Verdict
Fold
6 outs, flop, three-quarter-pot bet
- Chance to hit by the rivertwo cards to come24.14%
- Equity the call needs$75 into a pot of $25030.00%
- Margin over the priceyour chance minus the price-5.86 points
What the numbers say
The odds you are given are worse than the odds you need: 30.00% needed, 24.14% held, 5.86 points missing.
6 out of 47 unseen cards is the shape of two overcards, and a single card hits 12.77% of the time.
One hand, in dollars
- Pot before the bet$100
- The bet$75
- You call$75
- Final pot if you call$250
- Net gain when you hit$175
- Loss on a miss$75
- Probability of a hit24.14%
- Expected value of a call-$14.64
- Price of the call30.00%
- Exact margin over the price-5.8557 points
- Break-even count of outs7.59 outs
- Outs above the price-1.59 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call loses $14.64 on average. The hit side averages $42.25, the miss side $56.89, and each dollar called returns -0.195.
Odds say the same thing. Hitting is 3.14 : 1 against, and the pot lays 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 -18.7128 points; on 75.00%, the bet over the starting pot, it would read -50.8557 points.
What implied odds would have to do
The call becomes fair only if a hit brings in $60.63 more after the draw arrives. Measured against the $75 you pay, that is 0.81 times your call.
Reaching 30.00% takes 8 outs on the flop, which hit 31.45%. With 6, the distance is 2 outs.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 30.00% | -5.86 points | -$14.64 | Fold |
| $50 | 25.00% | -0.86 points | -$2.57 | Fold |
| $100 | 21.43% | +2.72 points | +$9.51 | Call |
| $250 | 15.00% | +9.14 points | +$45.72 | Call |
| $500 | 10.00% | +14.14 points | +$106.08 | Call |
Two cards to come, or just one
You can skip the usual debate over one card versus two, because 12.77% and 24.14% both give a fold against 30.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 24.14% | -5.8557 points | -$14.64 | Fold |
| Next card only | 12.77% | -17.2340 points | -$43.09 | Fold |
The call as outs change
One out can change the answer, so the table lists the counts on either side of 6. Each out adds roughly 3.70 points against the 30.00% price.
Other bet sizes for this draw
Keep 6 outs and change only the bet. The price rises from the smallest size to the largest, and the three-quarter-pot row is marked as this page.
6 outs stop paying at 0.47 times the pot ($46.69 on a $100 pot). The call holds up against 3 of the 12 bet sizes.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +7.48 points | Call |
| third-pot | 20.00% | +4.14 points | Call |
| two-fifths-pot | 22.22% | +1.92 points | Call |
| half-pot | 25.00% | -0.86 points | Fold |
| two-thirds-pot | 28.57% | -4.43 points | Fold |
| three-quarter-pot, this page | 30.00% | -5.86 points | Fold |
| pot-size | 33.33% | -9.19 points | Fold |
| 1.25x-pot | 35.71% | -11.57 points | Fold |
| 1.5x-pot | 37.50% | -13.36 points | Fold |
| 2x-pot | 40.00% | -15.86 points | Fold |
| 3x-pot | 42.86% | -18.71 points | Fold |
| 4x-pot | 44.44% | -20.30 points | Fold |
How this is computed
Counting is exact: the pairs of unseen cards with no out number 820 out of 1,081, so hitting by the river has chance 24.14%.
The numbers are a baseline rather than a prediction for one hand. The price is 30.00%, from $75 into $250, and the chance assumes a whole pot won on a hit, no more betting, 47 equally likely unseen cards, and no cards removed for the other player.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Does the math favor calling a three-quarter-pot bet with 6 outs on the flop?
Your chance, 24.14%, set against the 30.00% price gives -5.86 points and a fold. With a $100 pot, a $75 call and no more betting, the average value of the call is -$14.64.
How many outs make a call correct against three quarters of the pot on the flop?
8 outs is the line. At 8 the chance is 31.45%, enough for 30.00%; one fewer gives 27.84%, which is not. Your 6 outs sit 2 below it on the flop, at 24.14%.
Should you use the chance on the next card or by the river?
Use the by-the-river chance, 24.14%, when no more betting follows, and the next-card chance, 12.77%, when you must pay again on the turn. Against the 30.00% price both give a fold, so the choice does not change the play here.
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