Skip to content
Little GolemMake your next move.

Positions where the second player can resolve the number of chains

Public forum discussion.

#1 · shinnosuke

9 May 2015

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?

#3 · _syLph_

9 May 2015

This is the positon from Berlekamp's book. And this is another one.

#5 · William Fraser

13 May 2015

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".

#6 · William Fraser

13 May 2015

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).

#7 · al_ef13

14 May 2015

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.

#8 · shinnosuke

14 May 2015

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.