Set-mining
Additional call cost C (BB)
Net gain on a hit G (BB)
Minimum net gain G (BB)
Set-mining call EV (BB)
- 1 Blinds
- 2 Open raise
- 3 Hero → call?
Hero
Villain
On a hit
Supplied assumptionX = future extra payment. The opponent’s additional chips after your call, averaged over the times you hit. This amount is assumed by the exercise.
At a real table, estimate the bets this opponent would pay on flop, turn and river, including hits where they pay nothing. Their stack only sets the maximum; it does not tell you X.
≈ 11.7551% → 11.76%
Same chance for any pocket pair, with no other known cards: at least one matching card on the flop, including when both appear. Only preflop → flop; not the chance of winning the hand.
A quick reference for the table
(1 − p) ÷ p = 0.8824 ÷ 0.1176 ≈ 7.5
The 7.5 factor comes from miss probability divided by hit probability. It stays fixed while p stays the same. X is the future payment, not this multiplier.
Compare your estimated G with the minimum: above it, positive EV; below it, negative EV; exactly equal, break-even. Near the boundary, use the exact calculation.
Minimum G by call cost
| Call cost C | Gmin ≈ |
|---|---|
| 1 | 7.50 |
| 1.5 | 11.26 |
| 2 | 15.01 |
| 2.5 | 18.76 |
| 3 | 22.51 |
| 4 | 30.01 |
Example EVs by cost and gain
G = Pot + X
20 BB = 4.5 BB + 15.5 BB
The columns are example total profits G when you hit. For the 20 BB column, one example is a 4.5 BB pot plus 15.5 BB of extra opponent payments. Find your G by adding Pot + X, then choose its column.
| C ↓ / G → | 10 | 15 | 20 | 30 | 40 |
|---|---|---|---|---|---|
| 1 | +0.29 | +0.88 | +1.47 | +2.65 | +3.82 |
| 1.5 | -0.15 | +0.44 | +1.03 | +2.20 | +3.38 |
| 2 | -0.59 | ≈0.00 | +0.59 | +1.76 | +2.94 |
| 2.5 | -1.03 | -0.44 | +0.15 | +1.32 | +2.50 |
| 3 | -1.47 | -0.88 | -0.30 | +0.88 | +2.06 |
| 4 | -2.35 | -1.77 | -1.18 | ≈0.00 | +1.17 |
These are reference hands, not the answers to your current choices. The shortcut is approximate; exercise answers use p = 0.1176 and two decimals.
Model: fold every miss, win every hit, no rake. Use it to judge the payment you need; a positive model EV does not guarantee a good call in real play.