Political parties and candidates usually prefer to make ambiguous promises, a practice referred to as “political ambiguity.” This chapter extends the standard political competition model with fully office-motivated candidates to allow a candidate to choose a lottery, rather than a single policy. The model then identifies the conditions under which candidates choose ambiguous promises in equilibrium, given the convex utility functions of voters. The results show that in a deterministic model, no equilibrium exists when voters have convex utility functions. However, in a probabilistic voting model, candidates make ambiguous promises in equilibrium when (i) voters have convex utility functions and (ii) the distribution of voters’ most preferred policies is polarized.