Is Connect Four Solved? The First Player Advantage Explained

If you've ever felt like the first player in Connect Four has an unfair advantage, you're not imagining things. In 1988, computer scientists proved mathematically that Connect Four is a "solved game"—and the first player can always force a win with perfect play. This revelation transformed Connect Four from a casual pastime into a fascinating case study in game theory, computational complexity, and the limits of human strategic thinking.

Understanding why and how Connect Four is solved doesn't just satisfy intellectual curiosity—it makes you a better player. Let's dive into the mathematics, the history, and the practical implications of this discovery.

What Does It Mean for a Game to Be "Solved"?

In game theory, a game is considered solved when we can determine the outcome with certainty, assuming both players make optimal moves. There are different levels of "solved":

Types of Game Solutions:

Ultra-weakly solved: We know the outcome from the starting position (win/loss/draw) but not necessarily the optimal strategy
Weakly solved: We know the outcome and have an algorithm to achieve it from the starting position
Strongly solved: We know the outcome and optimal strategy from every possible position, not just the start

Connect Four is weakly solved. We know that with perfect play, the first player wins, and we know the optimal first move. However, we don't have a complete database of optimal moves for every single board position (which would require analyzing trillions of positions).

The 1988 Computer Solution: How It Was Proven

In 1988, James D. Allen and Victor Allis independently proved that Connect Four is a first-player win. Allis's solution was particularly elegant, using a combination of knowledge-based approach and brute-force computation to demonstrate that the first player can force a win within 41 moves. This work was documented in Allis's master's thesis "A Knowledge-Based Approach of Connect-Four" (1988, University of Limburg).

The Computational Challenge:

Connect Four has approximately 4.5 trillion possible board positions. Analyzing every single one would have been computationally impossible in 1988 (and is still impractical today). Instead, Allis used strategic rules and pattern recognition to prune the search tree, reducing the problem to a manageable size.

Key Insights from the Proof:

The first player can guarantee a win by playing optimally
The optimal first move is the center column (column 4 on a standard 7-column board)
With perfect play, the first player wins in at most 41 moves
The second player cannot force a draw, no matter how well they play

This was a landmark achievement in computational game theory, demonstrating that even games with trillions of positions could be "solved" with clever algorithms and strategic insights.

Why the First Player Can Always Win

The first-player advantage in Connect Four comes down to tempo and initiative. The first player gets to establish threats before the second player can build their own strategy, and this head start is mathematically insurmountable.

The Tempo Advantage:

In Connect Four, every move serves two purposes: building your own threats and responding to your opponent's threats. The first player gets to make the first threat, forcing the second player into a reactive position. This single-move advantage compounds over the course of the game.

The Center Column Dominance:

The center column (column 4) is involved in more potential four-in-a-rows than any other column. By claiming it first, the first player controls the most strategically valuable position on the board. The second player must either contest the center (giving up initiative elsewhere) or concede central control (allowing the first player to build an overwhelming position).

The Mathematical Proof (Simplified):

The first player opens in the center column
No matter how the second player responds, the first player can maintain central dominance
By move 7-9, the first player has established multiple threats that the second player cannot simultaneously defend
The first player forces a win through a series of "zugzwang" positions—situations where any move the second player makes worsens their position

This doesn't mean the first player will always win in practice—it means they can always win if they play perfectly. Human players (and most AI) don't play perfectly, which is why games remain competitive.

The Optimal First Move: Why Center Wins

The 1988 proof established that the optimal first move is the center column. But why is this move so powerful?

Center Column Advantages:

Maximum connectivity: The center column intersects with 13 different potential four-in-a-rows
Diagonal control: Both major diagonals pass through the center, giving dual-threat potential
Symmetry breaking: Playing center forces the second player to make an asymmetric response, limiting their options
Vertical threat: Building vertically in the center creates immediate pressure

What If You Don't Play Center First?

If the first player opens with any column other than the center, the second player can force a draw (or potentially even win) with optimal play. The center opening is the only first move that guarantees a first-player win.

This is why, in competitive Connect Four, the first player almost always opens in the center. Deviating from this move is essentially giving up your mathematical advantage.

What This Means for Casual Players

So if Connect Four is solved and the first player always wins with perfect play, does that make the game pointless? Absolutely not. Here's why:

Perfect Play Is Incredibly Difficult:

Knowing that the first player can win doesn't mean you will win. The optimal strategy requires calculating 10-15 moves ahead, tracking multiple threats simultaneously, and never making a single mistake. Even strong players deviate from perfect play regularly.

The Second Player Can Still Win:

In practice, the first player makes mistakes. If you're playing as the second player, your goal is to:

Force the first player into complex positions where mistakes are likely
Create multiple threats that require perfect defense
Exploit any suboptimal moves immediately
Apply psychological pressure through aggressive play

Against human opponents, the second player wins approximately 45% of games at intermediate skill levels. The first-player advantage only becomes overwhelming at expert levels.

The Game Remains Strategically Rich:

Just because a game is solved doesn't mean it's "figured out" for practical purposes. Chess has been studied for centuries, and while we know a lot about optimal play, humans still discover new strategies and tactics. Connect Four is similar—there's always more to learn about positioning, threats, and tactical patterns.

