Verdict
Call
11 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come41.72%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+21.72 points
Reading the verdict
Your draw is priced at 20.00% and it arrives 41.72% of the time. A lead of 21.72 points is wide enough that the call stands even if the numbers shift a little.
A total of 11 outs tends to come from stacking several ways to improve. The next card is an out 23.40% of the time, 11 in 47.
Worked through on a $100 pot
- Pot when the bet arrives$100
- Size of the bet$33.33
- Chips you put in$33.33
- Final pot if you call$166.67
- What a hit wins$133.33
- You lose on a miss$33.33
- Your chance to hit41.72%
- Average value of the call+$36.20
- Equity the call needs20.00%
- Unrounded margin+21.7206 points
- Outs that exactly reach the price4.91 outs
- Outs above the price+6.09 outs
If you win the whole pot on a hit and lose your call otherwise, with no more betting, calling gains $36.20 on average. Hits add $55.63 on average and misses cost $19.43 on average, or +1.086 per dollar called.
Put as odds, the draw is 1.4 : 1 against, and the pot offers 4 : 1 for the call.
Skipping your own call in the pot gives a price of 25.00% where 20.00% is correct, and a margin of +16.7206 points instead of +21.72 points. The starting pot gives 33.33% and a margin of +8.3873 points, which is wrong by even more.
How many outs you could lose
Against this bet the draw needs 5 outs at the least. You have 6 outs more than that, so the call has some room.
Later betting can cut into the call. You may surrender $86.77, or 2.60 times your call, after a hit and still break even.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +21.72 points | +$36.20 | Call |
| $10 | 21.28% | +20.44 points | +$32.03 | Call |
| $25 | 23.53% | +18.19 points | +$25.77 | Call |
| $50 | 28.57% | +13.15 points | +$15.34 | Call |
| $100 | 50.00% | -8.28 points | -$5.52 | Fold |
Two cards to come, or just one
No conflict here: 41.72% for two cards and 23.40% for one both give a call against the 20.00% price, so you need not decide which view applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 41.72% | +21.7206 points | +$36.20 | Call |
| Next card only | 23.40% | +3.4043 points | +$5.67 | Call |
Neighbors of this draw
Draws close to yours, on the same street and against the same bet: the price is fixed at 20.00%, and each out moves the chance about 3.24 points.
Every bet size, one draw
Look down the margin column to see where the draw stops paying. Every row uses 11 outs on the flop and a bet of a different size.
Past 2.52 times the pot ($251.96 on a $100 pot) the price outruns your chance. Of the 12 sizes, 10 are calls for 11 outs on the flop.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +25.05 points | Call |
| third-pot, this page | 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 | 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 20.00%, from $33.33 into $166.67, 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
Should you call a third-pot bet with 11 outs on the flop?
The answer is a call, with a margin of +21.72 points. 11 outs on the flop reach 41.72%; a bet of $33.33 into $100 needs 20.00%. Win the whole pot on a hit and lose the call on a miss, and the call is worth +$36.20 on average.
How many outs make a call correct against a third of the pot on the flop?
The threshold is 5 outs. It gives 20.35%, clearing 20.00%, whereas 4 gives only 16.47%. Holding 11 puts you 6 above it, with a chance of 41.72%.
One card or two: which number belongs next to the 20.00% price?
The river figure of 41.72% assumes no further betting; the next-card figure of 23.40% assumes you pay again on the turn. Against 20.00%, both say call, so you can use either.
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