Verdict
Call
16 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come56.98%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+26.98 points
The price of the call
The price is 30.00% and your chance is 56.98%. You sit 26.98 points above the line, which is a wide gap, so you 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
- The pot before betting$100
- Bet$75
- Chips you put in$75
- Pot with your call in$250
- Net gain when you hit$175
- You lose on a miss$75
- Probability of a hit56.98%
- Expected value of a call+$67.46
- Price of the call30.00%
- Exact margin over the price+26.9843 points
- Outs at break-even7.59 outs
- Outs to spare, exactly+8.41 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $99.72, the average loss is $32.26, and calling gains $67.46 on average, or +0.899 per dollar called.
Written as odds, the pot lays 2.33 : 1 while the draw is 0.75 : 1 against.
Watch the pot you divide by. Leaving your call out turns 30.00% into 42.86%, and the margin into +14.1271 points. Dividing by the starting pot gives 75.00% and a margin of -18.0157 points, further from the truth.
How many outs you could lose
8 outs is the line for a three-quarter-pot bet on the flop. Your 16 sit 8 outs above it, and the chance at the line is 31.45%.
Think of $118.38 as your safety room: the most you can give back after a hit, 1.58 times your call, with the call still level.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +26.98 points | +$67.46 | Call |
| $10 | 31.25% | +25.73 points | +$61.76 | Call |
| $25 | 33.33% | +23.65 points | +$53.21 | Call |
| $50 | 37.50% | +19.48 points | +$38.97 | Call |
| $100 | 50.00% | +6.98 points | +$10.48 | Call |
By the river or next card
You can skip the usual debate over one card versus two, because 34.04% and 56.98% both give a call against 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 56.98% | +26.9843 points | +$67.46 | Call |
| Next card only | 34.04% | +4.0426 points | +$10.11 | Call |
One out more or less
Here are the neighbors of 16 outs, priced against the same 30.00%. One more out lifts your chance by about 2.78 points.
How bet size moves the answer
Bet size sets the price, so the verdict changes as you scan the table. The three-quarter-pot bet of this page is marked in the first column.
A draw this strong has no ceiling inside the table. 56.98% tops every price from the smallest bet to the largest.
| 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 | 25.00% | +31.98 points | Call |
| two-thirds-pot | 28.57% | +28.41 points | Call |
| three-quarter-pot, this page | 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
The number is exact rather than estimated. 465 of the 1,081 pairs that could come are blanks, which leaves 56.98% for a hit.
The price is call / (pot + bet + call), here $75 / $250 = 30.00%, and the margin is your chance minus it. The page assumes you call the whole bet, win the whole pot whenever you hit, and see no more betting. All 47 unseen cards are equally likely and none is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against one hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Call or fold with 16 outs on the flop against a bet of three quarters of the pot?
Math says call. The three-quarter-pot bet of $75 needs 30.00% equity, 16 outs on the flop give 56.98%, and the margin is +26.98 points. Assuming a whole pot won on a hit and no further bets, the call is worth +$67.46 on average.
How many outs make a call correct against three quarters of the pot on the flop?
Look for 8 outs. That is the smallest count whose chance, 31.45%, reaches the 30.00% price; 7 manages 27.84%. You have 16, so you are 8 ahead of the minimum.
When is the next-card chance the better comparison?
Both figures are right for their own situation: 56.98% with no more betting, 34.04% when the turn brings a bet. Facing 30.00%, each one gives a call.
Related pages
Check your own hands against the numbers
Bring a hand you played and we will work through the price, the chance to hit and the decision together.
Book a session