  Bertrand et al. [1] (LMCS 2019) describe two-player zero-sum games in which
one player tries to achieve a reachability objective in $n$ games (on the same
finite arena) simultaneously by broadcasting actions, and where the opponent
has full control of resolving non-deterministic choices. They show EXPTIME
completeness for the question if such games can be won for every number $n$ of
games.
  We consider the almost-sure variant in which the opponent randomizes their
actions, and where the player tries to achieve the reachability objective
eventually with probability one. The lower bound construction in [1] does not
directly carry over to this randomized setting. In this note we show EXPTIME
hardness for the almost-sure problem by reduction from Countdown Games.
