\begin{definition}[Definition:Consequence Function with Probability]
Let $G$ be a game.
Let $P$ be a player of $G$.
Let $A$ be the set of moves available to $P$.
Let $C$ be the set of consequences of those moves.
Let the consequences of those moves be affected by a random variable on a probability space $\Omega$ whose realization is not known to the players before they make their moves.
A '''consequence function''' for $P$ is a mapping from $A \times \Omega$ to $C$:
:$g: A \times \Omega \to C$
interpreted as that $g \left({a, \omega}\right)$ is the consequence when the move is $a \in A$ and the realization $\omega$ of the random variable is $\omega \in \Omega$.
\end{definition}