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octal game 0.15 |
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Octal Game 0.15 The 0.15 nim sequence is periodic of length 10—the values in final row of the table repeat themselves indefinitely. Normal Play Nim Sequence
0 1 2 3 4 5 6 7 8 9
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0+ 0 1 1 0 1 1 2 2 1 2
10+ 2 1 1 0 1 1 2 2 1 2
Solution for misere play Note added 29 July 2005 Aaron Siegel has found a complete analysis of this game by using his recently developed standalone java program, MisereSolver. The misere quotient semigroup of Guiles has 42 elements, and its pretending function has period 10. There will be a paper coming out in the next year or so that gives more information. If you want to wade through the details now, before it's cleaned up for publication, here's the solution file that gives its misere indistinguishability quotient semigroups to heap 160. That's more than long enough to guarantee that the periodicity continues indefinitely. And here's an even bigger log file documenting the same computation, also to heap 160. |