Verdict
Fold
1 out, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come4.26%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-24.32 points
Chance against price
4.26% against 28.57%: the draw trails the price by 24.32 points. On this flop against a two-thirds-pot bet, that is an easy fold.
The deck holds 47 unseen cards and one of them is your out, so a single card hits 2.13% of the time.
A $100 pot, step by step
- Pot before the bet$100
- The bet$66.67
- Chips you put in$66.67
- Pot with your call in$233.33
- Net gain when you hit$166.67
- Loss on a miss$66.67
- How often you hit4.26%
- Expected value of a call-$56.74
- Break-even equity28.57%
- Your chance minus the price, unrounded-24.3161 points
- Fractional outs at the price7.20 outs
- Margin measured in outs-6.20 outs
Over many identical spots, with the whole pot won on every hit, the call lost on every miss and no extra betting, calling loses $56.74 on average. Hits bring in $7.09, misses cost $63.83, and the ratio is -0.851 per dollar called.
Stated as odds, you are 22.5 : 1 against hitting and the call gets 2.5 : 1 from the pot.
Counting the pot without your call makes the price look like 40.00%, when the real price is 28.57%. On that mistaken price the margin would read -35.7447 points; on 66.67%, the bet over the starting pot, it would read -62.4113 points.
Implied odds that would change the answer
The shortfall in dollars is $1,333.33: the amount a hit would have to win later for 4.26% to be enough. It equals 20.00 times your $66.67 call.
Another way to close the gap is more outs. The fewest outs that call a two-thirds-pot bet on the flop is 8; with 8 outs you would hit 31.45%. That is 7 more outs than the 1 you hold.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -24.32 points | -$56.74 | Fold |
| $50 | 23.53% | -19.27 points | -$54.61 | Fold |
| $100 | 20.00% | -15.74 points | -$52.48 | Fold |
| $250 | 13.79% | -9.54 points | -$46.10 | Fold |
| $500 | 9.09% | -4.84 points | -$35.46 | Fold |
Two cards to come, or just one
Here the cards to come do not matter for the verdict. 2.13% on one card and 4.26% on two both say fold at a price of 28.57%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 4.26% | -24.3161 points | -$56.74 | Fold |
| Next card only | 2.13% | -26.4438 points | -$61.70 | Fold |
Neighbors of this draw
How fast does the margin move? About 4.16 points per out on the flop. The rows below keep the two-thirds-pot bet fixed and change only the outs.
Changing the bet, keeping the draw
Your 4.26% 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 in the table is a call. The smallest, quarter-pot, needs 16.67% against your 4.26%, and the largest bet this draw could call is only 0.05 times the pot ($4.65 on a $100 pot).
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -12.41 points | Fold |
| third-pot | 20.00% | -15.74 points | Fold |
| two-fifths-pot | 22.22% | -17.97 points | Fold |
| half-pot | 25.00% | -20.74 points | Fold |
| two-thirds-pot, this page | 28.57% | -24.32 points | Fold |
| three-quarter-pot | 30.00% | -25.74 points | Fold |
| pot-size | 33.33% | -29.08 points | Fold |
| 1.25x-pot | 35.71% | -31.46 points | Fold |
| 1.5x-pot | 37.50% | -33.24 points | Fold |
| 2x-pot | 40.00% | -35.74 points | Fold |
| 3x-pot | 42.86% | -38.60 points | Fold |
| 4x-pot | 44.44% | -40.19 points | Fold |
Pages that use the same math
How this is computed
The chance rests on counting, not on a rule of thumb. Blank pairs: 1,035 out of 1,081; hit chance: 4.26%.
The model is deliberately simple: call everything, win everything on a hit, face no more bets, deal from 47 equally likely unseen cards, and ignore an opponent's holding. With the price at $66.67 / $233.33 = 28.57%, later streets and shared outs are what change the real answer.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Call or fold with 1 out on the flop against a bet of two thirds of the pot?
Your chance, 4.26%, set against the 28.57% price gives -24.32 points and a fold. With a $100 pot, a $66.67 call and no more betting, the average value of the call is -$56.74.
At what count of outs does a two-thirds-pot bet on the flop become a call?
8 outs is the line. At 8 the chance is 31.45%, enough for 28.57%; one fewer gives 27.84%, which is not. Your 1 out sits 7 below it on the flop, at 4.26%.
One card or two: which number belongs next to the 28.57% price?
Both figures are right for their own situation: 4.26% with no more betting, 2.13% when the turn brings a bet. Facing 28.57%, each one gives a fold.
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