• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 40,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

PLL Probability?

TimMc

Premium Member
Joined
Aug 12, 2007
Messages
1,741
Location
Melbourne, Australia
WCA
2009MCMA01
Hi All,

Has anyone done the math for figuring out PLL Probability?

To narrow down the probability here's the only OLL algorithms that I use:
1) R' F' U' F U R (x1) (x2) (x3)
2) R U' L' U R' U' L (Niklas)
Special thanks to Werner Randelshofer for his Java Applet...

Some common PLL algorithms after my OLL seem to be:
- J Perm
- U Perm
- Z Perm
- T Perm
- H Perm

At the moment when I'm faced with a PLL case that I don't know I just do a J Perm and another algorithm in the list above to solve the cube. In theory it'd be faster to just do one short algorithm instead of two.

I don't know all PLL algorithms so I can't identify the other common cases after my OLL method. Knowing the exact probability would allow me to selectively learn few more algorithms to try to get near 20 seconds :)

Any help would be greatly appreciated!

Tim.
 

TimMc

Premium Member
Joined
Aug 12, 2007
Messages
1,741
Location
Melbourne, Australia
WCA
2009MCMA01
So...

PLL:
- G (4 algorithms)
- A J R U (including reflections)
- F T V Y
- E N Z
- H

EDIT: I'll start working on G A and R. I already know J U T Z H from that list :)

Tim.
 
Last edited:

tegalogic

Member
Joined
Dec 8, 2007
Messages
34
The OLL leading up to the PLL doesn't matter. Last layer cases for every OLL and PLL case combination is possible (I'm quite sure), you can create them using PLL then commutators to flip the corners and edges "individually" (paying attention to the law of the cube, of course).
 

cmhardw

Premium Member
Joined
Apr 5, 2006
Messages
4,115
Location
Orlando, Florida
WCA
2003HARD01
YouTube
Visit Channel
The OLL leading up to the PLL doesn't matter.

What he means is were any influencing effects on the PLL done during the OLL step or not? Such as does the probability include the possibility that you used a COLL alg during the OLL step if the edges were oriented. This would leave an oriented OLL and the corners solved relative to each other. Or sometimes people form a 2x2x1 block in the LL during F2L, and then preserve that block during the OLL step which leaves fewer possible LL cases.

Chris
 

tegalogic

Member
Joined
Dec 8, 2007
Messages
34
Oh, well, if an OLL was supposed to do a 3-cycle PLL for instance (above Niklas does UBL to UFL to UBR), the OLL could solved the orientation, but sometimes the target PLL (not symmetrical) was not reached because the PLL was not aligned correctly for the OLL (for example, UBR to UBL to UFR).
I'm not sure if this makes any sense, but... I'm guessing that the differences in probablility will differ very little.
 

qqwref

Member
Joined
Dec 18, 2007
Messages
7,834
Location
a <script> tag near you
WCA
2006GOTT01
YouTube
Visit Channel
If you aren't deliberately trying to affect the PLL during OLL, it will remain random and the probabilities will remain the same. Of course some people will deliberately affect PLL in order to get a nicer one, which *would* change the probabilities, because then you make certain PLLs impossible to get in certain cases. For instance, if I have a Sune OLL but a solved 2x2x1 block, I'll do Niklas instead to preserve the block, which means I can only get A (1/3), J (1/3), V (1/6), or solved (1/6).
 

TimMc

Premium Member
Joined
Aug 12, 2007
Messages
1,741
Location
Melbourne, Australia
WCA
2009MCMA01
If you aren't deliberately trying to affect the PLL during OLL

After Orienting the Edges if the case isn't Sune or Anti-Sune then I perform Niklas or Anti-Niklas to make it so. Then I perform Niklas or Anti-Niklas to have it ready for PLL.

I wouldn't say I'm deliberately setting it up like that. I just do it that way because I can perform Niklas faster than other OLL algorithms.

Tim.
 
Top