Exactly whata re the chances iof getting a LL skip on a nxnxn cube when using LBL
Assuming you have solved 6 layers, all center pieces are solved.
The corner chances are constant on every cube.
An nxnxn cube has 4(n-2) edges in the last layer. There is a number of different edge pieces (4x4 has 1, 5x5 has 2, 6x6 has 2, 7x7 has 3 etc.) on each cube. You can calculate the number of different edge pieces by dividing n by 2, then subtracting 1. If you round it you have the number of different edges. In the last layer, there are 8 of each type, except for a middle edge piece, which only exists on odd cubes, of which there are 4.
Middle edge pieces have orientation and permutation, the other edge pieces only have permutation.
The number of possibilities for 8 edges is 8!, (parity exists), one of which is the solved state. That's 1/40320. The chance that the middle edges are solved is 1/((2^4)/2)*((4!)/4) (parity doesn't exist), which is 1/48. The chance that this is also solved in relation to te corners is 1/2 (H-perm is possible) so the chance that the middle edges are solved is 1/92.
The chance that the corners are solved is 1/((3^4)/3)*((4!)/6) (parity doesn't exist), which is 1/162.
Odd cubes:
_________1_________
162*92*(n/2-2)*40320
Even cubes:
________1________
162*(n/2-1)*40320
I think I have made a mistake somewhere, but I don't know exactly. I hope the more advanced cube theorists can point out my mistake.
Maarten
Edit: 500th post
