King and short rook checkmate

Suppose White has a king and a range-x rook and black has a bare king on a chessboard with dimensions y times y. What is the minimum value of x such that for all sufficiently large y, White, moving first, can force a win no matter where the pieces are initially placed? Passing is not allowed and stalemate is a draw.

• 50 move rule in force? Jun 15 at 7:20
• I am pretty sure x=5 is enough and x=3 is too weak. x=4 is most likely the border case... Jun 15 at 12:31
• @IanBush : certainly not, otherwise there is no solution... Jun 15 at 12:32
• @Evargalo Well x=8;y=8 certainly has a solution with the 50 move rule in force - if it does apply it "just" make the problem more complex. Jun 15 at 13:07
• @IanBush : sure, but there is no x such that for all sufficiently large y, White, moving first, can force a win no matter where the pieces are initially placed if the 50 moves rules applies. (just place the bK 50*x files away from the rook and there won't even be a check). Anyway, the 50 moves never applies in fairy chess problems... Jun 15 at 20:58