1. 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 30,000+ people from around the world today!
    Dismiss Notice

Probability Thread

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

  1. 1001010101001

    1001010101001 Member

    920
    169
    Dec 18, 2017
    Australia
    WCA:
    2017WENR01
    What about ZZ users ( EO skip, EOLINe skip)
     
  2. 1001010101001

    1001010101001 Member

    920
    169
    Dec 18, 2017
    Australia
    WCA:
    2017WENR01
    What about ZZ users ( EO skip, EOLINe skip)
     
  3. Sue Doenim

    Sue Doenim Member

    376
    143
    Nov 9, 2016
    EO skip is 1/2048, EOline is 1/270336.
     
  4. dnguyen2204

    dnguyen2204 Member

    98
    43
    Nov 21, 2017
    What's the probability of having a "bad" cross case (optimal solution >6 moves) on white? On white and yellow?
     
  5. xyzzy

    xyzzy Member

    1,198
    644
    Dec 24, 2015
    18.45% and 3.44% respectively. (And you didn't ask about it, but for full CN it drops to 0.03%.)

    Source: http://www.cubezone.be/crossstudy.html
     
    Keroma12 likes this.
  6. Kumato

    Kumato Member

    176
    26
    Dec 29, 2017
    Abu Dhabi, UAE
    WCA:
    2017PARE13
    I have done around less than 12k solves on 3x3, and I have gotten both a LL skip, and a cross skip.
     
  7. shadowslice e

    shadowslice e Member

    2,827
    777
    Jun 16, 2015
    Hampshire, England
    YouTube:
    Shadowslice
    That's not unusual
     
  8. teboecubes

    teboecubes Member

    409
    134
    Aug 9, 2015
    WCA:
    2015TEBO01
    YouTube:
    channel/UCM7dSp9z0hkmytrPpe99e8A
    How many 2x2 first layer cases are there?
     
    Kumato likes this.
  9. alwin5b

    alwin5b Member

    24
    6
    Jan 5, 2017
    Germany
    without regarding symmetry/mirrors, it is (3^4) * [ 8! / (4! * 4!) ] = 5670
     
  10. Duncan Bannon

    Duncan Bannon Member

    1,663
    442
    Sep 9, 2017
    Here
    What I saw chance of OLL skip with Corner Permutation?
     
  11. Sue Doenim

    Sue Doenim Member

    376
    143
    Nov 9, 2016
    1/1296, or about 0.07%.
     
    Duncan Bannon likes this.
  12. teboecubes

    teboecubes Member

    409
    134
    Aug 9, 2015
    WCA:
    2015TEBO01
    YouTube:
    channel/UCM7dSp9z0hkmytrPpe99e8A
    What are, or how can I figure out, the probabilities of skewb OLLs (sarah intermediate)?
     
  13. whatshisbucket

    whatshisbucket Member

    114
    37
    Oct 17, 2017
    Here
    I believe each of the 11 unsolved cases has an equal 4/45 chance of occurring, and a skip occurs 1/45 of the time.
     
  14. Average # of cycles for 4x4 wings?
     
  15. xyzzy

    xyzzy Member

    1,198
    644
    Dec 24, 2015
    1/1 + 1/2 + 1/3 + … + 1/24 − 1 ≈ 2.776 if you don't count 1-cycles (pieces that are already solved).

    Quick proof: If you start with an empty set, there'll obviously be 0 cycles. The kth element added will introduce a new cycle with probability 1/k, so this gives the harmonic number H_24 ≈ 3.776. To exclude the solved pieces, note that each element is a fixed point (i.e. the piece is solved) with probability 1/24, so the expected number of solved pieces is 1 and we subtract that from H_24.

    A caveat is that this is assuming you don't change your orientation to influence the permutation, because that would make the problem intractable. Also, keep in mind stuff like the gambler's fallacy—just because you have three cycles already doesn't make it any more or less likely that you'll encounter a cycle break later. The probability of a cycle break only depends on how many pieces are left to trace, not on how many cycle breaks there already are.
     
  16. M0r0

    M0r0 Member

    12
    1
    Mar 16, 2018
    Michigan
    Chances of me solving a Skewb in four moves (It happened to me at a contest this morning.)

    Basically when solving the white side, I accidentally solved the whole thing.
     
  17. xyzzy

    xyzzy Member

    1,198
    644
    Dec 24, 2015
    0 with WCA-compliant scrambles:
    • 4b3c) Skewb: The (random) state must require at least 7 moves to solve.

    But this is the probability thread, not the regulations thread, so check out Jaap's Puzzle Page for statistics on how many moves are needed. 2073 out of 3149280 states can be solved in four moves or less, so the probability is 2073/3149280 ~ 0.07%.
     
  18. M0r0

    M0r0 Member

    12
    1
    Mar 16, 2018
    Michigan
    But it literally happened to me at a contest today...
    It was only around 4 or 5 moves.
     
  19. whatshisbucket

    whatshisbucket Member

    114
    37
    Oct 17, 2017
    Here
    Then it was a misscramble and you should contact someone to get that changed to a DNF (assuming it's too late to get an extra attempt).
     
  20. i have had a 4 move skewb scramble before, it was a hedge with the first move the other way
     

Share This Page