Verdict
Fold
6 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come24.14%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-4.43 points
How the verdict is reached
The odds you are given are worse than the odds you need: 28.57% needed, 24.14% held, 4.43 points missing.
For two overcards, 6 outs is the number to use, and one card hits 12.77% of the time out of 47 unseen.
The $100 pot example
- Starting pot$100
- Size of the bet$66.67
- Chips you put in$66.67
- Total pot after calling$233.33
- You can win on a hit$166.67
- You lose on a miss$66.67
- Chance to hit by the river24.14%
- Expected value of a call-$10.33
- Equity the call needs28.57%
- Exact margin over the price-4.4271 points
- Outs that exactly reach the price7.20 outs
- Your outs minus break-even outs-1.20 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling loses $10.33 on average. The hit side averages $40.24, the miss side $50.57, and each dollar called returns -0.155.
Written as odds, the pot lays 2.5 : 1 while the draw is 3.14 : 1 against.
The correct pot to divide by includes your call. Without it the price reads 40.00% rather than 28.57%, and the margin reads -15.8557 points. With the starting pot alone it reads 66.67% and -42.5224 points.
What implied odds would have to do
To make the call break even you would need to win another $42.78 after you hit, which is 0.64 times your call. Anything above that makes the call a good one.
The smallest count that pays for a two-thirds-pot bet is 8 outs at 31.45%. You hold 6, which is 2 outs fewer.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -4.43 points | -$10.33 | Fold |
| $50 | 23.53% | +0.61 points | +$1.74 | Call |
| $100 | 20.00% | +4.14 points | +$13.81 | Call |
| $250 | 13.79% | +10.35 points | +$50.03 | Call |
| $500 | 9.09% | +15.05 points | +$110.39 | Call |
Pricing one card at a time
No conflict here: 24.14% for two cards and 12.77% for one both give a fold against the 28.57% price, so you need not decide which view applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 24.14% | -4.4271 points | -$10.33 | Fold |
| Next card only | 12.77% | -15.8055 points | -$36.88 | Fold |
Neighbors of this draw
Here are the neighbors of 6 outs, priced against the same 28.57%. One more out lifts your chance by about 3.70 points.
How bet size moves the answer
Your 24.14% 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.
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, this page | 28.57% | -4.43 points | Fold |
| three-quarter-pot | 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
Everything is computed from the closed form. Pairs without an out: 820 of 1,081. The rest, 24.14%, hold at least one 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
Does the math favor calling a two-thirds-pot bet with 6 outs on the flop?
Compare 24.14%, your chance to hit by the river, with 28.57%, the equity a two-thirds-pot bet needs. The gap is -4.43 points, so this is a fold. In dollars on a $100 pot, the call averages -$10.33 when no more betting follows.
What is the minimum number of outs for 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 6, so you are 2 behind the minimum.
How many cards should you count when a two-thirds-pot bet arrives on the flop?
Count two cards, 24.14%, when the bet is the last money going in, and one card, 12.77%, when the next street brings another bet. At a price of 28.57%, either number leads to a fold.
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