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Probability Thread

vidcapper

Member
Joined
May 22, 2020
Messages
363
I dare say this has been asked many times here before, but I can't seem to ask the right search questions...

What are the probabilities of the dot, 'L', bar & and cross after finishing F2L? The 'L' seems most common...
 

xyzzy

Member
Joined
Dec 24, 2015
Messages
2,878
I dare say this has been asked many times here before, but I can't seem to ask the right search questions...

What are the probabilities of the dot, 'L', bar & and cross after finishing F2L? The 'L' seems most common...
There are 2^4 = 16 possible ways of assembling the last layer edges, if we look at only the edge orientation. Only 8 of these 16 ways will be solvable (since you can't have an odd number of bad edges), and if you don't do any LL influencing when solving F2L (but you should), the 8 solvable ways will show up equally frequently. These 8 solvable ways are (imagine "x" is the last layer colour):

Code:
. x .
x x x
. x .
(cross)

. x .
x x .
. . .
(L)

. x .
. x x
. . .
(L)

. x .
. x .
. x .
(bar)

. . .
x x x
. . .
(bar)

. . .
x x .
. x .
(L)

. . .
. x x
. x .
(L)

. . .
. x .
. . .
(dot)

Thus the probabilities are:
Cross: 1/8
Dot: 1/8
Bar: 2/8 = 1/4
L: 4/8 = 1/2

I might be wrong but

Cross=5/30
L=12/30
Bar=8/30
Dot=5/30
Legit curious about how in the world you got those numbers.
 

vidcapper

Member
Joined
May 22, 2020
Messages
363
There are 2^4 = 16 possible ways of assembling the last layer edges, if we look at only the edge orientation. Only 8 of these 16 ways will be solvable (since you can't have an odd number of bad edges), and if you don't do any LL influencing when solving F2L (but you should), the 8 solvable ways will show up equally frequently. These 8 solvable ways are (imagine "x" is the last layer colour):

Code:
. x .
x x x
. x .
(cross)

. x .
x x .
. . .
(L)

. x .
. x x
. . .
(L)

. x .
. x .
. x .
(bar)

. . .
x x x
. . .
(bar)

. . .
x x .
. x .
(L)

. . .
. x x
. x .
(L)

. . .
. x .
. . .
(dot)

Thus the probabilities are:
Cross: 1/8
Dot: 1/8
Bar: 2/8 = 1/4
L: 4/8 = 1/2

Thanks for that - now I feel foolish that the calculation was so simple. :p
 

ToastyTwurtle

Member
Joined
Jun 13, 2020
Messages
2
Search before asking a question. In this case, it was literally 3 posts ago
okayyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy that might be a little hard to depend on during solves.
I have done 1300 recorded solves and i haven't ever gotten one. I thought i was unlucky but i guess im "normally lucky"
 

CodingCuber

Member
Joined
Nov 10, 2019
Messages
703
Location
Melbourne
WCA
2019HERR14
There are 2^4 = 16 possible ways of assembling the last layer edges, if we look at only the edge orientation. Only 8 of these 16 ways will be solvable (since you can't have an odd number of bad edges), and if you don't do any LL influencing when solving F2L (but you should), the 8 solvable ways will show up equally frequently. These 8 solvable ways are (imagine "x" is the last layer colour):

Code:
. x .
x x x
. x .
(cross)

. x .
x x .
. . .
(L)

. x .
. x x
. . .
(L)

. x .
. x .
. x .
(bar)

. . .
x x x
. . .
(bar)

. . .
x x .
. x .
(L)

. . .
. x x
. x .
(L)

. . .
. x .
. . .
(dot)

Thus the probabilities are:
Cross: 1/8
Dot: 1/8
Bar: 2/8 = 1/4
L: 4/8 = 1/2


Legit curious about how in the world you got those numbers.
But dot case can be avoided pretty much all the time as explained in one of @Owen Morrison 's videos.
 
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