Open Problems

1. What is the minimum number of moves needed for Black to force an immortal stone (a stone of Black is said to be immortal if White cannot capture it with arbitrarily many moves while Black passes all moves) on an initially empty Z^2 (infinite lattice) under alternate play without ko rule (i.e. loops help White)? Find upper bounds.
   • Does it depend on whether suicide is allowed?
2. Let P be the statement "In go on a NxN board (N >= 9), even if Black is not allowed to pass for her first move, she still has a strategy enabling her to obtain a score >=0.". Is P decidable (in ZFC, for example)?^[1]

[1] This topic was raised by Ivan Dubois (4D, French) on 2008-04-23 on "frgo", a French discussion list. An alternative way of putting the problem is

Let Q(N) be the question "Is it a disadvantage for Black to have to actually play the first move on a (NxN) board rather than pass".

(Black is supposed to be a perfect player. ) The point is that intuitively the answer to Q(N) is "no" (for all N >= 9), but there is no easy way of proving it.