PLL skip? No problem, but...

Actually the title of the thread seems to imply that there's a problem with having 2 PLL skips in a row..

Anyway, I'm sure every cuber will happen to have 2 or more PLL skips in a row in their cubing lifetime...if they cube long enough...
 
Are you counting a solved LL requiring AUF as an LL-skip as well? Ie. would the probability of an LL-skip, including cases requiring U, U' and U2 still be 1/1944, or would it be 4/1944??
I ignored AUF, i.e., counted all groups of 4 positions a U-move away from each other as 1 position. Counting them separately, there are 16 T-perms, the number is 3^3 * 4! * 4! / 2 = 7776 = 4 * 1944, and the probability is 4/7776 = 1/1944.

Anyway, I'm sure every cuber will happen to have 2 or more PLL skips in a row in their cubing lifetime...if they cube long enough...
... and because everybody uses a method that ends with PLL.

Edit: Also, I'm 100% sure I will have over 9000 F3L skips in a row, if I cube long enough.
 
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Are you counting a solved LL requiring AUF as an LL-skip as well? Ie. would the probability of an LL-skip, including cases requiring U, U' and U2 still be 1/1944, or would it be 4/1944??
I ignored AUF, i.e., counted all groups of 4 positions a U-move away from each other as 1 position. Counting them separately, there are 16 T-perms, the number is 3^3 * 4! * 4! / 2 = 7776 = 4 * 1944, and the probability is 4/7776 = 1/1944.

Aah, right. I get what you're saying! I like your example. There are four possible T perms, and for each one, there are four ways it can be rotated on the U face, giving 16 distinct cases for T-perm.

Just to make sure I'm getting the theory>
  • There are 4 corners, each with 3 possible orientations, combined that's 3*3*3*3 = 3^4 possibilities, but because only a third of corner orientations are reachable, that's (3^4)/3 = 3^3.
  • There are 4! ways to arrange (permute) the four corner pieces, and 4! ways to permute the edge pieces which gives 4!*4! ways to permute them independently. However, since only an even number swaps is possible only the even permutations are valid, giving (4!*4!)/2.
Thus the total number of cases is (3^3) * (4!*4!)/2 = 7776, since one of these cases involves the LL solved, and three more involve the LL solved, but rotated, the chances of a ZBLL skip = 4/7776 = 1/1944

... sorry for the repetition, just had to be sure :)
 
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Yep, that's it. One nitpick: it's better to use "ZBLL" instead of "LL", the latter usually includes cases where EO isn't solved (adds a factor of 2^3).
 
Does it actually matter how many moves are made in a scramble? When I give it to somebody for a scramble and they don't know much about the cube, they always try to make it as scrambled as possible, they try to have it so that the same color is never 3 in a row. But does that actually make a difference between a quick 10 move hand scramble? More chance of a skip or easier F2L?
 
I got two in a row... in competition.

Did you really?!
That's awesome.

I don't know if that was meant to be a joke, but if it wasn't.. Here's my guess as to which two solves it was.. 13.75, 13.92, your last two solves during the first round of Discovery Science Center. Only guessing those because they were much faster then your other solves at that competition and it helped you break your AuR. :p
 
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