  This paper investigates repeated win-lose coordination games (WLC-games). We
analyse which protocols are optimal for these games covering both the worst
case and average case scenarios, i,e., optimizing the guaranteed and expected
coordination times. We begin by analysing Choice Matching Games (CM-games)
which are a simple yet fundamental type of WLC-games, where the goal of the
players is to pick the same choice from a finite set of initially
indistinguishable choices. We give a complete classification of optimal
expected and guaranteed coordination times in two-player CM-games and show that
the corresponding optimal protocols are unique in every case - except in the
CM-game with four choices, which we analyse separately.
  Our results on CM-games are also essential for proving a more general result
on the difficulty of all WLC-games: we provide a complete analysis of least
upper bounds for optimal expected coordination times in all two-player
WLC-games as a function of game size. We also show that CM-games can be seen as
the most difficult games among all two-player WLC-games, as they turn out to
have the greatest optimal expected coordination times.
