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I’m talking about positions like in figure 26 on Berlekamp’s book (pages 51-52). Does anyone know other positions in which the second player can choose the parity of the number of chains?
What about this? http://www.trmph.com/dnb/board#5,g2g4g6g8h9j9k8k6k4k2i4
Here is one more example.
I think there are quite a lot positions of this kind.
Basically, these positions can be described as “player two has won the chain batter -- i.e. the number of chains is in player two's favor -- but player one can threaten to form / destroy one”.
Looking at it from a nim-value point of view, neither *0 nor *1 is an option, hence the original value is *0. (Also, in my last post, “batter” is more properly spelled “battle” — darn this lack of edit).
I’d make a bit more precise statement: these positions not only have nim-value *0, but any (non-loony) move leads to a position which has nim-value *2 and has no “free” moves.
Thanks for the examples! Yes, this are *0 positions without *1 options/followers. I’m trying to prove some statements in Berlekamp’s book, and sometimes it’s not even clear (for me) what he is stating.