Fictitious play has recently emerged as the most accurate scalable algorithm for approximating Nash equilibrium strategies in multiplayer games. We show that the degree of equilibrium approximation error of fictitious play can be significantly reduced by carefully selecting the initial strategies. We present several new procedures for strategy initialization and compare them to the classic approach, which initializes all pure strategies to have equal probability. The best-performing approach, called maximin, solves a nonconvex quadratic program to compute initial strategies and results in a nearly 75% reduction in approximation error compared to the classic approach when 5 initializations are used.