Advocates of the instant-runoff voting system (IRV) often argue that it is less susceptible to strategic voting than plurality. Is this true? More generally, how should we define and measure a voting system's susceptibility to strategic voting? Previous research in this area is unsatisfying, partly because it ignores the uncertainty voters face when they vote; we introduce a better approach. We find that, when beliefs are precise and other voters are expected to vote sincerely, more voters would benefit from voting strategically in IRV than in plurality (contrary to what advocates suggest). The anticipated benefit for these voters is small, however, and for the average voter the benefit of taking strategy into account is many times larger in plurality than IRV-especially when beliefs are imprecise or voters expect other voters to behave strategically. The methods we introduce can be used to study other properties of voting systems when voters are strategic.