3x3 Speedcubing: The Ultimate Limits Forecast
History · Methods · Hardware · Math · Biomech · Top Cubers · Training · Statistics — toward a single & average forecast.
CFOP Anatomy: Cross → F2L → OLL → PLL
CFOP, published by Jessica Fridrich 1997 with 1980s independent work by Hans Dockhorn and Anneke Treep, 119 core algorithms (41 F2L + 57 OLL + 21 PLL), ~57.5 HTM at speed. Dominant method behind 23 years of WRs.
| Step | Algs | Avg STM | Recog (s) | Top time (s) | Description |
|---|---|---|---|---|---|
| Cross | 0 | 7 | 0.00 | 0.80 | Build the cross on bottom layer (4 edges). Plan during 15s inspection — elite cubers reach 100% inspection-planned at sub-5 level. Optimal HTM averages 7.42 moves. |
| F2L (4 pairs) | 41 | 28 | 0.05 | 2.00 | First Two Layers — insert 4 corner+edge pairs into bottom layer slots. 41 distinct cases (with mirrors → 119). Intuitive + memorized hybrid. Top cubers use "lookahead" — solving pair N while tracking N+1 in periphery. |
| OLL (Orient Last Layer) | 57 | 9.7 | 0.50 | 0.90 | 57 cases orienting the last-layer corners + edges so top face is uniform color. Avg alg length 9.7 STM. Recognition by yellow-sticker pattern. Pure CFOP elites finish this step in ~0.5 s after a ~0.5 s recognition. |
| PLL (Permute Last Layer) | 21 | 12.5 | 0.40 | 1.00 | 21 cases permuting last-layer pieces to solve cube. Includes AUF (alignment of U face). Avg alg length 12.5 STM. Recognition by side-color blocks ("blocks then bars then headlights"). |
Cross color neutrality (CN). Fixed color 5.81 HTM avg, full CN 4.81. The win isn't the mean — P(≤4-move cross) jumps from 5.99% to 29.17%, ~5× as many easy crosses. Why CN is universal at the top.
F2L 41 cases, 6.7 STM/slot avg, 26.8 total. Elite F2L tricks:
- Pseudoslotting: misalign F or B by 90° as setup.
- Multislotting: one sequence inserts two pairs.
- EO-during-F2L: i.e. ZBLS, last pair while orienting LL edges.
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