Counting an Opponent's Value Combos on a Board
Take a defined preflop range, put it on a real flop, apply every removal effect you can see, and produce an exact count of the sets, overpairs, and top pairs it contains — a value ladder measured in combos instead of vibes.
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.
"He's UTG, he c-bet, this board smashes his range." That sentence contains zero information you can act on. How much does it smash his range? Three combos' worth or thirty? This lesson is where the previous two pay off: you'll take a defined preflop range, drop it onto a specific flop, apply every removal effect in view — board cards and your own hand — and walk away with an exact census of what he can hold. The output is a value ladder: a list of his hand classes sorted by whether they beat you, tied to combo counts. Every bluff-catching and value-betting decision you'll make later in this module is built from exactly this raw material.
The setup: a range meets a board
UTG opens to $2.50. For counting practice we'll give him a tight, simplified opening range — premium-heavy and easy to enumerate:
In shorthand: {77+, AJs+, KQs, AQo+}. Fresh-deck size: 8 pairs (48) + 3 suited aces and KQs (16) + AKo and AQo (24) = 88 combos.
You defend the big blind with K♣Q♦ — a standard defend; KQo is in the site's BB-versus-UTG calling range. The flop comes:
Q♠ 8♦ 3♣
You've flopped top pair with a king kicker. Five cards are now visible — K♣, Q♦ in your hand; Q♠, 8♦, 3♣ on the board — and every one of them deletes combos from his 88. Let's count what's left, class by class. After removal, his range is exactly 62 live combos. Here's where they come from.
Counting his sets
QQ. Fresh deck: 6. But the Q♠ is on the board and the Q♦ is in your hand, so only two queens survive — Q♥ and Q♣. The pair formula n(n−1)/2 with n = 2 gives exactly 1 combo: Q♥Q♣. Enumerate it to feel the force of double removal: Q♥Q♦ is dead (your card), Q♥Q♠ and Q♦Q♠ and Q♣Q♠ are dead (board card), Q♦Q♣ is dead (your card). One single way to hold top set. The hand that "smashes his range" exists in precisely one configuration, and you personally block it.
88. The 8♦ is on the board, three eights remain: 3 combos.
33? Look back at the range — 33 isn't in it. A range that opens 77+ cannot flop bottom set here, no matter how scary the board pairs run out. This is a real and underused insight: sets require the pocket pair to have been in the range in the first place. Against the site's full UTG chart, which opens every pair down to 22, you'd add 33 at 3 combos (3♣ on board leaves three treys). Note what changes between the two reads: a nit has 4 set combos here; a standard opener has 7. Know which opponent you're facing before you panic about bottom set.
So against our practice range: sets = 4 combos (1 + 3).
Counting his overpairs
AA: no ace is visible anywhere — 6 combos, untouched.
KK: your K♣ removes one king. Three kings remain: n(n−1)/2 = 3 combos.
Overpairs total 9 combos — more than double his sets. Already the count is correcting instinct: facing aggression on this flop, "overpair" should come to mind before "set," roughly 9-to-4.
Counting his top pairs
AQ (he opens both AQs and AQo). Fresh deck: 16. Two queens are gone (Q♠ board, Q♦ your hand), so the multiplication is 4 aces × 2 queens = 8 total. Check the suit split: AQs needs ace and queen of matching suit — A♥Q♥ and A♣Q♣ survive, A♠Q♠ and A♦Q♦ are dead — so 2 suited; the other 4 × 2 − 2 = 6 are offsuit. AQ = 8 combos.
KQs. Fresh deck: 4. K♥Q♥ survives. K♠Q♠ dead (Q♠ on board), K♦Q♦ dead (your Q♦), K♣Q♣ dead (your K♣). 1 combo — and it doesn't even beat you; it chops, since K♥Q♥ and your K♣Q♦ play the same five cards.
Your own hand did serious work in this census. The K♣ cut his KK from 6 combos to 3 and killed K♣Q♣; the Q♦ cut what the board left of his QQ from 3 combos to 1, trimmed AQ from 12 to 8, and killed K♦Q♦. Holding top pair with blockers to the hands above you is structurally different from holding the same pair with two blanks — and you only see it by counting with your own cards included.
