Connect Four was solved in 1988 — but humans still don't know

Building Drop Four's AI, I found a slightly unsettling fact: this 50-year-old family game has been mathematically "solved" — 35 years ago. The first player wins under optimal play. But most people have played for decades without knowing.

What "solved" means

In game theory, a "solved" game means —

Under optimal play, the outcome is determined (first wins / second wins / forced draw).

Easy for some games:

• Tic-tac-toe: optimal play = forced draw. Everyone figures it out intuitively.
• English draughts (checkers): proved a forced draw by Jonathan Schaeffer's team in 2007. Took 18 years and thousands of CPU-years.
• Chess: theoretically "solvable" but state space ~10^46 — actually impossible to fully solve.
• Go: state space ~10^170, far exceeds chess — physically impossible to fully solve.

Connect Four's state space is roughly 4.5 × 10^12 (4.5 trillion). Sounds huge but —

Two independent proofs in 1988

October 1988, James D. Allen (a Texas mathematician) used a regular computer with smart pruning to solve Connect Four first. Two weeks later, Victor Allis (a master's student at the University of Amsterdam) independently solved it and published his now-famous thesis A Knowledge-Based Approach of Connect-Four.

Both reached the same conclusion:

On a standard 7x6 board, if the first player opens with the center column (column 4), first player wins. Other opening moves let the second player force a draw or win.

More specifically: Allis proved that after opening column 4, the first player wins by move 41 at the latest. Meaning a Connect Four game theoretically never exceeds 41 moves.

The proof's core idea: Allis found 9 "threat rules" — conversion functions between local patterns and global strategy. For instance "odd-threat rule" — a potential four-in-a-row on an odd row becomes harder to block as the board fills. The first player carefully controls odd threats to put the second player in dilemmas.

So why don't most people know?

This is an interesting phenomenon in game theory: "the game is solved" and "humans find it fun" are two different things.

Compare tic-tac-toe vs. Connect Four. Tic-tac-toe is also solved (forced draw), so primary schoolers stop playing — knowing the outcome makes it boring. But Connect Four's "solution" is so complex that intuitive players can't find the optimal path. Even knowing "open column 4," the following 40+ optimal moves exceed human memory capacity.

So Connect Four is theoretically dead but practically alive. This "theoretical death, practical life" state is the hallmark of good games — mathematically beautiful and operationally rich.

Comparison:

• Tic-tac-toe: state space ~10^4, easy mastery → no one plays after solved
• Connect Four: state space ~10^12, can't remember optimal → still played after solved
• Chess: state space ~10^46, far beyond human limits → not solved but AI surpasses humans
• Go: state space ~10^170 → never solvable, but AI beat humans in 2016

What "optimal strategy" looks like in practice

I distilled Allis's key findings into practical rules you can use in Drop Four:

Rule 1: First player must take the center column. The most important first move. Drop Four's "Challenge" AI does this without exception.

Rule 2: Watch "odd threats" vs. "even threats". A 7x6 board has 42 cells. Counting from bottom up, first player always fills odd-numbered cells (1, 3, 5, ..., 41); second player fills even cells. This means:

• Potential four-in-a-rows on odd rows will eventually be filled by first player
• Potential four-in-a-rows on even rows will eventually be filled by second player

So first player's long-term optimal strategy: create threats on rows 1, 3, 5 (odd rows), because these are hard for second player to preempt.

Rule 3: Avoid premature attack. Beginners' mistake: try to make 3-in-a-rows right away. This exposes your strategy and lets opponent block early. Better: stack 3-4 in center column first, then start flanking.

Rule 4: "Double threats" patterns. When you can create two threat lines (horizontal + diagonal) at one position, opponent can only block one; you win the other. This is Connect Four's "check."

About BverGame's AI difficulty

Drop Four's three difficulties are essentially increasing search depth:

• Easy: 2-ply search + 40% random perturbation. You win 2 out of 3 games.
• Medium: 3-ply search + alpha-beta pruning. Even match, ~50% win rate.
• Challenge: 5-ply search + full heuristics. Unless you also know Allis's strategy, you'll struggle to win.

Note: I haven't implemented Allis's full theorem (that would need a few million pre-stored positions), so even "Challenge" AI isn't 100% optimal. A human who deeply understands Connect Four strategy can beat it on certain non-center openings.

Knowing a game is solved upgrades your play — not because you can memorize every optimal move, but because you can recognize "when I've already lost."

Lessons for game design

What I take from this as a game developer:

1. "Depth" ≠ "complexity." Connect Four's rules are minimal, but its solution paper runs 100 pages. Simple rules can yield deep strategy spaces.

2. Perfect-information games are always solvable but not always boring to play. This counterintuitive fact tells us: game enjoyment isn't entirely about "unknown"; it's about "human brain capacity limits." Even a solved game is alive in practice as long as it exceeds brain capacity.

3. Good difficulty design = between "human-learnable" and "exceeds brain capacity." Too simple (tic-tac-toe) is boring; too complex (Go) has no entry. Connect Four's "30-minute entry, 30-year mastery" sweet spot is what makes a lasting design.

Closing

Connect Four was invented by Howard Wexler in 1974, commercialized by Milton Bradley that same year. 50 years later, over a hundred million copies sold worldwide. Even after the 1988 "solution," it's still a tabletop store evergreen.

The lesson for me: a game's longevity isn't about "mathematically unsolvable" but "humans actually playing imperfectly." That gap — roughly — is what makes a great game.

Next time you play Drop Four, try this: first move column 4, then watch the AI's response. If it retreats to a side column, you'll probably win. If it also stacks center (on top of yours), the real contest begins.

Leo is BverGame's co-engineer. Reference: Victor Allis, A Knowledge-Based Approach of Connect-Four: The Game is Solved: White Wins (master's thesis, University of Amsterdam, 1988). Allis later earned a PhD and worked on the Chinook checkers program. Connect Four solvers (c4-solver et al.) are now open-source on GitHub.