Verdict
Call
20 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come67.53%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+37.53 points
Reading the verdict
The price is 30.00% and your chance is 67.53%. You sit 37.53 points above the line, which is a wide gap, so you call.
No single everyday draw has exactly 20 outs, so a count like this usually combines draws. One card from the 47 unseen helps 42.55% of the time.
A $100 pot, step by step
- Pot when the bet arrives$100
- Your opponent bets$75
- You call$75
- Total pot after calling$250
- Net gain when you hit$175
- What a miss costs$75
- Chance to hit by the river67.53%
- Calling is worth, on average+$93.83
- Equity needed to break even30.00%
- Unrounded margin+37.5301 points
- Fractional outs at the price7.59 outs
- Margin measured in outs+12.41 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $118.18 in and $24.35 out, so calling gains $93.83 on average at +1.251 per dollar called.
Written as odds, the pot lays 2.33 : 1 while the draw is 0.48 : 1 against.
The correct pot to divide by includes your call. Without it the price reads 42.86% rather than 30.00%, and the margin reads +24.6729 points. With the starting pot alone it reads 75.00% and -7.4699 points.
Your cushion over the price
If some outs turned out to be shared with a better hand, you could give up 12 outs and still call. The floor is 8, at 31.45%.
After a hit you could give back up to $138.94 on later streets, 1.85 times your call, before the call stops paying.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +37.53 points | +$93.83 | Call |
| $10 | 31.25% | +36.28 points | +$87.07 | Call |
| $25 | 33.33% | +34.20 points | +$76.94 | Call |
| $50 | 37.50% | +30.03 points | +$60.06 | Call |
| $100 | 50.00% | +17.53 points | +$26.30 | Call |
Which chance to use
You can skip the usual debate over one card versus two, because 42.55% and 67.53% both give a call against 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 67.53% | +37.5301 points | +$93.83 | Call |
| Next card only | 42.55% | +12.5532 points | +$31.38 | Call |
How the answer moves with outs
Here are the closest counts to 20 outs, priced against the same 30.00%. One fewer out moves your chance by about 2.50 points.
How bet size moves the answer
Your 67.53% chance is fixed, so the only thing that moves is the price. The 12 rows below price the call at every bet size on the flop.
The call holds at every one of the 12 sizes. 67.53% is higher than the price of even the largest bet.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +50.86 points | Call |
| third-pot | 20.00% | +47.53 points | Call |
| two-fifths-pot | 22.22% | +45.31 points | Call |
| half-pot | 25.00% | +42.53 points | Call |
| two-thirds-pot | 28.57% | +38.96 points | Call |
| three-quarter-pot, this page | 30.00% | +37.53 points | Call |
| pot-size | 33.33% | +34.20 points | Call |
| 1.25x-pot | 35.71% | +31.82 points | Call |
| 1.5x-pot | 37.50% | +30.03 points | Call |
| 2x-pot | 40.00% | +27.53 points | Call |
| 3x-pot | 42.86% | +24.67 points | Call |
| 4x-pot | 44.44% | +23.09 points | Call |
How this is computed
Counting is exact: the pairs of unseen cards with no out number 351 out of 1,081, so hitting by the river has chance 67.53%.
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
Are 20 outs on the flop worth a call against a bet of three quarters of the pot?
Verdict: call. A three-quarter-pot bet asks for 30.00% and you have 67.53%, a margin of +37.53 points. For a $75 call into a $100 pot, with no later bets and the whole pot won on a hit, the average is +$93.83.
How many outs make a call correct against three quarters of the pot on the flop?
The threshold is 8 outs. It gives 31.45%, clearing 30.00%, whereas 7 gives only 27.84%. Holding 20 puts you 12 above it, with a chance of 67.53%.
How many cards should you count when a three-quarter-pot bet arrives on the flop?
Match the number to the betting: 67.53% if all-in or checked down, 42.55% if you face another bet on the turn. The price is 30.00%, and both numbers agree on call.
Related pages
Check your own hands against the numbers
Bring a hand you played and we will work through the price, the chance to hit and the decision together.
Book a session