- Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
- random game over the nonnegative orthant, and return the
- corresponding :class:`SymmetricLinearGame`.
+ Generate a random game over the nonnegative orthant.
+
+ We generate each of ``L``, ``K``, ``e1``, and ``e2`` randomly within
+ the constraints of the nonnegative orthant, and then construct a
+ game from them. The process is repeated until we generate a game with
+ a condition number under :const:`MAX_COND`.
+
+ Returns
+ -------
+
+ SymmetricLinearGame
+ A random game over some nonnegative orthant.
+
+ Examples
+ --------
+
+ >>> random_orthant_game()
+ <dunshire.games.SymmetricLinearGame object at 0x...>