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41008Re: Statistical analysis of (mostly megaminx) scramblers

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  • Stefan Pochmann
    May 1, 2008
      --- In speedsolvingrubikscube@yahoogroups.com, "Daniel
      Hayes" <swedishlf@...> wrote:
      >
      > Megaminx:
      > WCA Scrambler
      > Turns | Std Dev | Expected Std Dev | Confidence
      > 10 |108483.94| 279 | 0.3%
      > 50 | 21986.84| 279 | 0.9%
      > 70 | 12559.95| 279 | 1.7% *official scramble length
      > 100 | 5546.20| 279 | 5.0%
      > 150 | 1451.23| 279 | 19.2%
      > 200 | 469.90| 279 | 59.4%
      > 210 | 398.26| 279 | 70.1%
      > 220 | 351.96| 279 | 79.3%
      > 230 | 312.99| 279 | 89.2%
      > 240 | 307.22| 279 | 90.9%
      > 250 | 294.32| 279 | 94.8%
      > 260 | 285.37| 279 | 97.8%
      > 270 | 280.47| 279 | 99.5%
      > 300 | 278.30| 279 | 99.7%
      > 400 | 275.66| 279 | 98.7%
      > 500 | 269.56| 279 | 96.6%
      > 1000 | 264.62| 279 | 94.8%

      So 270 turns are considerably better than 1000? That seems wrong to
      me, along with the standard deviation droping considerably below the
      expected one.

      > 3x3x3 Cube, generic scrambler (avoids redundant turns, etc):
      > Turns | Std Dev | Expected Std Dev | Confidence
      > 1 |264953.60| 360 | 0.1%
      > 10 | 26320.07| 360 | 1.4%
      > 20 | 4274.47| 360 | 8.4%
      > 30 | 794.28| 360 | 45.3%
      > 35 | 514.75| 360 | 69.9%
      > 40 | 387.39| 360 | 92.9%
      > 45 | 347.40| 360 | 96.5%
      > 50 | 341.04| 360 | 94.7%
      > 75 | 350.58| 360 | 97.4%
      > 100 | 372.78| 360 | 96.6%
      > 500 | 347.09| 360 | 96.4%
      > 1000 | 355.14| 360 | 98.7%

      Same strange behaviour as the megaminx analysis, but in addition,
      here the standard deviation repeatedly jumps up and down at the end.

      Cheers!
      Stefan
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