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Baker's Game, Recent Results

The standard game uses four Free Cells.  The percentage of games that can be won is extremely dependent upon the number of Free Cells, with the percentage of games that can be won being much higher when there are more Free Cells.  My original 1981 solver only dealt with the normal case of four Free Cells.  With the new solver, it was easy to experiment with other cases.

Number of Free Cells Approximate percentage of positions that can be won Some sample runs
0 0.001% won 10 of 1000000
won 8 of 1000000
won 11 of 1000000
1 0.18% won 1776 of 1000000
won 1897 of 1000000
won 1819 of 1000000
2 4.25% won 42584 of 1000000
3 28.9% won 288889 of 1000000
won 289588 of 1000000
4 75.0% won 750611 of 1000000
5 97.9% won 979429 of 1000000
6 99.98% won 999847 of 1000000
7 100.0% won 1000000 of 1000000

Note that the results for 7 Free Cells do not prove that 100% of all games can be won when there are 7 Free Cells.  Rather, the results simply show that the percentage of games that cannot be won when there are 7 Free Cells must be extremely small.

Results copyrighted by Jerry Bryan, posted on the Internet 21 September 2004.  Permission to copy is granted provided that Jerry Bryan is cited as the source of the data, and provided that this copyright notice accompanies any posting of the data.

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This page last edited on 23 Aug 2011.