Verdict
Fold
3 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come12.49%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price-20.84 points
How the verdict is reached
The price is 33.33% and your chance is 12.49%. You sit 20.84 points below the line, which is a wide gap, so you fold.
3 out of 47 unseen cards is the shape of one overcard to top pair, and a single card hits 6.38% of the time.
One hand, in dollars
- Pot when the bet arrives$100
- Size of the bet$100
- Chips you put in$100
- Final pot if you call$300
- Gain on a hit$200
- Net loss when you miss$100
- Chance to hit by the river12.49%
- Expected value of calling-$62.53
- Equity needed to break even33.33%
- Margin, to four decimals-20.8449 points
- Outs that exactly reach the price8.53 outs
- Margin measured in outs-5.53 outs
Price it in dollars, with no later bets: win the whole pot on a hit, lose the call on a miss. That averages $24.98 in and $87.51 out, so calling loses $62.53 on average at -0.625 per dollar called.
Put as odds, the draw is 7.01 : 1 against, and the pot offers 2 : 1 for the call.
A common slip is to divide the bet by the pot after the bet but before your call. That gives 50.00% instead of 33.33% and would put your margin at -37.5116 points.
When later betting could rescue the call
The call becomes fair only if a hit brings in $500.74 more after the draw arrives. Measured against the $100 you pay, that is 5.01 times your call.
9 outs is the threshold against a pot-size bet on the flop, a chance of 34.97%. That is 6 more than your 3.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | -20.84 points | -$62.53 | Fold |
| $50 | 28.57% | -16.08 points | -$56.29 | Fold |
| $100 | 25.00% | -12.51 points | -$50.05 | Fold |
| $250 | 18.18% | -5.69 points | -$31.31 | Fold |
| $500 | 12.50% | -0.01 points | -$0.09 | Fold |
One card or two
The two chances agree on the verdict. 12.49% by the river and 6.38% on one card each lead to a fold against 33.33%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 12.49% | -20.8449 points | -$62.53 | Fold |
| Next card only | 6.38% | -26.9504 points | -$80.85 | Fold |
Neighbors of this draw
How fast does the margin move? About 3.98 points per out on the flop. The rows below keep the pot-size bet fixed and change only the outs.
Where the bet size flips the call
Keep 3 outs and change only the bet. The price rises from the smallest size to the largest, and the pot-size row is marked as this page.
No bet size in the table is a call. The smallest, quarter-pot, needs 16.67% against your 12.49%, and the largest bet this draw could call is only 0.17 times the pot ($16.65 on a $100 pot).
| 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 | 28.57% | -16.08 points | Fold |
| three-quarter-pot | 30.00% | -17.51 points | Fold |
| pot-size, this page | 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
Here is how 12.49% was found. Deal every pair of the 47 unseen cards: 946 of 1,081 pairs contain no out.
The price is call / (pot + bet + call), here $100 / $300 = 33.33%, and the margin is your chance minus it. The page assumes you call the whole bet, win the whole pot whenever you hit, and see no more betting. All 47 unseen cards are equally likely and none is removed for an opponent's hand, so this is the chance to hit your outs, not your equity against one hand.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How should you respond to a pot-size bet on the flop when you hold 3 outs?
The verdict is fold. Your chance is 12.49% and the price is 33.33%, which leaves -20.84 points. On a $100 pot with a $100 bet, calling is worth -$62.53 on average if the whole pot is won on a hit and nothing more is bet.
How many outs are enough to continue against a bet of the full pot on the flop?
Look for 9 outs. That is the smallest count whose chance, 34.97%, reaches the 33.33% price; 8 manages 31.45%. You have 3, so you are 6 behind the minimum.
Should you use the chance on the next card or by the river?
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 33.33%, both say fold, so you can use either.
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