Probability Thread

[cuBerBruce]

Skip on Guimond 1st step (3/4 of a face with opposite colours)

Assuming you're interested in the probability for the color neutral solving...
http://www.speedsolving.com/forum/showthread.php?p=147363

So probability is 3097152/3674160 or approximately 84.3%.

and Ortega step 1 (face)?

http://www.speedsolving.com/forum/showthread.php?p=152726
http://www.speedsolving.com/forum/showthread.php?p=737035

So probability (again, assuming color neutral) is 22654/3674160 (approximately 0.617% or about 1 in 162).

[Pokerizer]

To give a comparison, the chance of a LL skip with no partial edge control, and with the possibility of AUF, is
1 / 15552

I thought it was pretty neat.

Chris

well that sux, I had a solve the other day with a LL skip without having to align edges.... So much for seeing that again any time soon lmao

[Ickathu]

What's the probability of each of the LL cases on pyraminx? I'm referring to the last layer that you get with Oka, not the LBL LL. This LL involves 3 edges and 3 centers.
Does that make sense?

[Schmidt]

Last 2 Center skip on 5x5?

So far: 1/Lifetime
I was just casually solving while my kids played on the playground, so I wasn't paying 100% attention to the solving, so when I had solved the first 4 centers I was turning the cube around to find the next unsolved centers. After a few x-y-z's I couldn't find any

[Bob]

So far: 1/Lifetime
I was just casually solving while my kids played on the playground, so I wasn't paying 100% attention to the solving, so when I had solved the first 4 centers I was turning the cube around to find the next unsolved centers. After a few x-y-z's I couldn't find any

I think the probability that you counted wrong is higher than the probability that you skipped 2 centers.

[JasonK]

What's the probability of each of the LL cases on pyraminx? I'm referring to the last layer that you get with Oka, not the LBL LL. This LL involves 3 edges and 3 centers.
Does that make sense?

Skip = 1/12
U-perm = 1/6
2flip = 1/4
Flipcycle = 1/2

[mDiPalma]

this question has likely been answered before, but advanced search has wierded out on me:

what is the distribution for the minimum amount of 2-generator [RU] moves it can take to solve a cube that CAN be solved 2-generator, without rotations? like if you perform an antisune on your cube, then the fewest moves it would take to be solved would be 7, and this state would be tallied in the 7 column.

does that make sense?

is this an impossibly hard question to answer? if it is, then don't bother.

[Stefan]

Look for "Analysis of the 3x3x3 <U, R> group" here: http://cubezzz.dyndns.org/drupal/text/fullcube.txt

[mDiPalma]

Thanks! I have some more questions!

What is the probability of a last layer skip on a 3x3 given that the cube is in a state that can be solved 2 generator <RU> and has the F2L completed?

How does this compare with a standard LL skip after standard F2L?

[Bob]

Thanks! I have some more questions!

What is the probability of a last layer skip on a 3x3 given that the cube is in a state that can be solved 2 generator <RU> and has the F2L completed?

How does this compare with a standard LL skip after standard F2L?

<RU> gen means that edge orientation is solved and corner permutation is solved.
P(OLL skip) = 1/27
P(PLL skip) = 1/12
P(LL skip) = 1/324

For a typical 3x3 solve, P(LL skip) = 1/15552, so it is 48 times more likely with <RU> gen.

Where did my numbers come from?
<RU> OLL: You can count them (4 each of S, As, L, Pi, U, T, 2 H, and 1 solved) or you can calculate them (3^4/3 [each corner has 3 orientations, but divide by 3 because only 1/3 of these is possible])

<RU> PLL: You can count them again (4 Ua, 4 Ub, 2 Z, 1H, 1 solved) or you can calculate them (4!/2 [4 positions for first edge, 3 for second, 2 for 3rd, and 1 for last edge, but divide by 2 because only 1/2 of all PLL are possible])

3x3 LL: P(OLL skip) = 1/216 and P(PLL skip) = 1/72. Multiply for your answer.