# Cube probability and coin flips

#### campos20

##### Member
Have you ever considered the probability of getting a random state cube solvable optimally with n moves? Well, I have. Since normal probability are not that readable when talking about cube, one can picture the scene with exciting coin flips.

The chance you get a cube that can be solved with 10 moves is approximately the same as getting 28 Heads in a row in a coin flip (or 5.37e-07%. See, coin flips are better).

Here's a table:

Moves

Flips

Now, how was that calculated? Well, first we can go to http://cube20.org/. The number of cubes solvable with 10 moves is c10 = 232,248,063,316 and but the total number is ctotal = 43,252,003,274,489,856,000. So, ctotal is approximately 186,231,922.2686 times c10. Taking log2 (to calculate coin flips) we have 27.4725. Its ceiling is 28. Repeating this process, we can build this table.

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Cool