Verdict
Call
6 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come24.14%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+4.14 points
The call in numbers
Your chance of 24.14% tops the 20.00% price by 4.14 points. That margin is on the side of the call.
6 out of 47 unseen cards is the shape of two overcards, and a single card hits 12.77% of the time.
The arithmetic of this call
- Pot before the bet$100
- Your opponent bets$33.33
- Cost to call$33.33
- Pot after your call$166.67
- Net gain when you hit$133.33
- Loss on a miss$33.33
- How often you hit24.14%
- Expected value of calling+$6.91
- Break-even equity20.00%
- Your chance minus the price, unrounded+4.1443 points
- Break-even count of outs4.91 outs
- Outs above the price+1.09 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call gains $6.91 on average. The hit side averages $32.19, the miss side $25.29, and each dollar called returns +0.207.
Odds say the same thing. Hitting is 3.14 : 1 against, and the pot lays 4 : 1.
Do not forget your own call. Dividing the bet by the pot without it gives 25.00%, not 20.00%, and would show a margin of -0.8557 points. The bet over the starting pot, 33.33%, is worse and would show -9.1890 points.
How safe the call is
The fewest outs that still call a third-pot bet on the flop is 5. You hold 6, so you have 1 out to spare before the call flips to a fold.
Think of $28.61 as your safety room: the most you can give back after a hit, 0.86 times your call, with the call still level.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +4.14 points | +$6.91 | Call |
| $10 | 21.28% | +2.87 points | +$4.49 | Call |
| $25 | 23.53% | +0.61 points | +$0.87 | Call |
| $50 | 28.57% | -4.43 points | -$5.16 | Fold |
| $100 | 50.00% | -25.86 points | -$17.24 | Fold |
Which chance to use
Same draw, two answers. Count both cards and the chance is 24.14%, a call; count just the next card and it is 12.77%, a fold. The price in both cases is 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 24.14% | +4.1443 points | +$6.91 | Call |
| Next card only | 12.77% | -7.2340 points | -$12.06 | Fold |
Nearby draws
Draws close to yours, on the same street and against the same bet: the price is fixed at 20.00%, and each out moves the chance about 3.70 points.
The same draw against other bet sizes
Look down the margin column to see where the draw stops paying. Every row uses 6 outs on the flop and a bet of a different size.
A bet larger than 0.47 times the pot ($46.69 on a $100 pot) asks for more than 24.14%. For this draw, 3 of the 12 sizes are calls.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +7.48 points | Call |
| third-pot, this page | 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 | 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
The chance to hit is the exact closed form, with no simulation. From the flop, 820 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 820 / 1,081, which is 24.14%.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $33.33 / $166.67 = 20.00%. 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
Does the math favor calling a third-pot bet with 6 outs on the flop?
The verdict is call. Your chance is 24.14% and the price is 20.00%, which leaves +4.14 points. On a $100 pot with a $33.33 bet, calling is worth +$6.91 on average if the whole pot is won on a hit and nothing more is bet.
How strong must a draw be to call a third-pot bet on the flop?
The threshold is 5 outs. It gives 20.35%, clearing 20.00%, whereas 4 gives only 16.47%. Holding 6 puts you 1 above it, with a chance of 24.14%.
When is the next-card chance the better comparison?
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 20.00%, the two numbers give a call and a fold.
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