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This paper considers coercion contracts in voting systems with end-to-end (E2E) verifiability. Contracts are a set of instructions that an adversary can dictate to a voter, either through duress or by offering payment, that increase the probability of a compliant voter constructing a vote for the adversary's preferred candidate. Using a representative E2E system, we place the attacks in game-theoretic terms and study the effectiveness of three proposed contracts from the literature. We offer a definition of optimality for contracts, provide an algorithm for generating optimal contracts, and show that as the number of candidates increases, the adversary's advantage through the use of contracts decreases. We also consider the use of contracts in a heterogeneous population of voters and for financially constrained adversaries.