Verdict
Fold
7 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come27.84%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price-5.49 points
Chance against price
Your 27.84% chance falls below the 33.33% price by 5.49 points. The shortfall is real, and the call loses money on average.
You will reach 7 outs by adding up separate draws. With 47 cards unseen, the next card helps 14.89% of the time.
A $100 pot, step by step
- The pot before betting$100
- Size of the bet$100
- Cost to call$100
- Total pot after calling$300
- What a hit wins$200
- What a miss costs$100
- Probability of a hit27.84%
- Expected value of a call-$16.47
- Equity needed to break even33.33%
- Margin, to four decimals-5.4887 points
- Break-even count of outs8.53 outs
- Outs to spare, exactly-1.53 outs
Assume the whole pot goes to you when you hit, the call is lost when you miss, and nothing more is bet. Calling then loses $16.47 on average: $55.69 from hits, minus $72.16 from misses, -0.165 per dollar called.
Odds say the same thing. Hitting is 2.59 : 1 against, and the pot lays 2 : 1.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 50.00% instead of 33.33% and would put your margin at -22.1554 points.
Implied odds that would change the answer
Break-even needs $59.14 of future winnings on top of the $300 already in the pot, which is 0.59 times the cost of your call.
The smallest count that pays for a pot-size bet is 9 outs at 34.97%. You hold 7, which is 2 outs fewer.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | -5.49 points | -$16.47 | Fold |
| $50 | 28.57% | -0.73 points | -$2.54 | Fold |
| $100 | 25.00% | +2.84 points | +$11.38 | Call |
| $250 | 18.18% | +9.66 points | +$53.15 | Call |
| $500 | 12.50% | +15.34 points | +$122.76 | Call |
Next card or river
One card or two, the call comes out the same way. 14.89% on the next card and 27.84% by the river both sit on the fold side of 33.33%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 27.84% | -5.4887 points | -$16.47 | Fold |
| Next card only | 14.89% | -18.4397 points | -$55.32 | Fold |
Draws around this one
Here are the neighbors of 7 outs, priced against the same 33.33%. One more out lifts your chance by about 3.61 points.
Every bet size, one draw
Bigger bets ask for more equity while your chance stays at 27.84%. Here is every bet size against the same draw, with the row for this page marked.
A bet larger than 0.63 times the pot ($62.84 on a $100 pot) asks for more than 27.84%. For this draw, 4 of the 12 sizes are calls.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +11.18 points | Call |
| third-pot | 20.00% | +7.84 points | Call |
| two-fifths-pot | 22.22% | +5.62 points | Call |
| half-pot | 25.00% | +2.84 points | Call |
| two-thirds-pot | 28.57% | -0.73 points | Fold |
| three-quarter-pot | 30.00% | -2.16 points | Fold |
| pot-size, this page | 33.33% | -5.49 points | Fold |
| 1.25x-pot | 35.71% | -7.87 points | Fold |
| 1.5x-pot | 37.50% | -9.66 points | Fold |
| 2x-pot | 40.00% | -12.16 points | Fold |
| 3x-pot | 42.86% | -15.01 points | Fold |
| 4x-pot | 44.44% | -16.60 points | Fold |
How this is computed
The chance to hit is the exact closed form, with no simulation. From the flop, 780 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 780 / 1,081, which is 27.84%.
The price is call / (pot + bet + call), here $100 / $300 = 33.33%, 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 7 outs on the flop against a bet of the full pot?
Your chance, 27.84%, set against the 33.33% price gives -5.49 points and a fold. With a $100 pot, a $100 call and no more betting, the average value of the call is -$16.47.
How many outs do you need to call a pot-size bet on the flop?
Against 33.33%, the first count that works on the flop is 9, at 34.97%. At 8 the chance is 31.45%, too low. Compared with that threshold, your 7 outs are 2 below.
Which chance should you compare with the price, the next card or the river?
It depends on what follows, but here it does not matter. If the hand ends here, count both cards: 27.84%. If another bet is coming on the turn, count one card: 14.89%. Against 33.33%, both say fold.
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