Toads and Frogs (game) - Notation

Notation

A position of Toads-and-Frogs is usually represented with a string of three characters : for a toad, for a frog, and for an empty space. For example, the string represents a strip of four squares with a toad on the first one, and a frog on the last one.

In the combinatorial game theory, a position can be described recursively in terms of its options, i.e. the positions that the Left player and the Right player can move to. If Left can move from a position to the positions, ... and Right to the positions, ..., then the position is written conventionnally

With this notation, we can write for example . It means that if it is Left turn, he can move his toad one square to the right, and if it is Right turn, he can move his frog one square to the left.