ABSTRACT

Hackenbush and Ski-Jumps are often composed of non-interacting parts. Each player can move in either the first or the second component, but must then leave the other component untouched. There are no fuzzy positions in Blue-Red Hackenbush, which makes it rather unusual, because in most games it is some advantage to be the first player. It might be thought that, like a zero game, a fuzzy game confers no particular advantage on either player, and so should also be said to have value 0. But this would be a misleading convention, because often a fuzzy game can be more in favor of one player than the other, even though either player can win starting first. Colin Vout has invented the map-coloring game. Each player, when it is his turn to move, paints one region of the map, Left using the color blue and Right using red. No two regions having a common frontier edge may be painted the same color.