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Solving Statistics for the first 10 Million MS-Freecell-like Baker's Game Deals

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  • Shlomi Fish
    Hi all, after a lot of work on the infrastructure (you can see the Freecell Solver trunk about that: ( http://svn.berlios.de/viewvc/fc-solve/fc-solve/trunk/ )
    Message 1 of 1 , Jun 12, 2011
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      Hi all,

      after a lot of work on the infrastructure (you can see the Freecell
      Solver trunk about that: (
      http://svn.berlios.de/viewvc/fc-solve/fc-solve/trunk/ ) I have ran
      Freecell Solver on the first 10 million deals of Baker's Game based on
      that of the MS-Freecell / Freecell-Pro layouts. The preset chosen was
      such that first ran the default heuristic (which may have some false
      negatives) and then ran an atomic moves-based solution that guarantees
      an accurate verdict.

      Here are the results. “gen_states” are the generated states. “iters”
      are the iterations' count (they are only different for the solved
      boards). sol_lens are the solutions' lengths.

      Count solved/gen_states == 7,431,962
      Max solved/gen_states == 893,848
      Min solved/gen_states == 66
      Mean solved/gen_states == 774.802232
      StdDev solved/gen_states == 2,043.686579
      Median solved/gen_states == 261

      Count solved/iters == 7,431,962
      Max solved/iters == 893,777
      Min solved/iters == 53
      Mean solved/iters == 737.625714
      StdDev solved/iters == 2,041.805056
      Median solved/iters == 223

      Count solved/sol_lens == 7,431,962
      Max solved/sol_lens == 246
      Min solved/sol_lens == 63
      Mean solved/sol_lens == 107.457259
      StdDev solved/sol_lens == 10.863272
      Median solved/sol_lens == 107

      Count unsolved/gen_states == 2,568,038
      Max unsolved/gen_states == 1,411,608
      Min unsolved/gen_states == 38
      Mean unsolved/gen_states == 6,668.607073
      StdDev unsolved/gen_states == 8,535.782652
      Median unsolved/gen_states == 4,160

      Count unsolved/iters == 2,568,038
      Max unsolved/iters == 1,411,608
      Min unsolved/iters == 38
      Mean unsolved/iters == 6,668.607073
      StdDev unsolved/iters == 8,535.782652
      Median unsolved/iters == 4,160

      A few observations:

      1. The FreeCell FAQ ( http://www.solitairelaboratory.com/fcfaq.html )
      claim that Baker's Game has a win rate of 75%) was confirmed as 74.3%
      of the deals are solvable.

      2. The maximal iterations count for unsolved boards is 1.4 million,
      which indicates that unsolvable Baker's Game deals do not usually span
      as many positions as their Freecell counterparts.

      3. The solution lengths for unoptimised solutions are pretty long at
      107 moves mean and median.

      You can find the data that was used to calculate the summary here:

      http://prdownload.berlios.de/fc-solve/Bakers-Game-First-10Million-Deals-Statistics-4-Freecells-v0.2.0.perl-storable.xz

      Regards,

      -- Shlomi Fish

      --
      ------------------------------------------
      Shlomi Fish http://www.shlomifish.org/

      Electrical Engineering studies. In the Technion. Been there. Done
      that. Forgot a lot. Remember too much.
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