We consider two fundamental problems in stochastic optimization: approximation algorithms for stochastic matching, and sampling bounds in the black-box model. For the former, we improve the current-best bound of 3.709 due to Adamczyk, Grandoni, and Mukherjee [1], to 3.224; we also present improvements on Bansal, Gupta, Li, Mestre, Nagarajan, and Rudra [2] for hypergraph matching and for relaxed versions of the problem. In the context of stochastic optimization, we improve upon the sampling bounds of Charikar, Chekuri, and Pál [3].

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