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3x3 Deep Dive
01Top Line0223-Year WR Chronicle03Famous Reconstructions04State Space 4.3×10¹⁹05God's Number Evolution06Optimal HTM Distribution07HTM/STM/QTM/ATM08CFOP Anatomy09OLL 57 Cases10PLL 21 Cases11ZB / ZBLS / ZBLL12Roux / ZZ / Petrus / Mehta13F2L Lookahead Theory14Inspection Strategy15Lucky Scrambles + Skip Probability16Hardware 1980-202617Smart Cube Revolution18Biomech: TPS Ceiling19Top Cuber Profiles20Training Methodology21Statistical Modeling22GEV Theory23Final Forecast24Scenarios25Caveats

3x3 Speedcubing: The Ultimate Limits Forecast

History · Methods · Hardware · Math · Biomech · Top Cubers · Training · Statistics — toward a single & average forecast.

Section 06 / 25 · ← → to navigate

Random Scramble Optimal HTM Distribution

cube20.org full enumeration: 67% need exactly 18 HTM; mean 17.92, median 18. Only ~4.9 × 10⁸ states need 20 HTM (~10⁻¹¹).

0e+0%10.0%20.0%30.0%40.0%50.0%60.0%1314151617181920P(random)optimal HTM depth
P (random scramble)

Implication for single WRs. Top CFOP 50-58 STM, ZB 48-52 STM — both 2-3× optimal. A "lucky scramble" = low-optimal scramble admitting X-cross / XX-cross or natural skips. Du's scramble had optimal HTM = 18, his CFOP path was 28 STM — no violation of God's number; CFOP pays a +10-20 STM method tax.

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This is the 3x3 deep-dive of /wca/prediction. Data May 2026.