Verdict
Call
20 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come67.53%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+47.53 points
Reading the verdict
Pay the third-pot bet and you get a better deal than the draw needs. You need 20.00%, you have 67.53%, and the 47.53-point difference is large.
20 out of 47 unseen cards is a combined count rather than one named draw, and one card hits 42.55% of the time.
A $100 pot, step by step
- The pot before betting$100
- The bet$33.33
- You call$33.33
- Total pot after calling$166.67
- Gain on a hit$133.33
- Loss on a miss$33.33
- Probability of a hit67.53%
- Expected value of calling+$79.22
- Equity needed to break even20.00%
- Margin, to four decimals+47.5301 points
- Fractional outs at the price4.91 outs
- Outs above the price+15.09 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 $79.22 on average. Hits bring in $90.04, misses cost $10.82, and the ratio is +2.377 per dollar called.
Put as odds, the draw is 0.48 : 1 against, and the pot offers 4 : 1 for the call.
Watch the pot you divide by. Leaving your call out turns 20.00% into 25.00%, and the margin into +42.5301 points. Dividing by the starting pot gives 33.33% and a margin of +34.1967 points, further from the truth.
Your cushion over the price
Against this bet the draw needs 5 outs at the least. You have 15 outs more than that, so the call has some room.
Your margin is worth $117.31 in later losses. Past that, 3.52 times your call, folding would have been better.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +47.53 points | +$79.22 | Call |
| $10 | 21.28% | +46.25 points | +$72.46 | Call |
| $25 | 23.53% | +44.00 points | +$62.33 | Call |
| $50 | 28.57% | +38.96 points | +$45.45 | Call |
| $100 | 50.00% | +17.53 points | +$11.69 | Call |
Two cards to come, or just one
The two chances agree on the verdict. 67.53% by the river and 42.55% on one card each lead to a call against 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 67.53% | +47.5301 points | +$79.22 | Call |
| Next card only | 42.55% | +22.5532 points | +$37.59 | Call |
Neighbors of this draw
Remove a few outs and watch the verdict. Every out is worth about 2.50 points on the flop, and the price stays at 20.00%.
Every bet size, one draw
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 20 outs on the flop.
Your chance is high enough that any bet in the table is a call. All 12 sizes clear with 67.53%.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +50.86 points | Call |
| third-pot, this page | 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 | 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 hit chance comes straight from combinations. Out of 1,081 pairs of unseen cards, 351 miss every out, so you hit 67.53% of the time.
Keep the assumptions in view: a full call ($33.33 into $166.67, or 20.00%), the whole pot on a hit, no more betting, and 47 unseen cards that are equally likely. The math does not know what the other player holds.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What is the right play with 20 outs when a third-pot bet comes on the flop?
Your chance, 67.53%, set against the 20.00% price gives +47.53 points and a call. With a $100 pot, a $33.33 call and no more betting, the average value of the call is +$79.22.
What count of outs clears the price of a third-pot bet on the flop?
5 outs is the line. At 5 the chance is 20.35%, enough for 20.00%; one fewer gives 16.47%, which is not. Your 20 outs sit 15 above it on the flop, at 67.53%.
When is the next-card chance the better comparison?
Two cards cost one bet only if the hand really ends here, and then 67.53% applies. If you will face the turn bet as well, 42.55% applies. Versus 20.00%, both views give a call.
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