ZBLL probability

[deadalnix]

Does someone know where I can found the probability of occurence of each ZBLL ?

The difference between the most probables and the least seems bug and should be exploited to learn optimal solution only for some of them. A COLL/ELL in one look could be used for the others.

 

[deadalnix]

Ok I found the solution :

T, U, S, Ssym, Pi, L : each case is 1/486

PLL are 1/27*p(pll)

H orient is much more complex :
pll type B and U, Usym, Z, E, V, Y, N, Nsym are 1/27*p(pll)
H and pll skip are 2/27*1/72 = 1/972

Be sure I'm not wrong before using this results.

ZBLL skip is 1/1944 (27*72 = 1944)

So, theyre is no "very probable" ZBLL but some are very "unprobable".

EDIT: this is probaly completely wrong. DO NOT USE AT HOME !

 

[jazzthief81]

There are 444 cases that have a probability of 1/576. These cases include:
- All cases with a Sune, Anti-Sune, Pi, L, T or U orientation.
- The cases with a Double-Sune orientation and that have PLL E (both directions), Z (both directions), N (both), H or the solved permutation.
- The PLL's H, N (both) and the soved last layer.

There are 34 cases that have a probability of 2/576. These cases include:
- The cases with a Double-Sune orientation and that don't have PLL E (both directions), Z (both directions), N (both), H or the solved permutation.
- The PLL's Z and E

There are 16 cases that have a probability of 4/576. These cases include:
- The PLL's J (both), A (both), U (both), T, F, R (both), G (all four), V and Y

 

[deadalnix]

So i'm wrong.

Do you know how the calcul is done ?

 

[deadalnix]

I'll take the exemple of T pll :

You have a probability of 1/18 to get a T perm when you have your LL oriented. And when you finnish your f2l and your EO, you have a probability of 1/27 to get a pll skip.

So the T perm probability should be 1/27*1/18 = 1/486 and not 4/576 .

Am I wrong ?

 

[Lucas Garron]

I'll take the exemple of T pll :

You have a probability of 1/18 to get a T perm when you have your LL oriented. And when you finnish your f2l and your EO, you have a probability of 1/27 to get a pll skip.

So the T perm probability should be 1/27*1/18 = 1/486 and not 4/576 .

Am I wrong ?

That actually looks right to me.
ZBLL should be out of 3^3*3!*4*3 states, T-perm has 4 symmetries, which makes 4/1944 = 1/486.

 

[deadalnix]

Interesting way to solve the problem.

3³ is corner orientation case. 4!² is corner and edge permutation. We have to divide by 2 for parity and 4 for equivalent cases modulo U move.

So we have 1944 states for ZBLL.

Standard cases are T, U, S, Ssym, Pi, L orientation case and regroup 24 case on 27. Each case in this category can occur in 4 different direction so each are 4 / 1944 = 1 / 486 .

These case occurs 4*432 / 1944 = 1728 / 1944.

PLL are categorized as follow (pll and his symmetry are equivalent in term of probability) :
type A : A, T, F, G, J, R, U, Y, V .
type B : Z, E .
type C : H, N, skip.

Type A can occur in 4 different directions and have a probability of 4 / 1944 = 1/486 .
Type B can occur in 2 different directions and have a probability of 2 / 1944 = 1/972 .
Type C can occur in 1 direction and have a probability of 1 / 1944 .

PLL occurs (4*16 + 2*2 + 3) / 1944 = 71 / 1944 and skip 1 / 1944 .

H orientation is the most complex one.In this orientation :
Type A occur in 4 different directions in 2 different cases with a probability of 4 / 1944 = 1 / 486 .
Type B occur in 2 different directions in 2 different cases with a probability of 2 / 1944 = 1 / 972.
Type C occur in 2 different directions in 1 different cases with a probability of 2 / 1944 = 1 / 972.

The H case probability is (4*2*16 + 2*2*2 + 4*2) / 1944 = 144 / 1944 .

I think I got the solution now