24.9460 points.
How many outs you could lose
Against this bet the draw needs 8 outs at the least. You have 3 outs more than that, so the call has some room.
Think of $73.54 as your safety room: the most you can give back after a hit, 1.10 times your call, with the call still level.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +13.15 points | +$30.68 | Call |
| $10 | 29.85% | +11.87 points | +$26.51 | Call |
| $25 | 32.00% | +9.72 points | +$20.25 | Call |
| $50 | 36.36% | +5.36 points | +$9.82 | Call |
| $100 | 50.00% | -8.28 points | -$11.04 | Fold |
One card or two
Same draw, two answers. Count both cards and the chance is 41.72%, a call; count just the next card and it is 23.40%, a fold. The price in both cases is 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 41.72% | +13.1492 points | +$30.68 | Call |
| Next card only | 23.40% | -5.1672 points | -$12.06 | Fold |
Draws around this one
One out can change the answer, so the table lists the counts on either side of 11. Each out adds roughly 3.24 points against the 28.57% price.
Where the bet size flips the call
Keep 11 outs and change only the bet. The price rises from the smallest size to the largest, and the two-thirds-pot row is marked as this page.
11 outs stop paying at 2.52 times the pot ($251.96 on a $100 pot). The call holds up against 10 of the 12 bet sizes.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +25.05 points | Call |
| third-pot | 20.00% | +21.72 points | Call |
| two-fifths-pot | 22.22% | +19.50 points | Call |
| half-pot | 25.00% | +16.72 points | Call |
| two-thirds-pot, this page | 28.57% | +13.15 points | Call |
| three-quarter-pot | 30.00% | +11.72 points | Call |
| pot-size | 33.33% | +8.39 points | Call |
| 1.25x-pot | 35.71% | +6.01 points | Call |
| 1.5x-pot | 37.50% | +4.22 points | Call |
| 2x-pot | 40.00% | +1.72 points | Call |
| 3x-pot | 42.86% | -1.14 points | Fold |
| 4x-pot | 44.44% | -2.72 points | Fold |
Pages that use the same math
How this is computed
Counting is exact: the pairs of unseen cards with no out number 630 out of 1,081, so hitting by the river has chance 41.72%.
The numbers are a baseline rather than a prediction for one hand. The price is 28.57%, from $66.67 into $233.33, and the chance assumes a whole pot won on a hit, no more betting, 47 equally likely unseen cards, and no cards removed for the other player.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 11 outs when a two-thirds-pot bet comes on the flop?
The answer is a call, with a margin of +13.15 points. 11 outs on the flop reach 41.72%; a bet of $66.67 into $100 needs 28.57%. Win the whole pot on a hit and lose the call on a miss, and the call is worth +$30.68 on average.
How many outs are enough to continue against a bet of 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 11 puts you 3 above it, with a chance of 41.72%.
Which hit chance fits a two-thirds-pot bet on the flop?
Match the number to the betting. All-in or checked down: 41.72%. Facing another bet on the turn: 23.40%. The price is 28.57%, so the verdicts are call and fold in that order.
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