  We compare games under delayed control and delay games, two types of infinite
games modelling asynchronicity in reactive synthesis. In games under delayed
control both players suffer from partial informedness due to symmetrically
delayed communication, while in delay games, the protagonist has to grant
lookahead to the alter player. Our first main result, the interreducibility of
the existence of sure winning strategies for the protagonist, allows to
transfer known complexity results and bounds on the delay from delay games to
games under delayed control, for which no such results had been known. We
furthermore analyse existence of randomized strategies that win almost surely,
where this correspondence between the two types of games breaks down. In this
setting, some games surely won by the alter player in delay games can now be
won almost surely by the protagonist in the corresponding game under delayed
control, showing that it indeed makes a difference whether the protagonist has
to grant lookahead or both players suffer from partial informedness. These
results get even more pronounced when we finally address the quantitative goal
of winning with a probability in $[0,1]$. We show that for any rational
threshold $\theta \in [0,1]$ there is a game that can be won by the protagonist
with exactly probability $\theta$ under delayed control, while being surely won
by alter in the delay game setting. All these findings refine our original
result that games under delayed control are not determined.
