  We consider two-player games with imperfect information and the synthesis of
a randomized strategy for one player that ensures the objective is satisfied
almost-surely (i.e., with probability 1), regardless of the strategy of the
other player. Imperfect information is modeled by an indistinguishability
relation describing the pairs of histories that the first player cannot
distinguish, a generalization of the traditional model with partial
observations. The game is regular if it admits a regular function whose kernel
commutes with the indistinguishability relation.
  The synthesis of pure strategies that ensure all possible outcomes satisfy
the objective is possible in regular games, by a generic reduction that holds
for all objectives. While the solution for pure strategies extends to
randomized strategies in the traditional model with partial observations (which
is always regular), we show that a similar reduction does not exist in the more
general model. Despite that, we show that in regular games with Buechi
objectives the synthesis problem is decidable for randomized strategies that
ensure the outcome satisfies the objective almost-surely.
