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 2player Texas Hold’em, having size ¢¤£¦¥¨§©¨ , using closely related models each having size ¢¤£¦¥¨§¨ . 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 prosolutions 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.