Perfect Play in Connect Four

Connect Four is a solved game. This means that mathematicians have calculated the outcome of every possible position assuming both players make the best possible moves. The result: player 1 wins if they start in the center column and play perfectly from that point on. This was independently proven by James Allen and Victor Allis in 1988. It is one of the landmark achievements in combinatorial game theory.

What does "solved" actually mean? It means the entire game tree has been mapped. Every possible board position, every possible move sequence, every possible outcome has been computed and stored. The game tree for Connect Four contains approximately four trillion possible positions. Modern computers can evaluate all of them. The solution tells us that 4,531,985,219,092 positions exist in total, and for each one, we know whether it is a win for player 1, a win for player 2, or a draw with perfect play from both sides.

For practical play, this means something humbling: any game that does not end in a first-player win involved at least one mistake by player 1. If you are player 1 and you draw or lose, you made an error somewhere. If you are player 2 and you win, your opponent made an error. Perfect play from player 2 results in a loss. The best player 2 can achieve against a perfect player 1 is to delay the inevitable.

This does not make the game boring. Far from it. Perfect play requires calculating dozens of moves ahead. No human can do this consistently. Even strong players make mistakes. The engine on this site plays at perfect or near-perfect strength, giving you a training partner that exposes every error. Playing against the engine and reviewing your games teaches you which positions are winning and which moves are mistakes. Over time, your play approaches perfection, even if true perfection remains beyond human reach. The gap between your play and perfect play is where all the learning happens.