Set-Mining and the Hands That Print: 15-to-1 Math
Why small pocket pairs and suited connectors carry the best implied odds in poker, the full derivation of the 15-to-1 set-mining guideline, and how to apply it to real open sizes and stack depths.
Assumptions: All examples use a 6-max online cash game at 100bb effective stacks ($0.50/$1 where dollar amounts appear) with no rake unless a different setup is stated.
The previous lesson gave you the deficit calculation: how many future big blinds a call needs. This one answers the natural next question — which hands collect those big blinds most reliably? The answer isn't "big cards." It's the two hand families that make hidden, near-nut hands while your opponent makes strong second-best hands: small pocket pairs and suited connectors.
That pairing is the whole engine of implied odds. To get paid you need two things at once. You need a hand near the top of what's possible, so that when the money goes in you're not the one funding someone else. And you need your opponent to hold something strong enough to keep him in — top pair, an overpair — while believing he's good. A♠A♥ on K♦7♥2♦ against your bottom set will fire three barrels, because nothing about a deuce on the flop warns him. That invisibility is what separates these hand classes from, say, a flush draw everyone can see arrive.
Why "hidden" is worth so much money
Compare two ways of making a strong hand. With 9♦8♦ you flop a flush draw, the third diamond rolls off the turn, and a competent opponent with one pair taps the brakes — the danger is printed on the board. With 2♠2♣ you flop bottom set on K-7-2 and the board looks safer to your opponent than the flop he was hoping for. He can't see your hand class at all. Sets, and the sneaky straights suited connectors make on middling boards, get action on all three streets because the cards that complete them look like blanks.
There's a second, quieter reason these hands print: their disasters are cheap. When 2♠2♣ misses the flop, you have no pair, no kicker, no temptation — you check-fold and lose your preflop call. Contrast that with K♣J♦, which misses by making top pair with a dominated kicker and pays off three streets. Good implied-odds hands have a binary quality: hit big or get out for the minimum. That asymmetry — small fixed cost, occasional huge win — is what you're buying when you call preflop with them.
The set-mining math, derived in full
A pocket pair flops a set or better 11.76% of the time — almost exactly 7.5-to-1 against. (The exact figure: you miss when all three flop cards avoid your two remaining rank-mates, which happens C(48,3)/C(50,3) = 88.24% of the time.)
Naively, 7.5-to-1 against suggests you need 7.5 units of total winnings per unit called. So calling a 3bb open would need about 22.5bb of winnings — trivial at 100bb. Why does every serious resource, this site included, teach 15-to-1 instead? Because the 7.5 figure assumes a fantasy: that every set wins, and wins money.
Reality taxes you three ways:
- Sometimes you hit and win nothing. The opener holds A♣Q♥ on your 9-6-2 set board, misses, and check-folds. You win a 6.5bb pot, not a stack. This is the biggest tax — strong openers whiff the flop or refuse to commit a large fraction of the time.
- Sometimes you hit and lose. Set-over-set, a flush completing against your unimproved set, an overpair spiking a better set on the turn. Rare, but the losses are enormous precisely because sets don't fold.
- You never win when you miss. The 88% of the time you brick, your preflop call is simply gone — small pairs almost never win unimproved against an opening range.
Doubling the naive requirement to 15-to-1 absorbs all three taxes with margin. The working rule:
Set-mine when realistic total winnings ≥ 15 × your call.
For standard open sizes at 100bb effective:
| Open size | Your call | Need (15x) | Available at 100bb? |
|---|---|---|---|
| 2bb | 2bb | 30bb | Yes, easily |
| 2.5bb | 2.5bb | 37.5bb | Yes, easily |
| 3bb | 3bb | 45bb | Yes |
| 4bb | 4bb | 60bb | Yes, but the opener must be willing to commit |
"Realistic winnings" means the pot plus the future bets this opponent actually makes — not his entire stack by default. Against a strong, aggressive opener with 97bb behind, collecting 45bb when you flop a set is well within reach: a continuation bet, a turn barrel, and a modest river bet get there. Against someone who opens wide and gives up easily, discount hard. The 15-to-1 line is your minimum requirement; lesson five in this module covers raising or lowering it by opponent.
