  At the end of a round of this game the two players will have produced a real x, obtained through “interleaving” their plays. We say that Player I wins the round if x ∈ A; otherwise Player II wins the round. The set A is said to be determined if one of the players has a “winning strategy” in the associated game, that is, a strategy which ensures that the player wins a round regardless of how the other player plays. The Axiom of Determinacy (AD) is the statement that every set of reals is determined. This axiom was introduced by Mycielski and Steinhaus in 1962. 