Counting combinations in a range
A range is not a list of hand names. It is a count of concrete two-card holdings.
6 minute read
'Queens or better and ace-king' sounds like four hands. It is 34 combinations: three pairs at 6 each, plus 4 suited and 12 offsuit ace-kings. Counting this way is the difference between guessing what an opponent has and measuring it.
The three numbers
pair = 6 suited = 4 offsuit = 12
Any unpaired hand is 16 in total. The 13 × 13 matrix has 169 cells but 1,326 combinations.
Your hole cards, the board, anything exposed. Up to seven. Every count below is recomputed as you add or remove them.
Ace-King
16 / 16 combinations live| K | K | K | K | |
|---|---|---|---|---|
| A | suited | offsuit | offsuit | offsuit |
| A | offsuit | suited | offsuit | offsuit |
| A | offsuit | offsuit | suited | offsuit |
| A | offsuit | offsuit | offsuit | suited |
- Suited combinations4one per suit
- Offsuit combinations124 × 3
- All combinations164 × 4
Blockers at a glance
How the cards you can see change what an opponent can hold.
| Hand | Combos | Now | Removed |
|---|---|---|---|
| AA | 6 | 6 | 0% |
| KK | 6 | 6 | 0% |
| 6 | 6 | 0% | |
| AKs | 4 | 4 | 0% |
| AKo | 12 | 12 | 0% |
| AQs | 4 | 4 | 0% |
| AQo | 12 | 12 | 0% |
| KQs | 4 | 4 | 0% |
| JTs | 4 | 4 | 0% |
| 77 | 6 | 6 | 0% |
Card removal across a range
265.2 of 265.2 combos remain · 0.0% 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
Pick some known cards to see which hands they block.
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.
Two consequences follow immediately. First, an opponent 'has ace-king' offsuit three times out of four. Second, a range of '10% of hands' means 10% of 1,326 combinations, about 133 — not 17 cells.
Quick check
How many combinations are in the range 'JJ+, AQ+'?
Show answer
JJ, QQ, KK, AA = 24; AQ and AK = 16 each = 32. Total 56.