The second player uses a different color and colors any region of the map that does not share a boundary with the first player's region. The second player also keeps the same color throughout the game. Similarly, each time the second player colors, the region chosen can be one that shares a boundary with Player 2's colored regions already, or one which doesn't share a boundary with any colored regions. The game ends when one of the players cannot find a region to color. That player loses.
Coloring appears over and over again in mathematics.
Map coloring is a topic that has been studied for many years. Mathematicians have also thought about ways that knots can be colored. The game of Col is a variation on the game of Snort and also involves coloring maps.