What "45bb of realistic winnings" looks like in practice
Make the requirement concrete so it stops being abstract. You call a 3bb open, flop your set, and the strong opener does what strong openers do: continuation-bets 5bb into 7.5bb, barrels 13bb on the turn, and bets 30bb on the river. If you just call down, you collect his 48bb in postflop bets plus his share of the preflop pot — about 52bb total, comfortably past the 45bb requirement without ever raising. That's the point of demanding a strong opener: his range bets for you. When the opener is the type to fire once and quit, that ladder collapses to 5bb plus the pot, and your set-mine quietly stops paying for all the times you brick.
Example 1: the bread-and-butter set-mine
The button faces a 3bb UTG open holding 2♠2♣. Run the direct price first: call 3bb with 4.5bb out there (the open plus the blinds), so you need 3 ÷ 7.5 = 40% equity. A simulation of 2♠2♣ against this site's full UTG opening range comes back at about 40% — on paper, dead even. But that raw number is a mirage for a tiny pair: you flop an underpair to the board 88% of the time and can't continue against a bet, so you realize far less than your simulated share. On direct price plus realization, this is a fold.
The 15-to-1 test is what makes it a clear call: 3bb × 15 = 45bb of realistic winnings needed, against an opening range stuffed with big pairs and big aces — the hands that pay off sets — and 97bb behind. Available money dwarfs the requirement.
Watch the payoff mechanics in the hand block. The flop K♦7♥2♦ gives you bottom set; against pocket aces specifically you're about 91% to win from here. More important than the equity is why the money goes in: from the aces' point of view, he holds the second-nut overpair on a king-high board against a button caller. Every chip he commits feels justified. That's the implied-odds machine working as designed — your 3bb investment, his stack.
Suited connectors: the same engine, different fuel
Suited connectors like 8♠7♠ buy lottery tickets to straights and flushes instead of sets, plus a steady stream of strong draws that let them keep fighting. Here's the full flop map for 8♠7♠, from enumerating all 19,600 possible flops:
- Two pair or better (straights, flushes, trips, two pair): 5.6%
- Flush draw or 8-out straight draw (no made hand yet): 19.1%
- One pair, no big draw: 26%
- Gutshot only: 12%
- Nothing: 38%
So roughly a quarter of flops bring either a big hand or a big draw — and the draws matter because they carry their own implied odds, as you computed in the previous lesson. The continue/fold sorting writes itself: continue on the 5.6% monsters and the 19.1% big draws, usually peel one card with pair-plus-backdoor hands, and release the pure-gutshot and air flops cheaply against real pressure.
Which boards pay? Middling, connected ones. When you make your straight on T-9-6 or flop two pair on 8-7-3, the opener's AA/KK/AK/QQ class still holds an overpair or top pair and funds you. When your miracle arrives on A-K-Q, your opponent's range is so strong it sometimes beats you — and when it arrives on 9-8-4-2-2 after he whiffed with A♥Q♣, nobody pays. Suited connectors want the opener strong-but-second-best, same as small pairs.
Example 2: defending 8s7s from the big blind
- 1.Preflop: CO raises to $2.50, SB folds, BB calls (pot $5.50)
Analysis
The BB closes the action getting 1.5-to-call into 4bb — a 27.3% requirement — while 8s7s has about 40% equity against the CO range above. The call is automatic on price; the implied-odds work happens postflop: about 25% of flops bring two pair+ or a big draw to continue with, and the hand's straights and flushes land on middling boards where CO's overpairs and top pairs keep paying.
Against the cutoff's 2.5bb open shown in the chart, the big blind calls 1.5bb more into a 4bb pot: required equity 27.3%. A simulation of 8♠7♠ against that exact range gives about 40%. The discount price (your big blind is already posted) makes this a trivially correct defend — but notice the division of labor. The call is justified by pot odds; the profit comes from implied odds. You will realize less than your 40% playing out of position, and the gap is repaid on the flops where you make a disguised monster against a range that opens every pocket pair, every broadway, and big aces — hands that make exactly the strong-but-second-best holdings your straights feast on.
