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41245Re: Statistical analysis of (mostly megaminx) scramblers

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  • per_fredlund
    May 18, 2008
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      Yo Stefan :-)

      Any chance or releasing the code for this new "climbing" scrambler??
      Or is this too trivial to be released? I guess it depends on the data
      structures being used. Do you optimise the data structures for this
      somehow?

      I actually had similar couple yrs ago about breaking pairs
      deliberately, but i never formalised it or implemented anything :D

      Good to see old idea coming back to life. This way of scrambling
      should be generaliseable for almost every kind of twisty puzzle.
      Another benefit is that no solver whatsoever is required. It is also
      closer to RANDOM SCRAMBLING than previous positional approach(es).

      - Per

      > --- In speedsolvingrubikscube@yahoogroups.com, "Stefan Pochmann"
      <stefan.pochmann@...> wrote:
      >
      > --- In speedsolvingrubikscube@yahoogroups.com, "Daniel
      > Hayes" <swedishlf@> wrote:
      > >
      > > 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%
      >
      > I propose the following scrambler, which is hopefully an
      improvement,
      > which could be tested against Daniel's analyzer.
      >
      > The scrambler works like the generic one, except at each turn it
      > doesn't choose completely randomly between the possible sides.
      > Instead it prefers the side which breaks the most sticker pairs,
      more
      > precisely leads to the fewest sticker pairs after the turn. Here a
      > "sticker pair" are two adjacent stickers of the same color.
      >
      > It does this for the first half of the moves, the second half it
      > works the old generic way. So first it tries to break a lot
      quickly,
      > then goes on scrambling from there.
      >
      > To make it less deterministic, it chooses randomly from the three
      > sides which break the most. Or chooses the biggest breaker 1/2 of
      the
      > time, the second biggest 1/4 of the time, etc. Something like that.
      > Open to experimentation.
      >
      > Daniel, can you do this?
      >
      > Btw this is somewhat how I scramble at least the 5x5 and the
      megaminx
      > when I don't have computer generated scrambles. And I believe it
      > could lead to better/shorter scrambles.
      >
      > Cheers!
      > Stefan
      >
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