Hm. but then do we need to distinguish several kinds of winning: being able to force your opponent to lose on her first turn, her second turn, or whichever you like?
Cris Moore writes:
Right. Both 0 and 1 are losses for the first player. But clearly these are not equivalent, since 0+1 is a loss for the first player, while 1+1 is a win.
Clearly we need distinguish running out of moves on your first turn (like 0) from running out of moves on your second turn (like 1). These are two distinct ways to lose, which should be regarded as different values.
I like this suggestion.
Does X+1+1+1+1 always have the same outcome as X (in Cris' sense) for every Nim position X?
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute The Nature of Computation Cristopher Moore and Stephan Mertens Available now at all good bookstores, or through Oxford University Press http://www.nature-of-computation.org/