The computation of the first complete approximations of game-theoretic optimal strategies for fullscale poker is addressed. Several abstraction techniques are combined to represent the game of 2-player Texas Hold’em, having size O(10^18), using closely related models each having size O(10^7). Despite the reduction in size by a factor of 100 billion, the resulting models retain the key properties and structure of the real game. Linear programming solutions to the abstracted game are used to create substantially improved poker-playing programs, able to defeat strong human players and be competitive against world-class opponents.