🚀 go-pugleaf

In article <1992Sep27.161451.20136@cbnewsl.cb.att.com> ed@cbnewsl.cb.att.com (edward.m.hummel) writes:

> Consider the game 1. Nf3 Nf6 2. Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 5.Nf3 Nf6
> and so on, forever; with neither player choosing to claim a draw.  I 
> am asking for a proof that when collapsing the game tree to determine the
> value of the initial position, this sequence must have the value of a draw.

We can solve the problem in at least two ways.

1. Define it away by saying that any position from which neither player can
   force a win is a draw.

2. Ask why, in the situation you mention, neither player claims the draw after
   the third repetition.  Evidently the answer must be that they both think
   that playing indefinitely is preferable to ending the game with a draw.
   But in that case, the game is not zero-sum, which contradicts one of the
   conditions necessary for the theorem to apply in the first place.
-- 
				--Andrew Koenig
				  ark@europa.att.com