Weighted Ranges: Not All Combos Are Played Always
Real players take a line with some hands only part of the time, so combos carry weights. Multiply each class by its frequency, rerun the same value-to-bluff comparison, and watch a snap call become a fold — and a fold become a call.
Assumptions: All examples use a 6-max online cash game at 100 big blinds effective with no rake, unless a different stack depth or format is stated in the example.
Every count so far treated ranges like guest lists: a combo is either in the range or it isn't. Real players don't work that way. The reg who 3-bets AA also flat-calls it sometimes; the fish who bets his flush draws doesn't bet all of them, every time. A combo played half the time isn't in or out — it's in at weight 0.5, contributing half a combo to this line and half to the other one. Ignore weights and your beautifully precise counts inherit a silent, sometimes decision-flipping error. The fix costs one multiplication per class.
Combos split across lines
Start with the cleanest case: an opponent who slowplays AA exactly half the time he's 3-bet. AA is 6 combos preflop. If half of them 3-bet and half flat, then:
- His 3-betting range contains 6 × 0.5 = 3 effective combos of AA
- His flatting range contains the other 3 effective combos
Nothing was deleted — card removal hasn't touched anything. The 6 combos were split between lines by his strategy. That's the entire concept: a hand's combos get divided across the actions he takes with it, in proportion to how often he takes each. When you count the range for any one line, each class enters at (combos) × (frequency he takes this line with it). Fractional results like 4.5 effective combos are fine; they're frequencies, not physical cards.
The practical consequence shows up immediately: when this player just flat-calls your open, "he can't have aces" is wrong — he has 3 effective combos of them, the same as if a board ace had halved AA. Action removal, like card removal, is often partial.
Crude weights beat false precision
You will never know an opponent's true frequencies. You don't need to. Reads convert to weights coarsely, and coarse is enough:
| Read | Weight |
|---|---|
| "He never does this with that hand" | 0% |
| "Rarely" — he's capable, but it's exceptional | 25% |
| "Sometimes" — genuinely mixed | 50% |
| "Always" — automatic for him | 100% |
Four buckets. Resist inventing 70%s and 35%s — pretending to solver precision with read-based inputs adds noise, not accuracy. The bookkeeping is one line per class: effective combos = live combos × weight, where live combos already include all the card removal from earlier lessons. Then run exactly the same value-to-bluff comparison as before, using effective combos everywhere.
The flagship: a call flips to a fold
You open the button with Q♥Q♦ to $2.50 and the big blind — a tight, straightforward reg — calls. The flop comes J♣8♣3♦; he check-raises your $3 c-bet to $10.50, you call. Turn 7♠: he bets $20, you call. River 2♥ — every draw missed — and he jams $67 into the $66.50 pot. The price: 67 ÷ 200.5 = 33.4%.
Count his jamming range the unweighted way first. Your read on his flop check-raise: sets, plus his 12 best suited-club draws (you've tagged him doing exactly this). He flats all pocket pairs preflop, even JJ.
- Sets: JJ, 88, 33 — one card of each rank is on the board, so 3 + 3 + 3 = 9 combos, all jamming for value.
- Missed draws: the 12 club combos (A♣9♣, K♣9♣, K♣6♣, K♣5♣, K♣4♣, Q♣9♣, Q♣6♣, Q♣5♣, Q♣4♣, T♣9♣, 9♣6♣, 6♣4♣) all bricked — 12 combos of pure air that can only win by jamming.
Unweighted: 12 bluffs of 21 total = 57% bluffs against a 33.4% bar. Snap call, rivers like this are why you play poker.
Now apply the read that actually describes this player: he value-jams every set, but he's tight — he only finds the jam with about a third of his busted draws and check-folds the rest. Weight the classes:
- Sets: 9 × 100% = 9 effective combos
- Busted draws: 12 × 1/3 = 4 effective combos
His jamming range is now 13 effective combos, of which 4 are bluffs: 4 ÷ 13 = 30.8%. The bar is 33.4%. Fold. Same cards, same board, same stack of "he can have" combos — one frequency assumption moved the answer from a snap call to a fold, and not by a hair: unweighted said 57%, weighted says 31%. The membership question ("can he have busted draws?") was never the issue. The frequency question ("how often does he jam them?") was the entire decision.