Which pairs and which connectors qualify
Not every member of these families works the same way, so sort them before you memorize anything.
Pocket pairs 22–66 are nearly pure set-mines. Unimproved, they lose to any pair the board or your opponent makes, so their preflop calls live and die by the 15-to-1 test. If the test fails, there is no consolation prize — fold.
Pocket pairs 77–99 are dual-purpose. They still want to flop sets, but on low boards like 6-4-2 they're frequently the best hand unimproved, which means they realize meaningfully more of their raw equity. They can pass marginal spots the small pairs fail, because the set-mine isn't carrying the entire load.
High suited connectors (T9s, 98s, JTs) are the strongest implied-odds hands that aren't pairs: they make straights and flushes and flop top pair often enough to win small pots without improving. Their flush problem — a nine-high flush occasionally runs into a higher one — is real but modest, and covered in the reverse-implied-odds lesson.
Low suited connectors (54s, 65s) keep the draw frequency but lose the pair value: top pair of fives wins nothing. Treat them closer to pure speculative hands — they need better prices, better position, or deeper stacks than their taller siblings.
Offsuit connectors (87o, T9o) fail the audition entirely. Dropping suitedness deletes the flush half of the big-draw map — the enumeration above shrinks dramatically — while keeping all the dominated-pair downside. The site's opening and defending charts reflect this: suited connectors appear everywhere, their offsuit twins almost nowhere.
The multiway bonus
Everything above assumed a heads-up pot, and multiway pots make these hands better. If MP opens to 3bb, the cutoff calls, and you're on the button with 4♦4♣, your call still costs 3bb — but now two ranges can flop top pair against your set, and the preflop pot is bigger before you even hit. The chance someone pays you off rises with each extra opponent while your price stays fixed. This is why small pairs and suited connectors are the classic "overcall" hands: the worst thing that happens to a set-mine is everyone folding when it hits, and multiway pots make that outcome rare. One caution — suited connectors' one-pair and weak-draw flops shrink in value multiway, so tighten the postflop continues even as the preflop call improves.
The counterexample: when 15-to-1 says no
- 1.Preflop: MP raises to $3, BTN 3-bets to $12, blinds fold, MP ?
Analysis
Calling $9 more into $16.50 requires 35.3% — close to 33's ~35% raw equity against a tight QQ+/AK 3-bet range, but small pairs realize far below raw equity. The set-mine test fails outright: 9 x 15 = 135bb of needed winnings against a maximum of 28bb behind plus the pot. Even winning the opponent's entire stack every single time a set flops wouldn't reach half the requirement. Fold.
Now break the rule on purpose to see why it exists. You open 3♣3♥ to 3bb in middle position at 40bb effective (you're at a table with a short aggressive 3-bettor) and the button makes it 12bb. The direct price: call 9 into 16.5, requiring 35.3%. Against a tight 3-betting range of QQ+/AK, pocket threes simulate at about 35% — superficially fine, but you already know better: that equity comes from winning 52-card showdowns a tiny pair almost never gets to see cheaply. You'll face continuation bets on flops with two or three overcards to your threes, holding a hand that can beat nothing that continues.
So the call must justify itself as a set-mine, and the arithmetic is brutal: 9bb × 15 = 135bb of needed winnings. After calling, the button has only 28bb behind, plus the 25.5bb pot — about 53bb available in total, and that's awarding yourself his whole stack every time you flop a set against a range that will sometimes hold A♣K♦ and pay nothing on your 9-5-3 board. You're short of the requirement by more than half even in the dream scenario. The fold takes two seconds once the multiplication is done.
This failure mode — shallow stacks gutting the implied side of the calculation — is so important it gets its own treatment in the next lesson. For now, internalize the reflex: the 15-to-1 test is a multiplication against the effective stack, not against your optimism. Count the call, multiply by 15, compare to what's genuinely behind. Pocket pairs and suited connectors are the best implied-odds hands in the game, but only when someone at the table has both the money and the hand strength to pay them off.