Verdict
Call
16 outs, flop, half-pot bet
- Chance to hit by the rivertwo cards to come56.98%
- Equity the call needs$50 into a pot of $20025.00%
- Margin over the priceyour chance minus the price+31.98 points
What the numbers say
This is one of the easier spots. 16 outs on the flop reach 56.98% by the river, the half-pot bet asks for just 25.00%, and the 31.98-point margin favors the call.
A count of 16 outs is usually the sum of more than one draw. Out of 47 unseen cards, one card helps 34.04% of the time.
The $100 pot example
- Pot when the bet arrives$100
- Your opponent bets$50
- Chips you put in$50
- Pot after your call$200
- Net gain when you hit$150
- What a miss costs$50
- Your chance to hit56.98%
- Expected value of calling+$63.97
- Equity needed to break even25.00%
- Your chance minus the price, unrounded+31.9843 points
- Outs at break-even6.23 outs
- Outs above the price+9.77 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $85.48, the average loss is $21.51, and calling gains $63.97 on average, or +1.279 per dollar called.
In odds, you face 0.75 : 1 against you and the pot pays 3 : 1.
The correct pot to divide by includes your call. Without it the price reads 33.33% rather than 25.00%, and the margin reads +23.6509 points. With the starting pot alone it reads 50.00% and +6.9843 points.
What could go wrong before the call flips
With 16 outs you sit 9 outs above the minimum of 7 that a half-pot bet requires on the flop.
Think of $112.26 as your safety room: the most you can give back after a hit, 2.25 times your call, with the call still level.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 25.00% | +31.98 points | +$63.97 | Call |
| $10 | 26.32% | +30.67 points | +$58.27 | Call |
| $25 | 28.57% | +28.41 points | +$49.72 | Call |
| $50 | 33.33% | +23.65 points | +$35.48 | Call |
| $100 | 50.00% | +6.98 points | +$6.98 | Call |
Which chance to use
You can skip the usual debate over one card versus two, because 34.04% and 56.98% both give a call against 25.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 56.98% | +31.9843 points | +$63.97 | Call |
| Next card only | 34.04% | +9.0426 points | +$18.09 | Call |
The call as outs change
One out can change the answer, so the table lists the counts on either side of 16. Each out adds roughly 2.78 points against the 25.00% price.
How bet size moves the answer
Look down the margin column to see where the draw stops paying. Every row uses 16 outs on the flop and a bet of a different size.
No bet size here outprices a 56.98% chance. The call works at all 12 sizes, since the highest price is 44.44%.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +40.32 points | Call |
| third-pot | 20.00% | +36.98 points | Call |
| two-fifths-pot | 22.22% | +34.76 points | Call |
| half-pot, this page | 25.00% | +31.98 points | Call |
| two-thirds-pot | 28.57% | +28.41 points | Call |
| three-quarter-pot | 30.00% | +26.98 points | Call |
| pot-size | 33.33% | +23.65 points | Call |
| 1.25x-pot | 35.71% | +21.27 points | Call |
| 1.5x-pot | 37.50% | +19.48 points | Call |
| 2x-pot | 40.00% | +16.98 points | Call |
| 3x-pot | 42.86% | +14.13 points | Call |
| 4x-pot | 44.44% | +12.54 points | Call |
How this is computed
Everything is computed from the closed form. Pairs without an out: 465 of 1,081. The rest, 56.98%, hold at least one out.
Keep the assumptions in view: a full call ($50 into $200, or 25.00%), 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
Is a call correct with 16 outs against a half-pot bet on the flop?
Reduce the question to a comparison of two numbers: 56.98% to hit and 25.00% to break even. The first minus the second is +31.98 points, which makes this a call, and the call averages +$63.97 on a $100 pot if no more betting follows.
How many outs make a call correct against half the pot on the flop?
7 outs is the line. At 7 the chance is 27.84%, enough for 25.00%; one fewer gives 24.14%, which is not. Your 16 outs sit 9 above it on the flop, at 56.98%.
Is the by-the-river chance the right one to use on the flop?
It depends on what follows, but here it does not matter. If the hand ends here, count both cards: 56.98%. If another bet is coming on the turn, count one card: 34.04%. Against 25.00%, both say call.
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