Verdict
Call
20 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come67.53%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+42.53 points
How the verdict is reached
With 20 outs on the flop you hit 67.53% of the time by the river, and a half-pot bet only asks for 25.00%. That 42.53-point cushion makes this a clear call.
A total of 20 outs tends to come from stacking several ways to improve. The next card is an out 42.55% of the time, 20 in 47.
Worked through on a $100 pot
- Pot when the bet arrives$100
- Bet$50
- Chips you put in$50
- Final pot if you call$200
- Net gain when you hit$150
- Net loss when you miss$50
- Probability of a hit67.53%
- Expected value of a call+$85.06
- Break-even equity25.00%
- Exact margin over the price+42.5301 points
- Outs that exactly reach the price6.23 outs
- Margin measured in outs+13.77 outs
Expected value says the same in dollars. Win the whole pot on a hit, lose your call on a miss, add no more betting, and the call gains $85.06 on average: $101.30 in, $16.23 out, +1.701 per dollar called.
The same comparison in odds: the odds against hitting are 0.48 : 1, and the pot lays 3 : 1 on a call.
One easy error is to use 33.33%, the bet over the pot before your call, as the price. The right price is 25.00%, and the mistaken margin would be +34.1967 points. The bet over the starting pot, 50.00%, would claim +17.5301 points.
What could go wrong before the call flips
The threshold is 7 outs, a chance of 27.84%. With 20 in hand you are 13 outs clear of it.
Later betting can cut into the call. You may surrender $125.96, or 2.52 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 | 25.00% | +42.53 points | +$85.06 | Call |
| $10 | 26.32% | +41.21 points | +$78.31 | Call |
| $25 | 28.57% | +38.96 points | +$68.18 | Call |
| $50 | 33.33% | +34.20 points | +$51.30 | Call |
| $100 | 50.00% | +17.53 points | +$17.53 | Call |
Which chance to use
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 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 67.53% | +42.5301 points | +$85.06 | Call |
| Next card only | 42.55% | +17.5532 points | +$35.11 | Call |
Neighbors of this draw
One out can change the answer, so the table lists the counts just below 20. Each out moves the chance roughly 2.50 points against the 25.00% price.
Where the bet size flips the call
Look down the margin column to see where the draw stops paying. Every row uses 20 outs on the flop and a bet of a different size.
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, this page | 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.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $50 / $200 = 25.00%. A hit takes the whole pot, no later betting happens, and the 47 unseen cards are all equally likely, with none removed for an opponent's cards.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How should you respond to a half-pot bet on the flop when you hold 20 outs?
By the numbers it is a call. 20 outs on the flop hit 67.53% by the river, a half-pot bet needs 25.00%, and the margin is +42.53 points. That assumes you call the full $50 and no more betting follows, and it values the call at +$85.06 per $100 pot.
What is the minimum number of outs for a half-pot bet on the flop?
Against 25.00%, the first count that works on the flop is 7, at 27.84%. At 6 the chance is 24.14%, too low. Compared with that threshold, your 20 outs are 13 above.
Does it matter whether you count one card or two against a half-pot bet?
Pick the number that matches the street plan: 67.53% for seeing both cards for one bet, 42.55% for paying card by card. Both face 25.00%, and the verdict is call either way.
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