Verdict
Fold
2 outs, flop, pot-size bet
- Chance to hit by the rivertwo cards to come8.42%
- Equity the call needs$100 into a pot of $30033.33%
- Margin over the priceyour chance minus the price-24.92 points
Chance against price
A pot-size bet needs 33.33% equity from the call, and 2 outs on the flop supply only 8.42%. Missing the price by 24.92 points is far from a close decision.
The usual home for 2 outs is a pocket pair that wants a set. One card from the 47 unseen ones completes it 4.26% of the time.
A $100 pot, step by step
- Pot before the bet$100
- Size of the bet$100
- Chips you put in$100
- Final pot if you call$300
- What a hit wins$200
- You lose on a miss$100
- How often you hit8.42%
- Expected value of calling-$74.75
- Equity the call needs33.33%
- Margin, to four decimals-24.9152 points
- Outs that exactly reach the price8.53 outs
- Outs to spare, exactly-6.53 outs
With no more betting, the whole pot won on a hit and the call lost on a miss, the call loses $74.75 on average. The hit side averages $16.84, the miss side $91.58, and each dollar called returns -0.747.
Odds say the same thing. Hitting is 10.88 : 1 against, and the pot lays 2 : 1.
Do not forget your own call. Dividing the bet by the pot without it gives 50.00%, not 33.33%, and would show a margin of -41.5819 points.
How much more you would need to win
The call becomes fair only if a hit brings in $887.91 more after the draw arrives. Measured against the $100 you pay, that is 8.88 times your call.
Another way to close the gap is more outs. The fewest outs that call a pot-size bet on the flop is 9; with 9 outs you would hit 34.97%. That is 7 more outs than the 2 you hold.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 33.33% | -24.92 points | -$74.75 | Fold |
| $50 | 28.57% | -20.15 points | -$70.54 | Fold |
| $100 | 25.00% | -16.58 points | -$66.33 | Fold |
| $250 | 18.18% | -9.76 points | -$53.70 | Fold |
| $500 | 12.50% | -4.08 points | -$32.65 | Fold |
Which chance to use
Whether you count one card or two, the answer is a fold. The river figure is 8.42%, the next-card figure is 4.26%, and both are measured against 33.33%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 8.42% | -24.9152 points | -$74.75 | Fold |
| Next card only | 4.26% | -29.0780 points | -$87.23 | Fold |
How the answer moves with outs
A few outs either way, against a pot-size bet that needs 33.33%. The chance climbs about 4.07 points with each extra out.
How bet size moves the answer
Look down the margin column to see where the draw stops paying. Every row uses 2 outs on the flop and a bet of a different size.
No bet size in the table is a call. The smallest, quarter-pot, needs 16.67% against your 8.42%, and the largest bet this draw could call is only 0.10 times the pot ($10.12 on a $100 pot).
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | -8.25 points | Fold |
| third-pot | 20.00% | -11.58 points | Fold |
| two-fifths-pot | 22.22% | -13.80 points | Fold |
| half-pot | 25.00% | -16.58 points | Fold |
| two-thirds-pot | 28.57% | -20.15 points | Fold |
| three-quarter-pot | 30.00% | -21.58 points | Fold |
| pot-size, this page | 33.33% | -24.92 points | Fold |
| 1.25x-pot | 35.71% | -27.30 points | Fold |
| 1.5x-pot | 37.50% | -29.08 points | Fold |
| 2x-pot | 40.00% | -31.58 points | Fold |
| 3x-pot | 42.86% | -34.44 points | Fold |
| 4x-pot | 44.44% | -36.03 points | Fold |
How this is computed
The chance to hit is the exact closed form, with no simulation. From the flop, 990 of the 1,081 possible pairs of unseen cards hold no out, so the chance is 1 minus 990 / 1,081, which is 8.42%.
Read the verdict with its limits in mind. The call is the full bet, so the break-even equity is $100 / $300 = 33.33%. 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
Are 2 outs on the flop worth a call against a bet of the full pot?
Verdict: fold. A pot-size bet asks for 33.33% and you have 8.42%, a margin of -24.92 points. For a $100 call into a $100 pot, with no later bets and the whole pot won on a hit, the average is -$74.75.
What count of outs clears the price of a pot-size bet on the flop?
You need at least 9 outs against a pot-size bet on the flop. That count hits 34.97% against 33.33% needed, and 8 falls short at 31.45%. With 2 you are 7 short of the minimum.
How many cards should you count when a pot-size bet arrives on the flop?
Two cards cost one bet only if the hand really ends here, and then 8.42% applies. If you will face the turn bet as well, 4.26% applies. Versus 33.33%, both views give a fold.
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