Exact model
Two shuffled 3 × 3 cubes match
- Probability:
- 2.31 × 10⁻¹⁸%
- Odds:
- 1 to (4.33 × 10¹⁹)
- dBan
- −196.4 dBan
Scramble two 3 × 3 Rubik’s Cubes independently and align their centres. The chance that every piece ends in the same place on both cubes is about one in 43 quintillion.
Calculation
p = 1 matching state / 43,252,003,274,489,856,000 legal states
Assumptions
Each cube is sampled independently and uniformly from legal 3 × 3 × 3 states. Aligning like-coloured centres removes whole-cube rotations; a physical hand shuffle only illustrates this uniform-state model.