The following is a frequency distribution of solution lengths found for the 1000 random cubes that were solved optimally. Also shown are expected values based on distributions from much larger tests done by Herbert Kociemba and Tomas Rokicki as shown here (see bar charts in section "Optimal Cube Solver").
Expected | |||
Length | Count | Kociemba | Rokicki |
15 | 3 | 1.97 | 2.063 |
16 | 31 | 27.10 | 26.448 |
17 | 265 | 266.73 | 267.027 |
18 | 669 | 670.99 | 670.407 |
19 | 32 | 33.03 | 33.868 |
Of the 18 move solutions, 73% were sub-optimal solutions found at a lower
depth that were shown to be optimal by completion of depth 17.
The percentage is calculated using the number of 18 move solutions (669) and
the number of those that did not have a suboptimal solution (shown as [18+0]
in the log) which is 179, the calculation is: 1 - 179/669.
All of the 19 move solutions were sub-optimal solutions found at a lower
depth that were shown to be optimal by completion of depth 18.
Likewise for the 100 cubes in the 19 move test.