Is Connect Four Solved? Yes - Here Is the Proof
Connect Four is a solved game. With perfect play, the first player always wins. This has been mathematically proven twice - once in 1988 using knowledge-based reasoning, once by brute-force computer search. Here is what that actually means and why it matters.
What "solved" means in game theory
Game theorists classify solved games into three levels of completeness:
Ultra-weakly solved
We know the outcome of perfect play from the starting position, but we do not know the complete strategy for achieving it. Example: we know the first player wins chess if both play perfectly - but we do not have the full proof.
Weakly solved
We know both the outcome and a complete strategy for achieving it from the opening position. We can prove the first player wins and tell you every move they need to make from the start.
Strongly solved
We know the optimal move from every possible board position - not just the opening. Even if both players make mistakes and reach unusual positions, we can tell you the best move.
Connect Four is strongly solved. We know the optimal move from every possible position.
Victor Allis and the 1988 proof
Victor Allis was a 22-year-old computer science student at the Vrije Universiteit Amsterdam when he proved Connect Four was solved in his 1988 master's thesis. The title was "A Knowledge-Based Approach of Connect-Four." He did not use brute-force search. Instead, he identified nine strategic rules that together are sufficient to determine the outcome of any Connect Four position.
Allis's nine rules encoded concepts like: centre column control, threat sequencing, odd and even row advantages, and column Zugzwang patterns. He showed that if both players follow these rules, the first player always wins by opening in the centre column.
The knowledge-based approach was elegant but not complete on its own - it proved the outcome from the opening but did not compute every position. The same year, James Allen at the University of Albany solved it independently using a brute-force minimax search, computing the value of every reachable game position. Allen's approach confirmed Allis's result and extended it to strong solution status.
The complete game tree for Connect Four has approximately 4.5 trillion leaf nodes (terminal positions). Allen's computer, running at 1988 speeds, reportedly took several days to complete the search.
Why does the first player win?
The first player (Red) wins because of a combination of two factors: the centre column advantage and the parity of row occupation.
By opening in the centre column, Red occupies the cell that participates in the most winning lines (13). This gives Red more ways to build winning threats than Yellow can defend against. Yellow must respond to the centre opening or immediately concede strategic control.
The parity principle (odd row threats favour Red) means that with perfect play, Red can always manoeuvre to have threats in odd rows while forcing Yellow's threats into even rows. This structure eventually creates a position where Red wins before Yellow can use their own threats - a concrete Zugzwang position forced by the parity of piece placement.
What this means for casual players
In practice, the solved status of Connect Four makes almost no difference to casual games between humans. The solution requires perfect play - a sequence of specific moves from a library of 4.5 trillion positions. No human remembers all of this. Human games are decided by tactical errors, not opening theory.
What the solution does tell you: open in the centre column (this matters). Build threats in odd rows (this matters when you remember to do it). Avoid giving your opponent free tempo with pure defensive moves (this matters every game).
The solution also tells you that if your opponent plays our Impossible AI and goes first, you are in a losing position. Not because you played badly, but because the AI is approximating perfect play. See the Vs AI page for how our implementation works.
Questions about the solved game
Is Connect Four a solved game?
Yes. It is strongly solved - we know the optimal move from every possible position. The first player wins with perfect play.
What does it mean for a game to be solved?
A strongly solved game is one where we can compute the optimal move from every reachable position. For Connect Four, this means we have a complete lookup table: given any legal board state, we know the best move for the player to move. Tic-tac-toe, checkers, and Connect Four are all strongly solved. Chess is not - it is considered ultra-weakly solved at best.
Who proved Connect Four was solved?
Victor Allis proved it in 1988 using knowledge-based strategic rules in his master's thesis. James Allen independently proved it the same year using brute-force minimax search. Both results agree: first player wins with centre column opening.
Can the second player ever win in Connect Four?
With perfect play from both sides, no. The second player cannot win and cannot force a draw - the first player wins. Against imperfect human opponents, the second player wins frequently because the theoretical advantage disappears the moment either player makes a suboptimal move.