#### qwr

##### Member
anyone have distributions for avg moves to make an ortega face (color neutral) and average cross moves (for white cross)

#### Tito

##### Member
what is the probability of getting a winter variation at a solve

#### Cubing Forever

##### Member
Probabilities of all PLLs(Counting all cases including mirrors):
Ua: 1/18
Ub: 1/18
H: 1/72
Z: 1/36
Aa: 1/18
Ab: 1/18
E: 1/36
Ja: 1/18
Jb: 1/18
T: 1/18
F: 1/18
Ra: 1/18
Rb: 1/18
V: 1/18
Y: 1/18
Na: 1/72
Nb: 1/72
Ga: 1/18
Gb: 1/18
Gc: 1/18
Gd: 1/18

Either of the U Perms: 1/9
Either of the A perms: 1/9
Either of the J perms: 1/9
Either of the N perms: 1/36
Either of the 4 G perms: 2/9

(All symmetry based. Hope my math and grammar is correct. Coming from a total Math nerd here)

A question out of curiosity:
What is the probability of getting a Superflip as a scramble ? (either official or at home)

Mods please merge these. I double posted by accident.

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#### Devagio

##### Member
A question out of curiosity:
What is the probability of getting a Superflip as a scramble ? (either official or at home)

Mods please merge these. I double posted by accident.
For a random state scrambler, 1 in 43 quintillion.

#### DNF_Cuber

##### Member
what is the likelihood of having a pre built center on 5x5?Also, what are the odds of a white or yellow center being pre built?(for yau)

#### PingPongCuber

##### Member
what is the likelihood of having a pre built center on 5x5?Also, what are the odds of a white or yellow center being pre built?(for yau)
Well, assuming it is in a random state, let’s do the math.

There are 9 center pieces on each center.
Each one can be one of each center. The center one can be discounted because it can be the base center. The first corner one we do can be determined like this:
4 corner pieces per center.
6 colors. 6x4=24. This means that there are 24 possible pieces that could be there, and 4 of them are right, leaving a 1/6 chance it will be right. The next corner has 3/24 or 1/8 because there is one less correct center. Then 1/12 and finally 1/24. Multiply these and you get 1/13824 that all corners and the center are right. Then for edges, you can do the same thing because there are the same number as corners. So 1/13824 squared gets you 1/191102976 chance that a particular center will be solved, but for any of the 6 centers that goes up to:

1/31850496 chance that a center on the cube will be solved.

For yellow/white it would have to be 3X as unlikely, 1/95551488, because yellow/white make up a third of the 6 centers.

These numbers seem too high, but I think I did everything right, so would someone check it?

#### DNF_Cuber

##### Member
maybe that is for just one center you calculated so it is 1/5308416
also I think it should be 3/23 for the second one,2/22 for the third and so on since you are eliminating one piece

#### RiceMan_

##### Member
what is the probability of getting a sub-20 moves scrable

#### Nir1213

##### Member
chances of getting a ll skip no auf, combined with cross being a one mover, combined with all the pairs except one inserted already in f2l?

ok that was a joke but seriously, im thinking is there a difference in probability with ll skips having auf, or no auf. I think that the no auf ones are more rare.

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#### DNF_Cuber

##### Member
read the gods number article on ruwix.com "This number may seem low, but theoretically it should be even lower. Only around 490,000,000 combinations require the full 20 moves to be solved. Although 490 million is a huge number, it is only a fraction of the 43 quintillion possible combinations (0.0000011328955% to be precise). " so .0000011 percent of positions take 20 moves to solve

#### Nir1213

##### Member
read the gods number article on ruwix.com "This number may seem low, but theoretically it should be even lower. Only around 490,000,000 combinations require the full 20 moves to be solved. Although 490 million is a huge number, it is only a fraction of the 43 quintillion possible combinations (0.0000011328955% to be precise). " so .0000011 percent of positions take 20 moves to solve
that is a 1.1 in a million chance.

Not bad, if you think about it. The chances of being struck by lightning is 1 in a million, which means that the chance of the 20 move scramble would be less rarer.

#### Nir1213

##### Member
also i have another one: What is the possibility of getting the super-flip on a 3x3?

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#### xyzzy

##### Member
read the gods number article on ruwix.com "This number may seem low, but theoretically it should be even lower. Only around 490,000,000 combinations require the full 20 moves to be solved. Although 490 million is a huge number, it is only a fraction of the 43 quintillion possible combinations (0.0000011328955% to be precise). " so .0000011 percent of positions take 20 moves to solve
Please don't cite Ruwix as a source. The accuracy of the pages there is somewhat questionable.

#### PingPongCuber

##### Member
also i have another one: What is the possibility of getting the super-flip on a 3x3?
1. Someone asked that just a few post behind you...
2. 1/45 quintillion, as with any particular state