3 problems

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 m…

Horizontal initial-position conjecture. A game of Infinite Hex with initial position as in figure is a win for Red.

Red's one-tile advantage conjecture. A game of Infinite Hex with exactly one tile of the board assigned to Red at the initial position, and none to Blue, is a win for Red.