Blockers and card removal
Every card you can see is a card the opponent cannot hold, and combinations vanish accordingly.
6 minute read
Hold one ace and the opponent's pocket aces fall from 6 combinations to 3 — half of them are gone. Their ace-king falls from 16 to 12. Their ace-queen too. One card in your hand has quietly reshaped their entire range, and the arithmetic is nothing more than multiplying smaller numbers.
Card removal
pair with k cards visible: C(4 − k, 2) unpaired: (4 − a) × (4 − b)
With an ace and a king visible: AA = C(3, 2) = 3, AK = 3 × 3 = 9.
Your hole cards, the board, anything exposed. Up to seven. Every count below is recomputed as you add or remove them.
Ace-King
9 / 16 combinations live| K | K | K | K | |
|---|---|---|---|---|
| A | suited | blocked | offsuit | offsuit |
| A | offsuit | blocked | offsuit | offsuit |
| A | offsuit | blocked | suited | offsuit |
| A | blocked | blocked | blocked | blocked |
- Suited combinations4one per suit
- Offsuit combinations124 × 3
- All combinations164 × 4
- As you can see1
- Ks you can see1
- Live combinations93 × 3One high card times one low card; every pairing is a distinct combination.
Blockers at a glance
How the cards you can see change what an opponent can hold.
| Hand | Combos | Now | Removed |
|---|---|---|---|
| AA | 6 | 3 | 50% |
| KK | 6 | 3 | 50% |
| 6 | 6 | 0% | |
| AKs | 4 | 2 | 50% |
| AKo | 12 | 7 | 42% |
| AQs | 4 | 3 | 25% |
| AQo | 12 | 9 | 25% |
| KQs | 4 | 3 | 25% |
| JTs | 4 | 4 | 0% |
| 77 | 6 | 6 | 0% |
Card removal across a range
209.9 of 265.2 combos remain · 20.9% removedGreen: untouched. Red: combinations removed by the cards you can see; the deeper the red, the larger the share. Each cell reads live / total.
Most affected
- AKo12 → 7 (−5)
- AQo12 → 9 (−3)
- AJo12 → 9 (−3)
- ATo12 → 9 (−3)
- A9o12 → 9 (−3)
- A8o12 → 9 (−3)
- A7o12 → 9 (−3)
- A5o12 → 9 (−3)
This is the whole idea of a blocker: a card in your hand or on the board is a card the opponent cannot have, and every combination that needed it disappears from their range. Sample ranges are educational examples, ordered by equity against a random hand.
Blockers cut both ways
A card that blocks the opponent's strongest hands makes a bluff more credible (they have fewer hands that can call). A card that blocks their bluffs makes a call worse (they have more value). Which effect matters depends on the range — which is why the counts, not the slogans, decide.
Quick check
You hold K♠ Q♠ on a board of K♦ 7♣ 2♥. How many combinations of KK can the opponent have? Of AK?
Show answer
KK: two kings visible, C(2, 2) = 1. AK: 4 aces × 2 kings = 8.