Newsgroups: rec.games.abstract
From: hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Date: Wed, 6 Jan 1993 23:43:48 GMT
Subject: Sprouts and Nim (was Re: defects in abstract games)

kwh...@arthur.uchicago.edu (Kevin Whyte) writes:

> ... The games which can be reduced to Nim
> (Sprouts can't, and hasn't been solved ....) are exactly
           ^^^^^
> those where
> 1) The game always terminates, even it the players don't
> alternate moves.
> 2) From every position both players have exactly the same
> legal moves, and exactly the same winning positions, etc....

Sprouts has these features, and _can_ be reduced to Nim, at least with
in normal play (last player wins).  Misere Sprouts, where the last
player loses, has positions that aren't encountered in Nim, but they
can be dealt with using the extended Sprague-Grundy theory you can
find in On_Numbers_And_Games or Winning_Ways.

I suspect that ``can't'' is a misprint for ``can''.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil