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Using my relatively new Core i7 920 CPU machine (Linux 64-bit with 12GB of RAM) I solved 1,000,000 random cubes optimally at a rate of about 20 cubes per minute. The computation took about four weeks (I also used a few other slower boxes to do some of them). I got the following results:

12f*: 1
13f*: 14
14f*: 172
15f*: 2063
16f*: 26448
17f*: 267027
18f*: 670407
19f*: 33868

No 20f* cube was encountered, which is as expected. No symmetrical or anti-symmetrical positions were encountered.

These results are very close to Kociemba's results for 100,000 cubes; much closer to his overall predictions than those extrapolated from the 250 cosets I ran completely. This seems to indicate that running random cubes may be a more effective way to get a distribution estimate than by running many fewer random cosets (but which contain collectively many more individual positions).