## Scramble probabilites (cycle counts)

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• Hmm, my first message isn t even posted yet... http://cube.garron.us/scramblestat/kociembastat.txt and http://cube.garron.us/scramblestat/JNetstat.txt have
Message 1 of 1 , Apr 12, 2007
Hmm, my first message isn't even posted yet...

http://cube.garron.us/scramblestat/kociembastat.txt and http://cube.garron.us/scramblestat/JNetstat.txt have been updated with one more statistic: cycle count.
This is the number of disjoint cycles (of a certain type of piece) that comprise the cube, including cycles of length 1. If you subtract from this the number of placed pieces, you'll get the number of cycles (of arbitrary length) that need to be resolved, as in blindfolded solving.

Here are the total number of cycles (edges, then corners), listed by occurence of that number (1-12 or 1-8).

Cube Explorer set:
{824, 2461, 3145, 2215, 985, 306, 56, 7, 1, 0, 0, 0}, {1290, 3256, 3219, 1645, 497, 87, 5, 1}

JNetCube set:
{819, 2578, 3137, 2220, 943, 249, 48, 6, 0, 0, 0, 0}, {1238, 3247, 3248, 1725, 456, 81, 5, 0}

Theoretical Distribution (Stirling numbers of the first kind -normalized):
{833.3, 2516.6, 3150.7, 2197.4, 960.2, 278.5, 55.1, 7.5, 0.7, 0.040, 0.0014, 0.000021}, {1250.0, 3241.1, 3256.9, 1678.8, 486.1, 79.9, 6.9, 0.25}

JNet doesn't seem too biased here...

-Lucas Garron

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