  We examine the advantages that quantum strategies afford in
communication-limited games. Inspired by the card game blackjack, we focus on
cooperative, two-party sequential games in which a single classical bit of
communication is allowed from the player who moves first to the player who
moves second. Within this setting, we explore the usage of quantum entanglement
between the players and find analytic and numerical conditions for quantum
advantage over classical strategies. Using these conditions, we study a family
of blackjack-type games with varying numbers of card types, and find a range of
parameters where quantum advantage is achieved. Furthermore, we give an
explicit quantum circuit for the strategy achieving quantum advantage.
