Positions where the second player can resolve the number of chains Dots and Boxes

8 replies. Last post: 2015-05-14

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Positions where the second player can resolve the number of chains
  • shinnosuke at 2015-05-09

    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?

  • Loony at 2015-05-09

    What about this? http://www.trmph.com/dnb/board#5,g2g4g6g8h9j9k8k6k4k2i4

  • purgency at 2015-05-09

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

  • al_ef13 at 2015-05-13

    Here is one more example.


    I think there are quite a lot positions of this kind.

  • William Fraser at 2015-05-13

    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”.

  • William Fraser at 2015-05-13

    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).

  • al_ef13 at 2015-05-14

    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.

  • shinnosuke at 2015-05-14

    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.

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