  We present new data structures for representing symmetric normal-form games.
These data structures are optimized for efficiently computing the expected
utility of each unilateral pure-strategy deviation from a symmetric
mixed-strategy profile. The cumulative effect of numerous incremental
innovations is a dramatic speedup in the computation of symmetric
mixed-strategy Nash equilibria, making it practical to represent and solve
games with dozens to hundreds of players. These data structures naturally
extend to role-symmetric and action-graph games with similar benefits.
