Module 4 · Lesson 22 of 39 · Free
Pocket pairs and set mining
A pocket pair flops a set or better 11.8% of the time, about once in 8.5 flops. Call 3 bb to see the flop with a small pair, and each set has to pay for the 7.5 flops that miss: 7.5 × 3 = 22.5 bb. Calling to flop a set pays only when you can win that much when it comes.
The hand
Before the flop at six players. The Tight-aggressive player raises to 3 bb under the gun, and everyone folds to you on the button with 5♣ 5♦. The blinds have 1.5 bb in the pot, and both of you started with 100 bb.
Predict first
If both of you had only 20 bb, would calling to flop a set still pay?
- Yes: the set comes just as often
- No: he cannot pay you enough
- Yes, if he always pays you off
Show the answer
Answer: No: he cannot pay you enough
Each set must win 22.5 bb. The blinds and his raise put 4.5 bb in the pot, so 18 bb must come from his stack after the flop, and with 20 bb he has only 17 bb left after your call. Even all his chips are not enough.
Working it out
As the lesson on what the flop brings counted, the flop misses your pair 17,296 times in 19,600 and gives you a set or better 2,304 times: 17,296 ÷ 2,304 ≈ 7.5 misses for every set. Each miss costs your 3 bb call, so each set must win 7.5 × 3 = 22.5 bb. The pot already holds 4.5 bb of other players' chips, the blinds and his raise, and the set wins them; the other 22.5 − 4.5 = 18 bb must come from his stack after the flop. These are your implied odds, and the formula of the Mathematics lesson on pot odds gives the same: 3 ÷ 0.1176 − (4.5 + 3) ≈ 18 bb. With 100 bb each he has 97 bb left, and you need 18 of them, 18.6%, every time the set comes.
Stacks set the limit: you can never win more than the smaller stack has left after your call. So set mining needs deep stacks and small raises: call 5 bb, and each set must win 7.5 × 5 = 37.5 bb. Position helps too: from the button you see what he does on the flop before you put in another chip, as the second lesson of this module showed.
Formula
Needed from each set = 7.5 × call; needed after the flop = 7.5 × call − other players' chips in the pot: 7.5 × 3 − 4.5 = 18 bb
Check your understanding
He raises to 4 bb, you call with a small pair, and both blinds fold. In the lesson's model, how much must you win after the flop each time you flop a set, in bb?
Show the answer
Answer: 24.5 bb
Each set must win 7.5 × 4 = 30 bb. The pot holds 0.5 + 1 + 4 = 5.5 bb of other players' chips, so you need 30 − 5.5 = 24.5 bb after the flop.
Both stacks are 40 bb. He raises to 5 bb and you hold a small pair; the blinds will fold. Should you call to flop a set?
- No: each set would need 31 bb of his last 35 bb
- Yes: his 35 bb is more than the 31 bb you need
- Yes: a set wins most pots
Show the answer
Answer: No: each set would need 31 bb of his last 35 bb
Each set must win 7.5 × 5 = 37.5 bb, and 37.5 − 6.5 = 31 bb of it after the flop, while he has 40 − 5 = 35 bb left. He would have to pay almost all of it, almost every time: fold.
You have 30 bb and he has 200 bb. He raises to 3 bb and you call. What is the most you can win from him after the flop, in bb?
Show the answer
Answer: 27 bb
Only as many chips as the smaller stack can still put in: 30 − 3 = 27 bb.