One process note from the exhibit: weight the value side too, every time. Here the read was "always jams sets" — weight 100%, no change. But if he slowplayed a third of his sets, value would drop to 6 effective combos and the bluff fraction would climb back to 4 ÷ 10 = 40%: call again. Run both multiplications before you trust the fraction.
Weights cut both ways: a fold flips to a call
Weighting isn't a fancier way to fold. The same arithmetic finds calls that membership-counting misses — especially line-based weights, where an opponent's earlier actions tell you which hands can't still be in his range at full strength.
You defend the big blind with 8♥8♦ against a hijack open ($2.50; you call). Flop Q♣6♠3♦: you check-call a $1.80 c-bet ($9.10 pot). Turn 2♥: checks through. River 9♣: you check, he bets $7 into $9.10 — you need 7 ÷ 23.1 = 30.3%.
The naive census of his river bets, with removal (Q♣, 9♣ visible): value AQ 12, KQ 12, 99 3, QQ 3 = 30 combos; bluffs — his missed gutshots and ace-high giveups that fit this line — A5s 4, A4s 4, T8s 2, 87s 2 (your eights block half of each of the last two) = 12 combos. That's 12 ÷ 42 = 28.6%: fold, barely.
But the naive census ignores his own turn check, and the turn check has consequences:
- QQ never checks back that turn (he always c-bets sets — your read, weight 0 in this line): 3 × 0% = 0
- AQ checks the turn about half the time for pot control: 12 × 50% = 6
- KQ almost always checks the turn this shallow in the pot: 12 × 100% = 12
- 99 checked the turn as an underpair and rivered a set: 3 × 100% = 3
Effective value: 21. Bluffs unchanged at 12 (this player stabs rivers with all his missed hands once the turn checks through — weight 100%). New fraction: 12 ÷ 33 = 36.4%, comfortably over the 30.3% bar. Call. The naive count folded the best bluff-catcher in your range; the line-weighted count calls and profits.
The bookkeeping, start to finish
The full weighted procedure adds exactly one step to what you already do:
- Count live combos per class — preflop range, minus card removal from board and your hand. (Lessons one through three.)
- Assign each class a bucket weight — 0%, 25%, 50%, or 100% — for this specific line, using reads and the logic of his earlier streets. Default to 100% when you have nothing; that's just the unweighted count.
- Multiply: effective combos = live combos × weight. Keep the fractions.
- Compare effective bluffs to the price bar, exactly as in the previous lesson.
Two warnings keep this honest. First, weights are your biggest source of error now — a class at 25% versus 50% can swing a decision more than any blocker, so reserve aggressive discounts (0%, 25%) for reads you'd bet money on, like "he has never check-raise-bluffed in 200 hands," and population tendencies that are boringly reliable, like "low-stakes pools under-bluff river jams." Second, don't double-discount: if you already excluded a hand from the preflop range, don't also weight it down postflop — every hand should be filtered once per decision it made, not once per time you remember it. Weighted counting is the last conceptual upgrade this module makes to the count itself; what remains is making all of it fast enough to use with a clock ticking.
Default weights when reads are thin
When you have no specific note, start from population shape rather than from fantasy precision. Preflop ranges and flop continuation bets can often stay near 100% for hands that clearly belong to the line; most players execute those automatic actions. River bluffs deserve more skepticism. At low and mid stakes, many opponents arrive with enough missed draws but do not pull the trigger often enough, so a 25% or 50% bluff weight is usually more honest than granting every busted draw full membership in a jam range.
Do the reverse for obvious value. Recreational players rarely miss river value with very strong hands, so sets, straights, and flushes often keep 100% weight when they bet big. Thin one-pair value is different: some opponents value-bet it, many check it, and a 50% bucket is usually the cleanest placeholder until you see proof. These defaults are not solver outputs. They are disciplined estimates that stop you from treating "can have" as "always bets."
The best practical test is sensitivity. After your first weighted count, ask what happens if the biggest uncertain class moves one bucket. If changing busted draws from 25% to 50% flips the decision, the hand is not a pure math spot anymore — it is a read spot about that class. If the answer survives the bucket change, act with confidence and save the detailed review for later.