# Open Problems

- 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?

- 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.