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Misere Sprouts: Keeping It Simple

January 9, 2007

After much analysis of the latest guesses for misere games, I have come increasingly to the conclusion that misere games are not more difficult than normal games. The most important point is to not deviate from the misere algorithm. Otherwise, very big problems can ensue. For example, I was shocked when Josh Purinton told me that Aunt Beast gives 8- 1(9)2 1(10)1[3,4] a Grundy number of 7!!! A human player cannot analyze positions of such high Grundy numbers well.

That is why I offer the following misere strategy. I hope its use will prevent such problems and let a person analyze misere situations as simply as situations in normal play.

I should mention that my conclusions are only my opinion. I am ready to play test games with anyone who disagrees with me.

Strategy for the first player (first player win):

n=6k+4 1(n+1)1[2-4] (n>4)
n=6k+5 1(n+1)1[2]
n=6k 1(n+1)1[2-6] or 1(n+1)1[2-3] (n>0)

Strategy for the second player (second player win):

(The first player's best chance is 1(n+1)2.)

n=6k+1 1(n+1)2 1(n+2)1[2]
n=6k+2 1(n+1)2 1(n+2)1[2]
n=6k+3 1(n+1)2 1(n+2)1[2,3]

A remark: Of course, even with the aid of this strategy, situations will arise:

6k+5 vs. 6k+1
6k+5 vs. 6k+2

Here it is impossible to use misere strategy for 6k+5. In these situations we use normal strategy!