# Equality of Games

In combinatorial game theory, equality of games is a defined concept. It certainly doesn’t coincide with the idea of having the same game (what you could call an identical copy).

Firstly one has an ordering of games, such that ``G >= H`` is a relation defined to hold just when the difference game ``G - H >= 0``.

Then two games ``G`` and ``H`` are by definition **equal** when ``G >= H`` and ``H >= G``.

This is an obvious definition to make, from a mathematical point of view. One also wants to be able to compute with this idea. The theory of canonical forms of games is designed to do that.

Two equal games ``G`` and ``H`` have the basic property that in a sum of games, one can be replaced by the other, without changing the overall outcome, i.e. who can win depending on who starts.