Re: There exists a Nim version that is a "draw" OS

From: Tralfaz (tralfaz_at_emailblackhole.com)
Date: 07/09/04 

Date: Fri, 9 Jul 2004 15:40:54 -0700

"David Kastrup" <dak@gnu.org> wrote in message
news:x5brio96su.fsf@lola.goethe.zz...
> Archimedes Plutonium <a_plutonium@iw.net> writes:
>
> > I am unsure of Nim rules and have never played the game. I remember
> > only that it is about picking up some objects so that the loser has
> > to pick up the last object. I forget whether the objects are in 3
> > separate boxes and those have to be emptied separately. I vaguely
> > remember a math formula placed on Nim game and this math formula
> > showing why second player will always win in OS of Nim.
> >
> > But my technique would predict that a morphed game of Nim exists
> > where the OS is a draw. This morphed game is every bit a game of
> > VonNeumann gametheory just as regular Nim is. But the difference is
> > that this morphed game of Nim is a ** draw in OS ** and not a sure
> > win for second player.
>
> How do you draw in a game where there is progress made in every move
> and the last one to pick an object loses?
>

Simple! Start with aleph-naught lines and each move consists of erasing a
finite number of lines.

Relevant Pages