Try the Strategy Yourself: Practical Application

Now that you understand the theory, let's put it into practice. Open Connect Four and play a few games first — this section assumes you know how pieces drop. Here's how to leverage the first-player advantage (or counter it as the second player):

If You're the First Player:

Always open in the center column—this is non-negotiable for optimal play
Build vertically in the center if your opponent doesn't contest it immediately
Create threats in columns 3 and 5 (adjacent to center) to maintain central dominance
Force your opponent to respond to your threats rather than building their own
Look for double threats (two ways to win simultaneously) by move 10-12

If You're the Second Player:

Contest the center immediately—don't let the first player build a vertical stack
Create your own threats as quickly as possible to regain initiative
Force complexity—the more complicated the board, the more likely the first player makes a mistake
Look for vertical traps where you can turn the first player's threats against them
Stay patient—you only need the first player to make one significant mistake

Practice these strategies on Connect Four. Start with medium difficulty to build your skills, then progress to hard and expert levels to test your understanding of optimal play.

The Broader Implications: What Connect Four Teaches Us

The solution of Connect Four has implications beyond the game itself:

Computational Game Theory:

Connect Four demonstrated that games with massive state spaces (trillions of positions) could be solved with clever algorithms. This paved the way for solving other games like checkers (solved in 2007) and made progress toward solving chess (still unsolved, but deeply understood).

AI and Machine Learning:

The techniques used to solve Connect Four—combining strategic knowledge with computational search—are the foundation of modern game-playing AI. The same principles power chess engines, Go AI, and even real-world decision-making systems.

The Limits of Perfect Information:

Connect Four is a game of perfect information (both players see the entire board state). The fact that it's solved shows that perfect information games have deterministic outcomes. This contrasts with imperfect information games (like poker) where probability and psychology play larger roles.

Human vs. Computer Cognition:

Humans can't calculate 15 moves ahead consistently, but we can recognize patterns and make intuitive judgments. The solution of Connect Four highlights the difference between human strategic thinking and computational brute force—both are valuable, but they work differently.

Beyond the Solution: Becoming a Better Player

Understanding that Connect Four is solved should motivate you, not discourage you. Here's why:

You have a roadmap: Knowing the optimal first move gives you a starting point for building your strategy
You can study perfect play: Analyzing games where the first player wins helps you understand winning patterns
You can exploit mistakes: Knowing what perfect play looks like helps you identify when your opponent deviates from it
You can appreciate the depth: Understanding the solution makes you appreciate the game's complexity even more

The goal isn't to memorize the perfect strategy (which would take years)—it's to understand the principles of optimal play and apply them in your games.

Test Your Understanding: Challenge the AI

Now that you know Connect Four is solved and understand the first-player advantage, put your knowledge to the test:

Play as the first player and always open in the center—can you maintain your advantage?
Play as the second player and try to force a draw or win by exploiting AI mistakes
Analyze your games: When did you deviate from optimal play? What were the consequences?

Our Connect Four game offers multiple difficulty levels. The hardest setting plays near-optimal strategy, giving you a chance to experience what perfect play feels like. Can you consistently win as the first player? Can you force draws as the second player?

Frequently Asked Questions

Is Connect Four always a first-player win?

With perfect play, yes. The 1988 proof by Victor Allis and James D. Allen demonstrated that the first player can force a win from the starting position. However, "perfect play" means calculating every possible response 10-15 moves ahead without a single error — something no human can do consistently.

Can the second player ever win in Connect Four?

In theory, no — perfect play by the first player guarantees a win. In practice, absolutely. Against human opponents, the second player wins roughly 45% of games at intermediate skill levels. The first player only needs to make one mistake for the advantage to disappear.

How many possible board positions does Connect Four have?

Approximately 4.5 trillion. That's 4,531,985,219,092 unique legal positions. It was far too many to brute-force in 1988, which is why Allis used strategic rules and pattern recognition to prune the search tree down to a manageable size.

What is the best first move in Connect Four?

The center column (column 4 on a standard 7-column board). It's involved in more potential four-in-a-rows than any other column — 13 in total. No other opening move guarantees a first-player win.

Has Connect Four been strongly solved?

No. Connect Four is only weakly solved — we know the outcome and an optimal strategy from the starting position. A strong solution would require knowing the optimal move from every single one of those 4.5 trillion board positions, which hasn't been computed.

The Final Answer: Solved, But Not Boring

Yes, Connect Four is mathematically solved. The first player can always win with perfect play, starting with the center column. But this doesn't diminish the game's value—it enhances it.

Knowing the solution gives you a target to aim for. It transforms Connect Four from a casual game into a puzzle: How close can you get to perfect play? How consistently can you execute the optimal strategy? How well can you exploit your opponent's deviations?

The next time someone dismisses Connect Four as "just a kids' game," you'll know better. It's a completely solved mathematical puzzle with a first-player advantage that has been proven computationally. Master it, and you'll have mastered one of the most elegant examples of strategic game theory.

Now go play — open Connect Four and start in the center column.