4x4 parity Algorithms

Every algorithm for all 25 parity cases, ranked by the alg sources that match real solves.

What makes this database different

Ranked by the alg sources that match real solves

Resources whose picks match what top solvers actually use count for more than resources whose picks don't.

Consensus scores every alg site and sheet against what top solvers were actually reconstructed doing, then adds up what those resources recommend for this case. A resource whose picks match real usage counts for several times more than one whose picks don't, and each resource's own top pick counts more than its alternates. So the order here is fed by pro solves, one step removed. How it works.

One row per algorithm

The same algorithm written in different ways collapses into one row.

Alg lists repeat themselves: the same turns show up reordered, behind a different alignment, or just spelled a different way - a slice M written as r'R , a wide l written as x'R . Those all move the cube through exactly the same states, so we fold them into one row and add up their votes.

Mirrors are the exception: a left-handed version keeps its own row, because doing an algorithm on the other side is a genuinely different thing to learn.

Grouped into triggers

Every algorithm is boxed into the triggers your hands already know.

Grouping gives an algorithm a shape you can picture instead of a string you have to spell, and it exposes the family resemblances: algorithms built from the same trigger carry the same colour, so the one you already know gives you a head start on the next. The Rightie RUR'U' gets one colour, the sledgehammer R'FRF' another. Hover any box for its name.

rU2rU2rU2

The parity engine: one wide turn and a double, repeated - read as one motion, not six.

rU2r' U2

The same shape spelled as an inner slice, which is a different grip, not a different algorithm.

RUR'U'

The Rightie, unchanged from a 3x3 - the last layer is still a last layer.

Cubers have always marked triggers by hand, in parentheses: F (R U R' U') (R U R' U') F'. The boxes are that convention drawn instead of typed, and they are worked out from the moves themselves rather than stored per algorithm - so every algorithm in the database has them, including the ones nobody ever bracketed.

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