Hand vs range
You never know the one hand. Equity against everything they could have is the number that matters.
7 minute read
Against pocket queens, ace-king suited has 46%. Against a range of 'queens or better plus ace-king', it has about 40%: the aces and kings in that range crush it, the queens flip, the ace-kings chop. Equity against a range is the combination-weighted average of equity against each hand in it.
Equity vs a range
Σ (live combos of hand × equity vs hand) ÷ Σ live combos
'Live' means not blocked by your cards or the board. Ace-king offsuit is 12 combos and pocket queens 6, so AKo pulls twice as hard.
Add a flop to see how the board changes the picture.
Opponent's range
12.0% of hands · 123.9 live combos (35.3 blocked)
Paint the matrix, or type ranges like 22+, A5s+, KTs-K7s, AA:0.5. Enter applies.
Card removal is doing quiet work
Holding an ace removes half of the opponent's possible aces and a quarter of their ace-x hands. The tool applies this before it averages anything — the note under the matrix tells you how many combinations were blocked.
Quick check
Ace-king has 12% against aces and 46% against queens. Against a range of exactly {AA, QQ} with no cards removed, what is its equity?
Show answer
Equal combos (6 and 6), so the plain average: 29%. Holding an ace makes AA 3 combos and QQ 6, so the weighted equity rises to about 35%.