The value ladder
Sort everything in his 62 live combos relative to your K♣Q♦:
| Class | Combos | vs your KQ |
|---|---|---|
| AA | 6 | ahead of you |
| KK | 3 | ahead of you |
| QQ (set) | 1 | ahead of you |
| 88 (set) | 3 | ahead of you |
| AQ | 8 | ahead of you (better kicker) |
| KQs | 1 | chop |
| AK | 12 | you're ahead (ace high) |
| AJs | 4 | you're ahead (ace high) |
Totals: 21 combos beat you, 1 chops, 40 lose to you. Of his entire arriving range, you beat or chop with 41 of 62 — about two-thirds. A Monte Carlo check agrees with the census: K♣Q♦ has about 61% equity against this full range on this flop.
Stare at the ladder's composition rather than just its total. The hands beating you are dominated-kicker nightmares (AQ, 8 combos) and overpairs (9 combos) far more than sets (4 combos). That tells you how to play the hand: against a flop c-bet you're comfortably continuing, but the hands that will pile in big money skew toward AQ/overpairs — hands your king kicker loses to by a hair, not monsters you can comfortably fold to. And if an ace rolls off on the turn, 12 combos of AK convert from "you're ahead" to "you're crushed" at once — the single most range-shifting card in the deck here, and you can see it coming because you counted.
The exhibit's last line is the lesson. Equity says "you're doing great"; the combo composition says how to convert that into money. Raising the flop folds out 24 combos of underpairs and 16 of unpaired ace-high overcards that might bluff or pay later streets, while the continuing range — the 21 combos ahead of you plus some AK with backdoors — has you in bad shape. Top pair good kicker against a tight range plays as a bluff-catcher-plus, and you only know that because you counted the classes, not just the total.
Second pass: counting a check-raise range
The same census works in reverse — when you're the one with the big hand facing aggression. You open K♦K♠ on the button to $2.50 and the big blind calls. Flop:
T♥ 9♥ 6♣
You c-bet $2.75 into $5.50 and the BB check-raises to $9. Time to count his value, using the site's BB-versus-BTN defending ranges. Two structural facts before any arithmetic:
- The site's BB strategy 3-bets TT and 99 preflop (they're in the 3-bet range, not the call range). Since he flatted, those sets are impossible — top set and middle set were removed by his preflop action, not by any card.
- The calling range does contain 66, T9s, T9o, and 96s — bottom set and the two-pair region.
Apply removal (T♥, 9♥, 6♣ on board; your K♦K♠ blocks nothing relevant):
- 66: one six on board → 3 combos
- T9s: T♥9♥ is dead on the board → 3 combos (spades, diamonds, clubs)
- T9o: 3 tens × 3 nines = 9 minus the 3 suited = 6 combos
- 96s: 9♥ and 6♣ each kill a suit's combo → 9♠6♠ and 9♦6♦ only: 2 combos
His entire sets-plus-two-pair region is 14 combos. That's the monster count — everything else in a check-raise here is one pair or a draw. Against just that 14-combo value cluster, your overpair has only about 24% equity, so if his check-raise were value-only, kings would already be in trouble on the flop. Whether it actually is value-only depends on how many draw combos the board offers him — and on T♥9♥6♣ the honest answer is "a lot," which is the entire subject of the next lesson.
Notice the two different removal engines at work in this hand: card removal (the board ate one card from each of 66, T9, 96) and action removal (his preflop flat deleted TT and 99 entirely). Both shrink ranges; only one shows up on the table. Strong players run both, every street, without being asked.
The counting routine
The full procedure, compressed into the order you should run it at the table:
- Fix the arriving range first. Write it in labels ({77+, AJs+, KQs, AQo+}), including what his actions have already removed. A range you haven't pinned down can't be counted.
- List the visible cards — board plus your hand. Five on the flop, six on the turn, seven on the river.
- Count the scariest classes first: sets (3 per matching pocket pair on an unpaired board, fewer if you block), then two pairs, then overpairs, then top pairs. Multiply available cards for unpaired hands; n(n−1)/2 for pairs.
- Build the ladder relative to your hand: ahead / chop / behind, with combo totals for each tier.
- Read the composition, not just the total. Which class dominates the "ahead" tier dictates your line; which cards convert big "behind" classes into "ahead" classes dictates which turns you fear.
Done honestly, the routine takes under a minute away from the table and — after the speed drills later in this module — a few seconds during play. What it buys you is immunity to the two great counting illusions: monsters feel more common than they are (sets were 4 of 62 combos in our flagship count), and dominated hands feel rarer than they are (AQ alone was twice the sets). The board doesn't smash ranges in general. It smashes specific combos, in numbers you can know.