 At the other extreme, if the host opens all losing doors but one ("p" = "N" − 2) the advantage increases as "N" grows large (the probability of winning by switching is , which approaches 1 as "N" grows very large).A quantum version of the paradox illustrates some points about the relation between classical or non-quantum information and quantum information, as encoded in the states of quantum mechanical systems.The formulation is loosely based on quantum game theory.