We establish two results regarding the query complexity of bounded-error randomized algorithms. * Bounded-error separation theorem. There exists a total function $f : \{0,1\}^n \to \{0,1\}$ whose $��$-error randomized query complexity satisfies $\overline{\mathrm{R}}_��(f) = ��( \mathrm{R}(f) \cdot \log\frac1��)$. * Strong direct sum theorem. For every function $f$ and every $k \ge 2$, the randomized query complexity of computing $k$ instances of $f$ simultaneously satisfies $\overline{\mathrm{R}}_��(f^k) = ��(k \cdot \overline{\mathrm{R}}_{\frac��k}(f))$. As a consequence of our two main results, we obtain an optimal superlinear direct-sum-type theorem for randomized query complexity: there exists a function $f$ for which $\mathrm{R}(f^k) = ��( k \log k \cdot \mathrm{R}(f))$. This answers an open question of Drucker (2012). Combining this result with the query-to-communication complexity lifting theorem of G����s, Pitassi, and Watson (2017), this also shows that there is a total function whose public-coin randomized communication complexity satisfies $\mathrm{R}^{\mathrm{cc}} (f^k) = ��( k \log k \cdot \mathrm{R}^{\mathrm{cc}}(f))$, answering a question of Feder, Kushilevitz, Naor, and Nisan (1995).

15 pages, 2 figures, CCC 2019