Verdict
Fold
2 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come8.42%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price-11.58 points
Chance against price
The call is clearly not worth making. 8.42% is your chance to hit, 20.00% is the price, and the gap between them is 11.58 points.
For a pocket pair that wants a set, 2 outs is the number to use, and one card hits 4.26% of the time out of 47 unseen.
The same spot in dollars
- Pot when the bet arrives$100
- Size of the bet$33.33
- You call$33.33
- Total pot after calling$166.67
- Gain on a hit$133.33
- You lose on a miss$33.33
- Probability of a hit8.42%
- Expected value of calling-$19.30
- Equity needed to break even20.00%
- Unrounded margin-11.5819 points
- Outs at break-even4.91 outs
- Margin measured in outs-2.91 outs
Assume the whole pot goes to you when you hit, the call is lost when you miss, and nothing more is bet. Calling then loses $19.30 on average: $11.22 from hits, minus $30.53 from misses, -0.579 per dollar called.
The same comparison in odds: the odds against hitting are 10.88 : 1, and the pot lays 4 : 1 on a call.
Skipping your own call in the pot gives a price of 25.00% where 20.00% is correct, and a margin of -16.5819 points instead of -11.58 points. The starting pot gives 33.33% and a margin of -24.9152 points, which is wrong by even more.
Closing the gap with future bets
Your chance is 8.42%, so a hit has to pay $395.97 in all, or $229.30 more than the pot you can see. That extra is 6.88 times what you call.
If the draw had 3 more outs, for 5 in all, the chance would be 20.35% and the call would clear 20.00%.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | -11.58 points | -$19.30 | Fold |
| $50 | 15.38% | -6.97 points | -$15.09 | Fold |
| $100 | 12.50% | -4.08 points | -$10.88 | Fold |
| $250 | 8.00% | +0.42 points | +$1.74 | Call |
| $500 | 5.00% | +3.42 points | +$22.79 | Call |
Two cards to come, or just one
No conflict here: 8.42% for two cards and 4.26% for one both give a fold against the 20.00% price, so you need not decide which view applies.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 8.42% | -11.5819 points | -$19.30 | Fold |
| Next card only | 4.26% | -15.7447 points | -$26.24 | Fold |
A few outs either way
Move up or down a few outs and watch the verdict. Every extra out is worth about 4.07 points on the flop, and the price stays at 20.00%.
Every bet size, one draw
One draw, 12 bets. Each row gives the equity the call needs, the margin over it, and the verdict for 2 outs on the flop.
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, this page | 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 | 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 number is exact rather than estimated. 990 of the 1,081 pairs that could come are blanks, which leaves 8.42% for a hit.
What is held fixed: the call equals the bet, so the price is $33.33 / $166.67 = 20.00%; the pot is won whole on a hit; there is no further betting; and each of the 47 unseen cards is as likely as any other. Opponent cards are not removed.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Should you call a third-pot bet with 2 outs on the flop?
Verdict: fold. A third-pot bet asks for 20.00% and you have 8.42%, a margin of -11.58 points. For a $33.33 call into a $100 pot, with no later bets and the whole pot won on a hit, the average is -$19.30.
How many outs make a call correct against a third of the pot on the flop?
The threshold is 5 outs. It gives 20.35%, clearing 20.00%, whereas 4 gives only 16.47%. Holding 2 puts you 3 below it, with a chance of 8.42%.
When is the next-card chance the better comparison?
Pick the number that matches the street plan: 8.42% for seeing both cards for one bet, 4.26% for paying card by card. Both face 20.00%, and the verdict is fold either way.
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