We examine strategic voting in open primary elections by developing a Poisson voting game. In the model, two parties simultaneously hold primary elections, with two candidates competing in each party. Each voter chooses to vote for one of the four candidates without knowing how many other voters participate in each primary. Analyzing the model, we investigate what types of strategic crossover voting occur in equilibrium and under what circumstances they occur. In particular, we focus on two types of crossover voting: hedging (voting for the moderate candidate of the opposite party) and raiding (voting for the extreme candidate of the opposite party). We show that the pattern of strategic voting in equilibrium critically depends on candidate positions and uncertainty about the outcome in the general election.