1. Originally Posted by CubeRoots
I don't know about OLL but PLL is definitely not p=1/720. Maybe you mean 1/72? there are 22 PLL cases (one of which is PLL skip), for almost every case there are 4 ways it could occur (just the way it is oriented), except the symetrical cases. The one that swaps opposite edges is an example, these can only occur in two ways because of the symmetry. I think there are 6 of these, So in total there are 15*4 + 6*2 = 72 cases + PLL skip so I guess it's roughly 1/72, 1/73 to be pedantic. Can anyone verify or fault my logic?
Well, it's pretty easy. Assume there are actually 73 different PLL cases, counting different orientations separately. Since 73 is prime, this is only possible if there are 73 pieces of the same kind on the LL; this is obviously not the case, hence your logic must be wrong

Actually the correct result for the cube ls 1/72. But as Rpotts pointed out, we were talking about the megaminx, for which the correct result is 1/720. (There are 60 possible permutations of corners (5!/2, since only even permutations are possible), same for edges, hence 3600 possibilities disregarding AUF, hence the probability of a PLL skip is 1 out of 3600/5=720.)

2. Originally Posted by TMOY
PLL skip is 1/720, OLL skip is 1/1296.
I'm guessing that an LL skip is 1/933120 chance of happening. Now we have to wait for Simon to report back to us to see when he gets an LL skip on megaminx.

3. Are the chances of getting an LL skip with winter variation (as in you have winter variation in the current solve) 1/22? Because there are 21 PLL's you might get and 1 just solved last layer? (don't count AUF's) Thanks.

4. Originally Posted by Riley
Are the chances of getting an LL skip with winter variation (as in you have winter variation in the current solve) 1/22? Because there are 21 PLL's you might get and 1 just solved last layer? (don't count AUF's) Thanks.
1/72 probly.

5. If you're just orienting the corners, then it would be 1/63.

Otherwise, no idea. You might also have to include half the F2L's, since mirrors make no extra contribution.

6. Originally Posted by IanTheCuber
If you're just orienting the corners, then it would be 1/63.

Otherwise, no idea. You might also have to include half the F2L's, since mirrors make no extra contribution.
I'm trying to say, if you have a R U' R' insertion with 3 edges on the top layer that are already correct (like yellow facing up, if white was your cross color), what is the chance of an LL skip, using WV, so that the corners orient? No mirrors. And if it's still 63, can you please explain how you get that? Thanks!

7. Originally Posted by Riley
I'm trying to say, if you have a R U' R' insertion with 3 edges on the top layer that are already correct (like yellow facing up, if white was your cross color), what is the chance of an LL skip, using WV, so that the corners orient? No mirrors. And if it's still 63, can you please explain how you get that? Thanks!
Same chance as a PLL skip - 1/72

8. Here is a good one: What is the propability of getting a Sub-30 solve on 4x4, considering your average is about 37 seconds, and about 1/150 you get is Sub-35? I don't think there is enough info to make the answer out, but try. I am.

9. Originally Posted by IanTheCuber
Here is a good one: What is the propability of getting a Sub-30 solve on 4x4, considering your average is about 37 seconds, and about 1/150 you get is Sub-35? I don't think there is enough info to make the answer out, but try. I am.
Well, I'm still in high school, but I don't think it's possible to calculate this. There are too many factors to consider as well.

10. Originally Posted by IanTheCuber
Here is a good one: What is the propability of getting a Sub-30 solve on 4x4, considering your average is about 37 seconds, and about 1/150 you get is Sub-35? I don't think there is enough info to make the answer out, but try. I am.
Hmm, you know you could probably draw a probability distribution, like a gaussian or something with the 1/150 defining the width. Should be possible to get a rough estimate. But I don't know how to do it :P

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