Poker range combinatorics calculator

How this is worked out

A range is not a list of hands but a set of concrete card combinations. While you think «he has ace-king», at the table that is sixteen different pairings, and the board rules some of them out.

Numbers worth knowing

• An unpaired hand — 16 combos: four suits for the first card, four for the second. Four of them are suited and twelve offsuit.
• A pocket pair — 6 combos: any two suits out of four.
• Everything possible in poker — 1,326 combos: every pair of cards from a full deck.

Blockers

Cards on the board and in your own hand remove combos from your opponent's range. A single ace on the board takes out a quarter of all ace combos: sixteen becomes twelve. The two cards in your hand cut sixteen down to nine. Hence the practical lesson: bluffing works better with the hands that block your opponent's value.

What the board breakdown shows

From three cards onwards the calculator sorts the range into categories: made hands, draws, backdoors and air. A backdoor is a draw that needs both remaining cards: two to a suit on the flop only becomes a flush by the river. Air is a hand with no made combination and no draw — no strength now and no way to get there. That is the material decisions are made of: a range with few made hands and lots of air stands up badly to pressure, and that cuts both ways.

The categories overlap: a pair with a flush draw counts among made hands and among draws, so the shares add up to more than 100%. Air is shown as its own block — if the range holds none, the block is not there.