# probability

1. ### Solvable cube if stickers randomly applied? What's the chance?

I know that I have 1/12 chance that my cube will be solvable if I take it apart and assemble it randomly (edge and corner parity combined). The question is what is the probability of a solvable cube if I peel off the stickers and stick them back randomly. :confused:
2. ### Branching OLL to PLL Cases?

I'm not sure if anyone has discovered this before but at some point when I was practicing OLLs, I noticed a few PLL cases pop up after OLL. However, only 6 or 5 out of the 21 were sure to have a chance of popping up. For example, I would finish this case: and then I'd get a Z perm or a U perm...
3. ### Is an infinite scramble really "random"?

If you scramble a Rubik's 3x3x3 with 20 moves (htm), you are less likely to reach some configurations than others. For example, there are usually many more ways to reach a 6 move configuration than a 20 move one using exactly 20 moves. I want to know if the probabilities "even out" after an...