Verdict
Call
20 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come67.53%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+38.96 points
What the numbers say
Pay the two-thirds-pot bet and you get a better deal than the draw needs. You need 28.57%, you have 67.53%, and the 38.96-point difference is large.
Think of 20 outs as a running total of every card that improves you. 20 of the 47 unseen cards qualify, which is 42.55% on one card.
Worked through on a $100 pot
- Pot when the bet arrives$100
- Your opponent bets$66.67
- Your call$66.67
- Pot with your call in$233.33
- What a hit wins$166.67
- You lose on a miss$66.67
- How often you hit67.53%
- Expected value of a call+$90.90
- Equity needed to break even28.57%
- Margin, to four decimals+38.9586 points
- Fractional outs at the price7.20 outs
- Margin measured in outs+12.80 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling gains $90.90 on average. The hit side averages $112.55, the miss side $21.65, and each dollar called returns +1.364.
In odds, you face 0.48 : 1 against you and the pot pays 2.5 : 1.
The price is 28.57% because your call goes into the pot too. Leave it out and you get 40.00%, a margin of +27.5301 points that does not exist; use the starting pot instead and 66.67% puts the margin at +0.8634 points.
Reverse implied odds and your margin
8 outs is the line for a two-thirds-pot bet on the flop. Your 20 sit 12 outs above it, and the chance at the line is 31.45%.
After a hit you could give back up to $134.61 on later streets, 2.02 times your call, before the call stops paying.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +38.96 points | +$90.90 | Call |
| $10 | 29.85% | +37.68 points | +$84.15 | Call |
| $25 | 32.00% | +35.53 points | +$74.02 | Call |
| $50 | 36.36% | +31.17 points | +$57.14 | Call |
| $100 | 50.00% | +17.53 points | +$23.37 | 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 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 67.53% | +38.9586 points | +$90.90 | Call |
| Next card only | 42.55% | +13.9818 points | +$32.62 | Call |
Nearby draws
Draws near yours, on the same street and against the same bet: the price is fixed at 28.57%, and each out moves the chance about 2.50 points.
Every bet size, one draw
Bet size sets the price, so the verdict changes as you scan the table. The two-thirds-pot bet of this page is marked in the first column.
20 outs are strong enough to call every size listed. A chance of 67.53% beats even the biggest price in the table.
| 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, this page | 28.57% | +38.96 points | Call |
| three-quarter-pot | 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
The chance to hit is the exact closed form, with no simulation. From the flop, 351 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 351 / 1,081, which is 67.53%.
What is held fixed: the call equals the bet, so the price is $66.67 / $233.33 = 28.57%; the pot is won whole on a hit; there is no further betting; and each of the 47 unseen cards is as likely as any other. Opponent cards are not removed.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 20 outs when a two-thirds-pot bet comes on the flop?
Your chance, 67.53%, set against the 28.57% price gives +38.96 points and a call. With a $100 pot, a $66.67 call and no more betting, the average value of the call is +$90.90.
What is the fewest outs that can call a two-thirds-pot bet on the flop?
You need at least 8 outs against a two-thirds-pot bet on the flop. That count hits 31.45% against 28.57% needed, and 7 falls short at 27.84%. With 20 you are 12 past the minimum.
One card or two: which number belongs next to the 28.57% price?
Both figures are right for their own situation: 67.53% with no more betting, 42.55% when the turn brings a bet. Facing 28.57%, each one gives a call.
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