The finite advantage conjecture for infinite Hex

Consider infinite Hex on the triangular lattice, with Red and Blue claiming unoccupied board positions according to the usual rules, but with a board position containing finitely many stones already placed. Finite advantage conjecture. Infinite Hex remains a draw when starting from a board position with finitely many stones already placed. This asks whether giving the first player any finite initial advantage changes the draw result established for the empty board; the source provides no resolution.