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E — Extra: Set-mining and the fifteen-times rule

Holding a small pocket pair? Only call a raise if the shorter stack is at least fifteen times that raise.

The old slogan for this rule was "only chase a set with 15x the call behind" — which is gibberish until someone translates it, so here's the translation, piece by piece.

A set is what happens when you hold a pocket pair — say 5♣5♦ — and a third 5 lands on the board. Now you have three of a kind, a Tier 2 hand, and here's the magic: it's invisible. Two of your three 5s are hidden in your hand. Your opponent proudly holding top pair cannot see it, cannot imagine it, and will happily pay you everything. Sets win stacks, not pots.

"Chasing" just means calling a bet now, hoping to hit that third 5 on the flop.

"Behind" means the chips still sitting in front of a player — money not yet in the pot, money still available to be won.

Now the math, gently. Your pocket pair turns into a set on the flop about one time in eight and a half. So picture playing this spot 8½ times: you'll pay the entry fee 8½ times and hit once. For that to be worth it, the one win has to be big — bigger than 8½ entry fees, because even when you hit, your opponent doesn't hand over his whole stack every time. Sometimes he has nothing and folds. Sometimes a scary board shuts him down.

Fold all of that into one number: fifteen. The payoff needs to be at least fifteen times your entry fee. And the payoff ceiling is the shorter stack between you and him — you can't win chips he doesn't have, and you can't bet chips you don't have.

The narration at the table:

"I've got fives. He raised to ten. What's the smaller stack — his or mine? His. He's got about two hundred behind. Two hundred divided by ten... twenty. Twenty's more than fifteen. Call."

One boundary: this gate is for small pairs — twos through eights — hands that almost never win without hitting their set. Big pairs (nines and up, and certainly J-J and better) are strong Tier 1 hands all by themselves; they're played on their own muscle, not on set-mining math.

Example 1 — the green light. You hold 5♣5♦. The raise is $10. He has $200 behind; you have $250. Smaller stack: his $200. Two hundred divided by ten is twenty. Twenty beats fifteen. Call, then live by ♠P: hit the set and play for everything; miss and fold without a sigh.

Example 2 — the red light. Same 5♣5♦, same $10 raise — but this opponent only has $60 behind. Sixty divided by ten is six. Six is nowhere near fifteen. Fold. And here's the part to sit with: even if you called and flopped the set, the call was still wrong. There was never enough money on the table to pay for the seven-and-a-half misses. One shiny outcome doesn't fix a losing price.

Example 3 — the crowd discount. Your 5♣5♦ again, a $10 raise, but this time three players call before it gets to you, each with about $130 behind. Against any single one of them: 130 ÷ 10 = 13 — fails. But four opponents means four separate chances that somebody has a hand worth stacking when your set arrives, and the pot is already $40 deep, sweetening the entry. Call. The fifteen rule is calibrated for one opponent; a crowded pot genuinely relaxes it.

DIAL — ♠E by table size. Fifteen is the eight-handed number. The multiplier moves because it's really a bet on someone having a hand strong enough to pay you, and that probability is the dial. 4-handed: use 20×. Fewer opponents, fewer payers, and short-handed players hold weaker hands that fold to your set. You need a steeper price. 8-handed: 15×, as written. 12-handed: 12×. With eleven opponents somebody holds a premium 29% of the time — the odds that your invisible set runs into a payer are dramatically better. Small pairs are among the best hands to play at a crowded table, provided the entry stays cheap.