About Resolve, from BoardGameGeek:
Resolve is a connection game for two players, Black and White, with sufficient black and white stones. Starting with Black, players take turns placing and swapping stones on the intersecting points of a square grid (with side lengths of either 5, 9, 13, or 19) which is initially empty. Passing is forbidden. Same-colored stones with orthogonal adjacency are connected. The game is over when a player wins by connecting their designated sides of the board with a single group of connected stones of their color, at any time during their turn or their opponent's turn. Cutting stones are four stones in the following generic crosscut configuration:
OX
XO
On your turn, place a stone of your color on an empty point, if possible. If that created a crosscut, swap the placed stone with different adjacent enemy stones that share a crosscut with it, until that stone is no longer part of a crosscut. If you haven't placed a stone this turn, then instead choose a friendly stone in a crosscut and resolve as above.
-description from the designer
