Verdict
Call
16 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come56.98%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price+28.41 points
The call in numbers
The call is clearly worth making. 56.98% is your chance to hit, 28.57% is the price, and the gap between them is 28.41 points.
You will reach 16 outs by adding up separate draws. With 47 cards unseen, the next card helps 34.04% of the time.
The $100 pot example
- Starting pot$100
- Your opponent bets$66.67
- Chips you put in$66.67
- Total pot after calling$233.33
- Gain on a hit$166.67
- What a miss costs$66.67
- How often you hit56.98%
- Average value of the call+$66.30
- Equity the call needs28.57%
- Your chance minus the price, unrounded+28.4128 points
- Outs at break-even7.20 outs
- Outs to spare, exactly+8.80 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $94.97, the average loss is $28.68, and calling gains $66.30 on average, or +0.994 per dollar called.
In odds, you face 0.75 : 1 against you and the pot pays 2.5 : 1.
Counting the pot without your call makes the price look like 40.00%, when the real price is 28.57%. On that mistaken price the margin would read +16.9843 points; on 66.67%, the bet over the starting pot, it would read -9.6824 points.
How safe the call is
The fewest outs that still call a two-thirds-pot bet on the flop is 8. You hold 16, so you have 8 outs to spare before the call flips to a fold.
Break-even on later streets sits at $116.34 given back, or 1.75 times your call.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | +28.41 points | +$66.30 | Call |
| $10 | 29.85% | +27.13 points | +$60.60 | Call |
| $25 | 32.00% | +24.98 points | +$52.05 | Call |
| $50 | 36.36% | +20.62 points | +$37.80 | Call |
| $100 | 50.00% | +6.98 points | +$9.31 | Call |
Two views of the same draw
The two chances agree on the verdict. 56.98% by the river and 34.04% on one card each lead to a call against 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 56.98% | +28.4128 points | +$66.30 | Call |
| Next card only | 34.04% | +5.4711 points | +$12.77 | Call |
Draws around this one
The table shows 16 outs and the draws around it on the flop, all against the same two-thirds-pot bet. Each extra out adds about 2.78 points to the chance here.
How bet size moves the answer
Bigger bets ask for more equity while your chance stays at 56.98%. Here is every bet size against the same draw, with the row for this page marked.
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 | 25.00% | +31.98 points | Call |
| two-thirds-pot, this page | 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
Here is how 56.98% was found. Deal every pair of the 47 unseen cards: 465 of 1,081 pairs contain no out.
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
Call or fold with 16 outs on the flop against a bet of two thirds of the pot?
The answer is a call, with a margin of +28.41 points. 16 outs on the flop reach 56.98%; a bet of $66.67 into $100 needs 28.57%. Win the whole pot on a hit and lose the call on a miss, and the call is worth +$66.30 on average.
What count of outs clears the price of a two-thirds-pot bet on the flop?
Look for 8 outs. That is the smallest count whose chance, 31.45%, reaches the 28.57% 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?
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 28.57%, both say 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