Fuzzy Game - Classification of Games

Classification of Games

In combinatorial game theory, there are four types of game. If we denote players as Left and Right, and G be a game with some value, we have the following types of game:

1. Left win: G > 0

No matter which player goes first, Left wins.

2. Right win: G < 0

No matter which player goes first, Right wins.

3. Second player win: G = 0

The first player (Left or Right) has no moves, and thus loses.

4. First player win: G ║ 0 (G is fuzzy with 0)

The first player (Left or Right) wins.

Using standard Dedekind-section game notation, {L|R}, where L is the list of undominated moves for Left and R is the list of undominated moves for Right, a fuzzy game is a game where all moves in L are strictly non-negative, and all moves in R are strictly non-positive.