Ranges — poker concepts

What it is

A range is the set of hands a player can have, given everything they have done so far, each with a weight for how likely it is. A button open might be 40% of all hands; the same player's 4-bet a few percent.

Ranges are counted in combos. There are 1,326 two-card starting hands, grouped into 169 classes: a pair (QQ) has 6 combos, a suited hand (AKs) 4, an offsuit hand (AKo) 12. Shorthand like "77+" (sevens and every bigger pair) or "ATs+" (AT suited up to AK suited) writes a range in one line.

Why it matters

You never see your opponent's cards, so a decision is only ever good or bad against the hands they could have. Putting someone on one exact hand is a guess; a range is the honest version of that guess.

Every action narrows a range. A call preflop removes the hands that would have raised; a check-raise on the river removes most of the hands that would have just called. Following that narrowing street by street is most of hand reading.

Your own range matters as much. If you only ever bet the river with the nuts, a thinking opponent folds everything else — your hand is read through your range.

The maths

A pocket pair has 6 combos, a suited hand 4, and an offsuit hand 12.

A range's share of all starting hands equals its combos divided by 1,326.

Worked example

J♥J♦ against a 3-bet

You open with J♥J♦ and an opponent 3-bets. Say they 3-bet only QQ+ and AK.

Count the range: AA, KK and QQ are 6 combos each, AK is 16 (4 suited, 12 offsuit). 34 combos in all.
Against QQ+, your jacks have about 18.4% equity. Against AK, about 56.1%.
Weighted by combos: (18 × 18.4% + 16 × 56.1%) / 34 ≈ 36.2%.

"Am I ahead of AK?" is the wrong question. Against the whole range the jacks have about 36% — and a wider 3-bet range with some bluffs in it changes that number fast.

Try it

Choose a hand and an illustrative range; the equity is against every combo in the range, with your own cards and the board removed.

Opponent's range

Pick your two cards

Pick 3 to 5 board cards

Nothing selected

Raw equity: 52.9%79 combos in the range after card removal

Illustrative ranges, written by hand for teaching — not solved. Estimated by sampling with a fixed seed

Common mistakes

Putting an opponent on one exact hand and playing against that.
Not narrowing: treating a player who bet three streets as if they could still hold every hand they opened.
Counting classes instead of combos — AK is not one hand, it is 16, and twice as common as any pair.
Forgetting your own range: what your line says about you to someone who is paying attention.

In your hands

Hands from your library where the analysis flagged this:

Hands flagged “Called with a hand that beats nothing”

Opens your analysis, filtered. You need to be signed in; nobody else sees your hands.