5 problems

Henderson–Hayward's conjecture. In the ziggurat, probes $3$, $5$, $6$, $7$ and $8$ are inferior; equivalently, $5$ of its $8$ possible intrusions are inferior.

For an integer $n>1$, consider the $n$-for-$n$ variation of infinite Hex, in which Red and Blue each place $n$ stones at every turn, starting from an empty board. Equal-move conjec…

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.