Martin Gardner's "Mathematical Games" column that popularized this game also included a description of a variant: Brussels Sprouts (http://en.wikipedia.org/wiki

Martin Gardner's "Mathematical Games" column that popularized this game also included a description of a variant: Brussels Sprouts (http://en.wikipedia.org/wiki/Sprouts_(game)#Brussels_Sprouts http://en.wikipedia.org/wiki/Sprouts_(game)#Brussels_Sprouts), played with small crosses instead of dots. While appearing similar, in Brussels Sprouts the result is always fixed: if there are an odd number of crosses initially, the first player wins; otherwise, the second does.