Verdict
Call
14 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come51.16%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price+21.16 points
The price of the call
The call is clearly worth making. 51.16% is your chance to hit, 30.00% is the price, and the gap between them is 21.16 points.
A total of 14 outs tends to come from stacking several ways to improve. The next card is an out 29.79% of the time, 14 in 47.
Worked through on a $100 pot
- Pot when the bet arrives$100
- The bet$75
- Your call$75
- Pot with your call in$250
- You can win on a hit$175
- Loss on a miss$75
- How often you hit51.16%
- Calling is worth, on average+$52.89
- Price of the call30.00%
- Unrounded margin+21.1563 points
- Outs at break-even7.59 outs
- Outs above the price+6.41 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 $52.89 on average. Hits bring in $89.52, misses cost $36.63, and the ratio is +0.705 per dollar called.
As odds, 0.95 : 1 against hitting meets pot odds of 2.33 : 1.
Counting the pot without your call makes the price look like 42.86%, when the real price is 30.00%. On that mistaken price the margin would read +8.2992 points; on 75.00%, the bet over the starting pot, it would read -23.8437 points.
Reverse implied odds and your margin
Against this bet the draw needs 8 outs at the least. You have 6 outs more than that, so the call has some room.
The call keeps its edge until you lose $103.39 on later streets after hitting. That is 1.38 times the $75 you pay now.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | +21.16 points | +$52.89 | Call |
| $10 | 31.25% | +19.91 points | +$47.78 | Call |
| $25 | 33.33% | +17.82 points | +$40.10 | Call |
| $50 | 37.50% | +13.66 points | +$27.31 | Call |
| $100 | 50.00% | +1.16 points | +$1.73 | Call |
Which chance to use
The verdict depends on how many cards you get to see. The runout figure is 51.16% (call), the next-card figure is 29.79% (fold), and the price is 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 51.16% | +21.1563 points | +$52.89 | Call |
| Next card only | 29.79% | -0.2128 points | -$0.53 | Fold |
Neighbors of this draw
Here are the neighbors of 14 outs, priced against the same 30.00%. One more out lifts your chance by about 2.96 points.
How bet size moves the answer
Your 51.16% chance is fixed, so the only thing that moves is the price. The 12 rows below price the call at every bet size on the flop.
No bet size here outprices a 51.16% 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% | +34.49 points | Call |
| third-pot | 20.00% | +31.16 points | Call |
| two-fifths-pot | 22.22% | +28.93 points | Call |
| half-pot | 25.00% | +26.16 points | Call |
| two-thirds-pot | 28.57% | +22.58 points | Call |
| three-quarter-pot, this page | 30.00% | +21.16 points | Call |
| pot-size | 33.33% | +17.82 points | Call |
| 1.25x-pot | 35.71% | +15.44 points | Call |
| 1.5x-pot | 37.50% | +13.66 points | Call |
| 2x-pot | 40.00% | +11.16 points | Call |
| 3x-pot | 42.86% | +8.30 points | Call |
| 4x-pot | 44.44% | +6.71 points | Call |
How this is computed
The hit chance comes straight from combinations. Out of 1,081 pairs of unseen cards, 528 miss every out, so you hit 51.16% of the time.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $75 / $250 = 30.00%. 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
What does the math say about calling a bet of three quarters of the pot with 14 outs on the flop?
Verdict: call. A three-quarter-pot bet asks for 30.00% and you have 51.16%, a margin of +21.16 points. For a $75 call into a $100 pot, with no later bets and the whole pot won on a hit, the average is +$52.89.
How many outs are enough to continue against a bet of 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 14, so you are 6 ahead of the minimum.
Does it matter whether you count one card or two against a three-quarter-pot bet?
Count two cards, 51.16%, when the bet is the last money going in, and one card, 29.79%, when the next street brings another bet. At a price of 30.00%, the two numbers give a call and a fold.
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