§ Analysing simple games
I found the clear articulation of these ideas quite nice.
- In a game with symmetry, a symmetric move can be blocked or prevented only by the previous move an opponent has just made .
- The symmetry in many games can be written as some kind of equality, where at each turn, one first player breaks the symmetry, and the other player (who has the winning strategy) restores it.
§ Example game
Consider a game where two players take turns placing bishops on a chessboard,
so that the pieces cannot capture each other. The player who cannot win
§ Winning strategy
place the bishop symmetrically about the line passing between the fourth and
fifth column (file). Note that the only way this bishop could be blocked is
if the move just made by the other player can block it.