Verdict
Call
11 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come41.72%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+11.72 points
Reading the verdict
Pay the three-quarter-pot bet and you get a better deal than the draw needs. You need 30.00%, you have 41.72%, and the 11.72-point difference is large.
You will reach 11 outs by adding up separate draws. With 47 cards unseen, the next card helps 23.40% of the time.
Counting the chips on a $100 pot
- The pot before betting$100
- Your opponent bets$75
- Your call$75
- Pot with your call in$250
- You can win on a hit$175
- You lose on a miss$75
- How often you hit41.72%
- Expected value of a call+$29.30
- Price of the call30.00%
- Margin, to four decimals+11.7206 points
- Outs at break-even7.59 outs
- Outs to spare, exactly+3.41 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $73.01 in and $43.71 out, so calling gains $29.30 on average at +0.391 per dollar called.
Written as odds, the pot lays 2.33 : 1 while the draw is 1.4 : 1 against.
Watch the pot you divide by. Leaving your call out turns 30.00% into 42.86%, and the margin into -1.1365 points. Dividing by the starting pot gives 75.00% and a margin of -33.2794 points, further from the truth.
How many outs you could lose
Count how many outs the call needs: 8 reach the 30.00% price, and you have 11. That leaves 3 outs of slack.
Later betting can cut into the call. You may surrender $70.23, or 0.94 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 | 30.00% | +11.72 points | +$29.30 | Call |
| $10 | 31.25% | +10.47 points | +$25.13 | Call |
| $25 | 33.33% | +8.39 points | +$18.87 | Call |
| $50 | 37.50% | +4.22 points | +$8.44 | Call |
| $100 | 50.00% | -8.28 points | -$12.42 | Fold |
Which chance to use
The verdict depends on how many cards you get to see. The runout figure is 41.72% (call), the next-card figure is 23.40% (fold), and the price is 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 41.72% | +11.7206 points | +$29.30 | Call |
| Next card only | 23.40% | -6.5957 points | -$16.49 | Fold |
One out more or less
Here are the neighbors of 11 outs, priced against the same 30.00%. One more out lifts your chance by about 3.24 points.
Every bet size, one draw
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 11 outs stay at 41.72%.
The ceiling for a call is a bet of 2.52 times the pot ($251.96 on a $100 pot). 10 out of 12 sizes sit under it on the flop.
| 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 | 28.57% | +13.15 points | Call |
| three-quarter-pot, this page | 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 |
How this is computed
Here is how 41.72% was found. Deal every pair of the 47 unseen cards: 630 of 1,081 pairs contain no out.
The price is call / (pot + bet + call), here $75 / $250 = 30.00%, and the margin is your chance minus it. The page assumes you call the whole bet, win the whole pot whenever you hit, and see no more betting. All 47 unseen cards are equally likely and none is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against one hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What does the math say about calling a bet of three quarters of the pot with 11 outs on the flop?
By the numbers it is a call. 11 outs on the flop hit 41.72% by the river, a three-quarter-pot bet needs 30.00%, and the margin is +11.72 points. That assumes you call the full $75 and no more betting follows, and it values the call at +$29.30 per $100 pot.
At what count of outs does a three-quarter-pot bet on the flop become a call?
To call a three-quarter-pot bet on the flop you want 8 outs or more. 8 reach 31.45% and 7 reach 27.84%, with 30.00% as the bar. Your 11 outs are 3 over.
Does it matter whether you count one card or two against a three-quarter-pot bet?
Pick the number that matches the street plan: 41.72% for seeing both cards for one bet, 23.40% for paying card by card. Both face 30.00%, and they lead to call and fold in that order.
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