Probability Thread

[xyzzy]

What is the probability of getting a 6 move Pyraminx scramble?

Jaap's Puzzle Page has complete move count distributions for the smaller puzzles, including pyraminx.

 

[Underwatercuber]

I have gotten
2 oll skips in a row
2 pll skips in a row
2 same ll cases in an ao100
A Cross skip
Some First Layer Skips
Some OLLCP Skips
A ZBLL Skip
5 PLL Skips in one day


And I've only been cubing for 6 months

1. What do you mean by first layer skip
2. what to you mean by a ZBLL skip
3. Skips are unrelated to how long you have been cubing

 

[Oliver1010]

Edit3- What are chances of full No AUF LL skip on 2x2? Thanks

There are 4!=24 ways to place the corners in the top layer, ignoring orientation.
Each of the corners has 3 different ways it can be twisted. The 4th corner's orientation depends on the orientation of the other corners. We take 1/(24*(3^3))= 1/648 chance of a LL skip no AUF

 

[obelisk477]

With TNoodle scrambles, what is the probability of any given tip on a pyraminx being scrambled? Is it 1/3 or 1/2?

 

[whatshisbucket]

With TNoodle scrambles, what is the probability of any given tip on a pyraminx being scrambled? Is it 1/3 or 1/2?

I had tnoodle generate 50 pyraminx scrambles and there were 129/200 tips scrampled, much closer to 2/3 than 1/2, so there is probably an equal chance of any given tip being in each of the three positions.

 

[Hazel]

is there a movecount distribution for 3x3 last layer?

 

[xyzzy]

is there a movecount distribution for 3x3 last layer?

http://cubezzz.dyndns.org/drupal/?q=node/view/137

 

[CLL Smooth]

How many cases are there if you have F2L-1 corner+ a tripod (1x2x2) in the LL? Does it matter the orientation of the tripod?

 

[teboecubes]

3. Skips are unrelated to how long you have been cubing

Sort of, because a cuber who got has only done 500 solves in month has a lesser chance than a cuber who has done 100,000 solves over 5 years.

 

[Sue Doenim]

How many cases are there if you have F2L-1 corner+ a tripod (1x2x2) in the LL? Does it matter the orientation of the tripod?

4!×27×2=1296 cases. Only 648 with EO. 162 if you do EO and force the F2L corner into place, not necessarily oriented.

Could anyone get me:
1- 2x2 face average optimal movecount
and
2- 2x2 orientation optimal average movecount?

EDIT: Never mind about the second one.

 

[dnguyen2204]

What are the chances of getting a half oll skip (corners or edges) or half pll skip (corners or edges) using CFOP 4LLL?

 

[xyzzy]

What are the chances of getting a half oll skip (corners or edges) or half pll skip (corners or edges) using CFOP 4LLL?

11/72 and 2/9 respectively, if full skips are excluded.

 

[dnguyen2204]

11/72 and 2/9 respectively, if full skips are excluded.

Nice, not too rare.

That's the combined probability? Can you separate edges and corners?

 

[Rpotts]

What are the chances of getting a half oll skip (corners or edges) or half pll skip (corners or edges) using CFOP 4LLL?

1/8 to skip Edge Orientation
1/27 to skip Corner Orientation
1/6 to skip Corner Permutation
1/12 to skip Edge Permutation

So about 16% to skip half or both steps of OLL, and about 25% to skip half or both steps of PLL.

 

[Hazel]

What are the chances of getting a solved 2x2x1 block with white as one of the 1x2 parts 2 scrambles in a row? I got that

 

[teboecubes]

What are the chances of getting a solved 2x2x1 block with white as one of the 1x2 parts 2 scrambles in a row? I got that

Dont know exactly, but I think it would be ((P Edge Solved)^2 x (P Corner Solved)) / 12. Im not sure though

 

[FastCubeMaster]

May have been asked before, but what is the probability of getting a 4 mover in 2x2?
I assume this is the same as getting one officially. (- the 3 moves or less cases, of course)

 

[AlphaSheep]

May have been asked before, but what is the probability of getting a 4 mover in 2x2?
I assume this is the same as getting one officially.

The probability is 1 in 1989.

There are 3 674 160 states, 1 of which is solved, and 384 of which can be solved in 3 moves or less (these are excluded in official scrambles). 1847 states can be solved in 4 moves.
(3674160 - 385) / 1847 = 1989.05

 

[Mellis Ferton]

Chance to get an xx-cross with an LL skip on 3x3?

 

[Duncan Bannon]

@AlphaSheep This is INSANE math. I’m pretty good in math, how can I do this? And thats about right as I’ve got a 4 mover and 5 mover in about 2k solves.