The game of Weeds

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Josh Jordan

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Jun 20, 2010, 12:37:23 PM6/20/10
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Weeds [1] is a variation of Sprouts in which the player has the option
to NOT add a new spot on the line she has just drawn. An immediate
consequence of this rule is: from a position with n initial spots,
both xLy and xPy are options (where x+y+1=n). The xPy options are
obtained by not adding the new spot to the line.

Two simple extensions to WGOSA notation would allow us to describe
Weeds games::
1. We could write an initial Weeds position with n spots as nW, to
show that the game of Weeds rather than Sprouts is intended.
2. We could write 1()6 to designate a move that connects spots 1 and
6, but without adding a new spot on the line. All the old moves are
still valid, so 1(7)6, for example, means the same thing it always has.

Aunt Beast has calculated the misere Grundy numbers for Weeds
positions with up to 6 initial spots:

G-(1W) = 1
G-(2W) = 3
G-(3W) = 3
G-(4W) = 3
G-(5W) = 4
G-(6W) = 0

[1] Mentioned at http://en.wikipedia.org/wiki/Sprouts_(game)

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