Connect Four on 6 high, 7 wide grid, there are 4,531,985,219,092 positions for all game boards populated with 0 to 42 pieces. The game was first solved by James Dow Allen (October 1, 1988), and independently by Victor Allis (October 16, 1988). Allis describes a knowledge-based approach, with nine strategies, as a solution for Connect Four. Allen also describes winning strategies in his analysis of the game. At the time of the initial solutions for Connect Four, brute-force analysis was not deemed feasible given the game's complexity and the computer technology available at the time. Connect Four has since been solved with
Standard probability space see . In the same section Rokhlin proved that if a probability space is complete mod 0 with respect to some basis, then it is complete mod 0 with respect to every other basis, and defines "Lebesgue spaces" by this completeness property. See also and . The four cases treated above are mutually equivalent, and can be united, since the measurable spaces formula_122 formula_123 formula_105 and formula_125 are mutually isomorphic; they all are standard measurable spaces (in other words, standard Borel spaces). Existence of an injective measurable function from formula_59 to a standard measurable space formula_63 does not depend on