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

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

Here is one more example.

http://www.trmph.com/dnb/board#5,b7d7b11d11e8f7h7i8i10h11f11

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.