Probability Thread

Discussion in 'Puzzle Theory' started by CubesOfTheWorld, Apr 8, 2010.

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  1. TipsterTrickster

    TipsterTrickster Member

    30
    8
    Sep 15, 2017
    WCA:
    2017BRYA06
    oh yea good point
     
  2. CuberFles

    CuberFles Member

    4
    0
    Sep 17, 2017
    What are the odds for hitting edge parity on a 4 x 4? I'd say 40 %, since there are 5 possible situations after F3L (0, 1, 2, 3 or 4 dedges flipped) and only 2 of these are "wrong" (1 and 3). However, after several dozens of solves I can't seem to get any less than a 60 % chance to hit edge parity. I'm using the 3 x 3 reduction method (centers first, then pair the edges, then solve like a 3 x 3). Is my method invoking unfair amounts of parity cases? Is there anything I can do to hit parity less frequently?
     
  3. Call the UB edge 1, the UR edge 2, the UF edge 3, and the UL edge 4, for the sake of this discussion. Now let us consider the ways that you can have parity.

    0 Edges
    1,2,3,4 are flipped - NO PARITY

    1 Edge
    1 is flipped - PARITY
    2 is flipped - PARITY
    3 is flipped - PARITY
    4 is flipped - PARITY

    2 Edges

    1 and 2 are flipped - NO PARITY
    2 and 3 are flipped - NO PARITY
    3 and 4 are flipped - NO PARITY
    4 and 1 are flipped - NO PARITY
    1 and 3 are flipped - NO PARITY
    2 and 4 are flipped - NO PARITY

    3 Edges

    1 is not flipped - PARITY
    2 is not flipped - PARITY
    3 is not flipped - PARITY
    4 is not flipped - PARITY

    4 ÖµEdges

    All four are not flipped - NO PARITY

    If you count up each of the 'Parity' and 'No parity', you'll see that the split is 50%. The fact that you're seeing 60% is just unfortunate, and over a long number of solves, you'd see it settle to 50%.
     
  4. CuberFles

    CuberFles Member

    4
    0
    Sep 17, 2017
    Aha, thanks for pointing that out :)
     
  5. Oliver1010

    Oliver1010 Member

    15
    7
    Aug 13, 2017

    https: //www.youtube.com/watch?v=v6s9l7kgwRM
    About 1 in 3.66 billion
     
  6. Oliver1010

    Oliver1010 Member

    15
    7
    Aug 13, 2017
    What are the odds of a last layer skip, oll skip, or pll skip on a 4x4 or even layered cube
     
  7. xyzzy

    xyzzy Member

    648
    259
    Dec 24, 2015
    OLL skip: 1 / (2^4 3^3) = 1/432
    Full PLL skip: 1 / (4! 4!) = 1/576
    PLL skip (allowing for AUF): 4 / (4! 4!) = 1/144
    Full LL skip: (1/432) (1/576) = 1/248832
    LL skip (allowing for AUF): (1/432) (1/144) = 1/62208
     
  8. 94matt

    94matt Member

    1
    0
    Oct 5, 2017
    HI guys just want to know that if you have all the corners and one side completed, how many possibilities do you have for the last 8 egdes?
     
  9. TDM

    TDM Super Moderator

    6,907
    171
    Mar 7, 2013
    Oxfordshire, UK
    WCA:
    2013MEND03
    YouTube:
    TDM028
    There are 8!/2 possible permutations and 2^7 possible orientations of the last eight edges. Multiplying those gives a total of 2,580,480 cases.
     
  10. guysensei1

    guysensei1 Member

    5,016
    396
    Nov 24, 2013
    Singing pores
    WCA:
    2014WENW01
    This only works if you are considering rotated versions of the same case as distinct. For example there are 8 'ways' for a clockwise U perm to appear that fits OP's description.
     
    TDM likes this.
  11. Duncan Bannon

    Duncan Bannon Member

    132
    17
    Sep 9, 2017
    Here
    Most of the people here probably know this, but the chance of a PLL skip is the same as getting a H perm. 1/72


    Also, how many algs would there be for FULL 1LLL
     
  12. Rubix Cubix

    Rubix Cubix Member

    137
    25
    Jul 24, 2016
    Bath, UK
    WCA:
    2016GLOZ01
    If you want to do 1LLL, then you could learn ZBLL, only 493 cases I think :p
     
  13. ErwinOlie

    ErwinOlie Member

    10
    7
    Oct 4, 2017
    Gouda, The Netherlands
    WCA:
    2014OLIE01
    The wiki gives the number 3915 with full explanation where that number comes from.
    https://www.speedsolving.com/wiki/index.php/1LLL
     
  14. Duncan Bannon

    Duncan Bannon Member

    132
    17
    Sep 9, 2017
    Here

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