Verdict
Fold
2 outs, flop, two-thirds-pot bet
- Chance to hit by the rivertwo cards to come8.42%
- Equity the call needs$66.67 into a pot of $233.3328.57%
- Margin over the priceyour chance minus the price-20.15 points
The price of the call
The price is 28.57% and your chance is 8.42%. You sit 20.15 points below the line, which is a wide gap, so you fold.
2 outs is the standard count for a pocket pair that wants a set. Of the 47 unseen cards on the flop, 2 complete it, which is 4.26% on the very next card.
Worked through on a $100 pot
- Pot before the bet$100
- Bet$66.67
- Your call$66.67
- Total pot after calling$233.33
- You can win on a hit$166.67
- Net loss when you miss$66.67
- Probability of a hit8.42%
- Expected value of calling-$47.02
- Equity the call needs28.57%
- Unrounded margin-20.1533 points
- Fractional outs at the price7.20 outs
- Margin measured in outs-5.20 outs
Stay with simple rules: the whole pot on a hit, the call lost on a miss, no more money in. Under them calling loses $47.02 on average. The hit side averages $14.03, the miss side $61.05, and each dollar called returns -0.705.
In odds, you face 10.88 : 1 against you and the pot pays 2.5 : 1.
The correct pot to divide by includes your call. Without it the price reads 40.00% rather than 28.57%, and the margin reads -31.5819 points. With the starting pot alone it reads 66.67% and -58.2485 points.
What it would take to call
The shortfall in dollars is $558.61: the amount a hit would have to win later for 8.42% to be enough. It equals 8.38 times your $66.67 call.
The smallest count that pays for a two-thirds-pot bet is 8 outs at 31.45%. You hold 2, which is 6 outs fewer.
| Future winnings | Price with them | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 28.57% | -20.15 points | -$47.02 | Fold |
| $50 | 23.53% | -15.11 points | -$42.82 | Fold |
| $100 | 20.00% | -11.58 points | -$38.61 | Fold |
| $250 | 13.79% | -5.37 points | -$25.98 | Fold |
| $500 | 9.09% | -0.67 points | -$4.93 | Fold |
Next card or river
No conflict here: 8.42% for two cards and 4.26% for one both give a fold against the 28.57% 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% | -20.1533 points | -$47.02 | Fold |
| Next card only | 4.26% | -24.3161 points | -$56.74 | Fold |
How the answer moves with outs
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 28.57%.
The draw across every bet size
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.
A bet larger than 0.10 times the pot ($10.12 on a $100 pot) asks for more than 8.42%, 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% | -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, this page | 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 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%.
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 is the right play with 2 outs when a two-thirds-pot bet comes on the flop?
By the numbers it is a fold. 2 outs on the flop hit 8.42% by the river, a two-thirds-pot bet needs 28.57%, and the margin is -20.15 points. That assumes you call the full $66.67 and no more betting follows, and it values the call at -$47.02 per $100 pot.
How many outs are enough to continue against a bet of two thirds of the pot on the flop?
The threshold is 8 outs. It gives 31.45%, clearing 28.57%, whereas 7 gives only 27.84%. Holding 2 puts you 6 below it, with a chance of 8.42%.
Which hit chance fits a two-thirds-pot bet on the flop?
The river figure of 8.42% assumes no further betting; the next-card figure of 4.26% assumes you pay again on the turn. Against 28.57%, both say fold, so you can use either.
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