switch

A switch in CGT is a game of type {a|-a}. Taking into account the change of signs, it is a very simple game conceptually: each player has the same amount to gain here (or lose, but then no one willingly plays in it).

It therefore models an option to take a stack of coins.

Any game {a|b} can be rendered simpler to understand by writing it as (a+b)/2 + {c|-c} where c = (a-b)/2. This has direct application to endgame counting in go, where one mentally tries to draw the mid-line in a gote endgame position; and regards each player as having the same amount to gain one or the other way from it.

Charles Matthews