  No-go theorems assert that hidden-variable theories, subject to appropriate
hypotheses, cannot reproduce the predictions of quantum theory. We examine two
species of such theorems, value no-go theorems and expectation no-go theorems.
The former assert that hidden-variables cannot match the predictions of quantum
theory about the possible values resulting from measurements; the latter assert
that hidden-variables cannot match the predictions of quantum theory about the
expectation values of measurements. We sharpen the known results of both
species, which allows us to clarify the similarities and differences between
the two species. We also repair some flaws in existing definitions and proofs.
