Verdict
Fold
3 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come12.49%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-16.08 points
Your chance and the price
The call is clearly not worth making. 12.49% is your chance to hit, 28.57% is the price, and the gap between them is 16.08 points.
Holding one overcard to top pair gives you exactly 3 outs, out of 47 unseen cards. One card hits 6.38% of the time.
Putting dollars on the call
- Pot when the bet arrives$100
- Your opponent bets$66.67
- Your call$66.67
- Pot with your call in$233.33
- Gain on a hit$166.67
- Net loss when you miss$66.67
- Probability of a hit12.49%
- Expected value of calling-$37.53
- Equity the call needs28.57%
- Your chance minus the price, unrounded-16.0830 points
- Outs that exactly reach the price7.20 outs
- Outs above the price-4.20 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $20.81 in and $58.34 out, so calling loses $37.53 on average at -0.563 per dollar called.
Stated as odds, you are 7.01 : 1 against hitting and the call gets 2.5 : 1 from the pot.
The correct pot to divide by includes your call. Without it the price reads 40.00% rather than 28.57%, and the margin reads -27.5116 points. With the starting pot alone it reads 66.67% and -54.1782 points.
What it would take to call
With 12.49% to hit, break-even sits $300.49 higher than the pot shows. Put another way, later bets must add 4.51 times your 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 5 more outs than the 3 you hold.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -16.08 points | -$37.53 | Fold |
| $50 | 23.53% | -11.04 points | -$31.28 | Fold |
| $100 | 20.00% | -7.51 points | -$25.04 | Fold |
| $250 | 13.79% | -1.30 points | -$6.31 | Fold |
| $500 | 9.09% | +3.40 points | +$24.92 | Call |
One card or two
Both views point the same way. By the river you hit 12.49%, on the next card 6.38%, and the price is 28.57%, so the fold holds whichever number applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 12.49% | -16.0830 points | -$37.53 | Fold |
| Next card only | 6.38% | -22.1884 points | -$51.77 | Fold |
Neighbors of this draw
Here are the neighbors of 3 outs, priced against the same 28.57%. One more out lifts your chance by about 3.98 points.
Where the bet size flips the call
Bigger bets ask for more equity while your chance stays at 12.49%. Here is every bet size against the same draw, with the row for this page marked.
Break-even for this draw is a bet of 0.17 times the pot ($16.65 on a $100 pot). Every size in the table is larger than that, so each row is a fold.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -4.18 points | Fold |
| third-pot | 20.00% | -7.51 points | Fold |
| two-fifths-pot | 22.22% | -9.73 points | Fold |
| half-pot | 25.00% | -12.51 points | Fold |
| two-thirds-pot, this page | 28.57% | -16.08 points | Fold |
| three-quarter-pot | 30.00% | -17.51 points | Fold |
| pot-size | 33.33% | -20.84 points | Fold |
| 1.25x-pot | 35.71% | -23.23 points | Fold |
| 1.5x-pot | 37.50% | -25.01 points | Fold |
| 2x-pot | 40.00% | -27.51 points | Fold |
| 3x-pot | 42.86% | -30.37 points | Fold |
| 4x-pot | 44.44% | -31.96 points | Fold |
How this is computed
The chance rests on counting, not on a rule of thumb. Blank pairs: 946 out of 1,081; hit chance: 12.49%.
The numbers are a baseline rather than a prediction for one hand. The price is 28.57%, from $66.67 into $233.33, 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 two-thirds-pot bet with 3 outs on the flop?
By the numbers it is a fold. 3 outs on the flop hit 12.49% by the river, a two-thirds-pot bet needs 28.57%, and the margin is -16.08 points. That assumes you call the full $66.67 and no more betting follows, and it values the call at -$37.53 per $100 pot.
How many outs do you need to call a two-thirds-pot bet on the flop?
Against 28.57%, the first count that works on the flop is 8, at 31.45%. At 7 the chance is 27.84%, too low. Compared with that threshold, your 3 outs are 5 below.
Which hit chance fits a two-thirds-pot bet on the flop?
The river figure of 12.49% assumes no further betting; the next-card figure of 6.38% assumes you pay again on the turn. Against 28.57%, both say fold, so you can use either.
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