Free Pair, decoded

What counts as free

Read from freePairTrainer.js. A pair in BL, BR or FL is free when any U turn plus one of four inserts solves it. Turn so the target slot is front right and you get exactly these shapes, each with white on a side and never on top. Any U turn of the shape still counts.

Shown for the FR slot with the top view unfolded, so the outer strips are the side stickers of the top layer. Pair colours are bright, everything else is blank. Say it as: joined means pair already built with white on its end. Split means corner and edge sit far apart and the edge's top colour matches the corner's non-white side colour. The exact test covers both in one rule.

Why it feels impossible

It is not easy, and the numbers say why. Every row of the All Algorithms preset, crossed with every setup the trainer can generate, gives 14,637 positions.

So no favourite alg exists. In four out of five positions the alg has to build the free pair, so you cannot get there by leaving it alone. Zones take you to 41% with no tracking, and following the corner alone reaches 52%. Past that you need both pieces through each alg. That is a tracking skill, and it is the thing being trained.

Decision flow

Drill

Same generator and same check as the trainer, same colours. Bright is the cross and front right pair, pale is the other F2L pieces, grey is last layer. The lower map shows the back stickers the trainer hides. Use 1 to 9 to answer, Space for the next case, and open any replay after you answer.

Heuristics, ranked

1. Touch zone beats everything when the pair is already free. If an alg's only effect on both pieces is a net U turn, the shape survives. Sledge-style algs (R' F R F') hit a different zone than R U' R', which is why a case offers both. Tick "Show touch zones": green tiles move rigidly, red tiles get disturbed.
2. Find the pair by absence. Pale pieces are in the top layer in most positions, and the other two slots stay solved. You only have one pair to locate.
3. Check white first. A corner with white on top is never free. Any alg that leaves it there is wrong, which is often the fastest cut when the pair sits still.
4. Track the edge, then the corner. Most moves in an alg miss the piece you are following. The replay underlines only the moves that touch either piece, so count those instead of the whole alg.
5. Use shared openings. (U') R U R' U2 R U' R' and (U') R U R' U R' F R F' share four moves. Replay once to the split point, then compare the tails only.
6. Drill 2gen first. That mode uses only the BR pair and only R' U R or R' U' R inserts, so the shape set drops from twelve slot and insert combinations to two. In this mode an edge with orange on top is always wrong, even when the pair looks joined.

Where EO fits

EO is not part of the answer, so an edge in any orientation can pass. It is useful for one thing: it tells you which insert you will end up doing. Using F/B-axis EO on the whole cube, a good edge goes in with R or L moves, for example R' U R into BR, and a bad edge needs an F or B insert. R, L, U and D turns never change EO, while F, B quarter turns and M-based moves can. An alg with none of those keeps the pair's insert family the same.

Practice order

Pass thresholds are left to you because no benchmark data exists. The stage order is my recommendation, not something measured.