Verdict
Fold
4 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come16.47%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-12.11 points
Comparing the draw with the bet
With 4 outs on the flop you hit 16.47% by the river, and a two-thirds-pot bet asks for 28.57%. A 12.11-point shortfall makes this a clear fold.
4 out of 47 unseen cards is the shape of a gutshot straight draw, and a single card hits 8.51% of the time.
The arithmetic of this call
- Starting pot$100
- The bet$66.67
- Chips you put in$66.67
- Pot with your call in$233.33
- You can win on a hit$166.67
- Net loss when you miss$66.67
- How often you hit16.47%
- Calling is worth, on average-$28.25
- Break-even equity28.57%
- Unrounded margin-12.1052 points
- Fractional outs at the price7.20 outs
- Margin measured in outs-3.20 outs
Expected value says the same in dollars. Win the whole pot on a hit, lose your call on a miss, add no more betting, and the call loses $28.25 on average: $27.44 in, $55.69 out, -0.424 per dollar called.
Put as odds, the draw is 5.07 : 1 against, and the pot offers 2.5 : 1 for the call.
Watch the pot you divide by. Leaving your call out turns 28.57% into 40.00%, and the margin into -23.5338 points. Dividing by the starting pot gives 66.67% and a margin of -50.2004 points, further from the truth.
The price with implied odds
Implied odds are the way to close the gap. You need $171.54 more on later streets after hitting, which is 2.57 times the call you make.
If the draw had 4 more outs, for 8 in all, the chance would be 31.45% and the call would clear 28.57%.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -12.11 points | -$28.25 | Fold |
| $50 | 23.53% | -7.06 points | -$20.01 | Fold |
| $100 | 20.00% | -3.53 points | -$11.78 | Fold |
| $250 | 13.79% | +2.67 points | +$12.92 | Call |
| $500 | 9.09% | +7.38 points | +$54.09 | Call |
Pricing one card at a time
Here the cards to come do not matter for the verdict. 8.51% on one card and 16.47% 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 | 16.47% | -12.1052 points | -$28.25 | Fold |
| Next card only | 8.51% | -20.0608 points | -$46.81 | Fold |
The call as outs change
A few outs either way, against a two-thirds-pot bet that needs 28.57%. The chance climbs about 3.89 points with each extra out.
Every bet size, one draw
Bet size sets the price, so the verdict changes as you scan the table. The two-thirds-pot bet of this page is marked in the first column.
A bet larger than 0.25 times the pot ($24.55 on a $100 pot) asks for more than 16.47%, and every size on this page is larger. The table is folds from top to bottom.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -0.20 points | Fold |
| third-pot | 20.00% | -3.53 points | Fold |
| two-fifths-pot | 22.22% | -5.76 points | Fold |
| half-pot | 25.00% | -8.53 points | Fold |
| two-thirds-pot, this page | 28.57% | -12.11 points | Fold |
| three-quarter-pot | 30.00% | -13.53 points | Fold |
| pot-size | 33.33% | -16.87 points | Fold |
| 1.25x-pot | 35.71% | -19.25 points | Fold |
| 1.5x-pot | 37.50% | -21.03 points | Fold |
| 2x-pot | 40.00% | -23.53 points | Fold |
| 3x-pot | 42.86% | -26.39 points | Fold |
| 4x-pot | 44.44% | -27.98 points | Fold |
Pages that use the same math
How this is computed
Everything is computed from the closed form. Pairs without an out: 903 of 1,081. The rest, 16.47%, hold at least one out.
Keep the assumptions in view: a full call ($66.67 into $233.33, or 28.57%), the whole pot on a hit, no more betting, and 47 unseen cards that are equally likely. The math does not know what the other player holds.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
What does the math say about calling a bet of two thirds of the pot with 4 outs on the flop?
The verdict is fold. Your chance is 16.47% and the price is 28.57%, which leaves -12.11 points. On a $100 pot with a $66.67 bet, calling is worth -$28.25 on average if the whole pot is won on a hit and nothing more is bet.
How many outs make a call correct against two thirds of the pot on the flop?
The fewest outs that call a two-thirds-pot bet on the flop is 8. With 8 outs you hit 31.45%, which reaches the 28.57% price, while 7 outs hit only 27.84%. You have 4, so you are 4 below that count.
When is the next-card chance the better comparison?
Both figures are right for their own situation: 16.47% with no more betting, 8.51% when the turn brings a bet. Facing 28.57%, each one gives a fold.
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