  We study the power of multiple choices in online stochastic matching. Despite
a long line of research, existing algorithms still only consider two choices of
offline neighbors for each online vertex because of the technical challenge in
analyzing multiple choices. This paper introduces two approaches for designing
and analyzing algorithms that use multiple choices. For unweighted and
vertex-weighted matching, we adopt the online correlated selection (OCS)
technique into the stochastic setting, and improve the competitive ratios to
$0.716$, from $0.711$ and $0.7$ respectively. For edge-weighted matching with
free disposal, we propose the Top Half Sampling algorithm. We directly
characterize the progress of the whole matching instead of individual vertices,
through a differential inequality. This improves the competitive ratio to
$0.706$, breaking the $1-\frac{1}{e}$ barrier in this setting for the first
time in the literature. Finally, for the harder edge-weighted problem without
free disposal, we prove that no algorithms can be $0.703$ competitive,
separating this setting from the aforementioned three.
