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Probability Thread

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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.
 
Last edited:

PingPongCuber

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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

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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

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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.
 

xyzzy

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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.
 

Kit Clement

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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
On top of Ruwix being a terrible source, the question was about the length of the scramble, not the optimal solution to that scramble's state.
 
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