Party competition is largely about making policy promises to voters. We argue that the clarity of the expressed policy position may be equally important. If blurred messages toward different audiences and therefore ambiguous positions can attract votes from different groups, parties have incentives to present ambiguous rather than clear-cut policy platforms. We present a formal model of multi-party competition with stochastic voting where party leaders make strategic choices on both the position and the level of ambiguity of their platforms. Leaders respond to the demands of two principals, the general public and party core constituencies. We derive two hypothesis on the location and ambiguity of party platforms and provide initial tests of these hypotheses in a comparative setting in 14 Western European democracies gathering data on voter and party left-right positions from Eurobarometer surveys and electoral manifestos. Ambiguity of party profiles is estimated using a variant of Wordscores on a newly established data set of electoral manifestos. We find that platforms become more ambiguous as the preferences of the two principals diverge. Our findings imply that ambiguity can be a winning strategy for parties, especially in settings with strong partisan lines.