Verdict
Call
20 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come67.53%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price+34.20 points
Chance against price
This is one of the easier spots. 20 outs on the flop reach 67.53% by the river, the pot-size bet asks for just 33.33%, and the 34.20-point margin favors the call.
A count of 20 outs is usually the sum of more than one draw. Out of 47 unseen cards, one card helps 42.55% of the time.
A $100 pot, step by step
- Starting pot$100
- The bet$100
- Chips you put in$100
- Pot after your call$300
- What a hit wins$200
- You lose on a miss$100
- Probability of a hit67.53%
- Expected value of calling+$102.59
- Equity the call needs33.33%
- Exact margin over the price+34.1967 points
- Fractional outs at the price8.53 outs
- Margin measured in outs+11.47 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 $102.59 on average. Hits bring in $135.06, misses cost $32.47, and the ratio is +1.026 per dollar called.
As odds, 0.48 : 1 against hitting meets pot odds of 2 : 1.
The correct pot to divide by includes your call. Without it the price reads 50.00% rather than 33.33%, and the margin reads +17.5301 points.
How much room the call has
Count how many outs the call needs: 9 reach the 33.33% price, and you have 20. That leaves 11 outs of slack.
Your margin is worth $151.92 in later losses. Past that, 1.52 times your call, folding would have been better.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | +34.20 points | +$102.59 | Call |
| $10 | 34.48% | +33.05 points | +$95.84 | Call |
| $25 | 36.36% | +31.17 points | +$85.71 | Call |
| $50 | 40.00% | +27.53 points | +$68.83 | Call |
| $100 | 50.00% | +17.53 points | +$35.06 | Call |
Two views of the same draw
Whether you count one card or two, the answer is a call. The river figure is 67.53%, the next-card figure is 42.55%, and both are measured against 33.33%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 67.53% | +34.1967 points | +$102.59 | Call |
| Next card only | 42.55% | +9.2199 points | +$27.66 | Call |
Counts close to yours
Remove a few outs and watch the verdict. Every out is worth about 2.50 points on the flop, and the price stays at 33.33%.
How bet size moves the answer
How much does bet size matter? The price climbs from 16.67% to 44.44% across the list, while 20 outs stay at 67.53%.
Nothing in the list is too big to call: 20 outs reach 67.53% on the flop, above every price on the page.
| 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 | 30.00% | +37.53 points | Call |
| pot-size, this page | 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
No sampling is involved. On the flop there are 1,081 pairs of unseen cards, and 351 of them contain no out, which leaves 67.53% for at least one out.
The numbers are a baseline rather than a prediction for one hand. The price is 33.33%, from $100 into $300, 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 pot-size bet with 20 outs on the flop?
Reduce the question to a comparison of two numbers: 67.53% to hit and 33.33% to break even. The first minus the second is +34.20 points, which makes this a call, and the call averages +$102.59 on a $100 pot if no more betting follows.
What is the minimum number of outs for a pot-size bet on the flop?
Look for 9 outs. That is the smallest count whose chance, 34.97%, reaches the 33.33% price; 8 manages 31.45%. You have 20, so you are 11 ahead of the minimum.
Does it matter whether you count one card or two against a pot-size bet?
The river figure of 67.53% assumes no further betting; the next-card figure of 42.55% assumes you pay again on the turn. Against 33.33%, both say call, so you can use either.
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