Connect Four is a solved game: how to win and why going first is an advantage

What it means for a game to be solved

A game is solved when the outcome under perfect play from the starting position is known. There are three usual levels. An "ultra-weak" solution only tells you who wins, or whether it is a draw, without giving the strategy. A "weak" solution also provides a strategy that guarantees that result from the start. A "strong" solution gives the best outcome from every possible position.

For Connect Four on the classic board of 7 columns and 6 rows, the result is clear: with perfect play, the player who moves first wins. That does not mean the first player always wins in practice, because they must find the right move on every turn, and games between people are full of mistakes.

Who solved it, and when

Two people reached the same conclusion independently in October 1988. The first was James Dow Allen, who announced his solution on October 1, 1988, in a post to the rec.games.programmer newsgroup. Fifteen days later, on October 16, the Dutch researcher Victor Allis presented his own solution, described in his thesis "A Knowledge-based Approach of Connect-Four" at the Vrije Universiteit.

Allis's method was knowledge-based: instead of checking every position, he formulated strategic rules, such as which squares are worth controlling and which threats matter, and combined them with search to show that the first player can force a win. The same result was later confirmed by brute force, using position databases and powerful computers; programmer John Tromp, for example, compiled a database of all positions with 8 pieces that served as a starting point. Both routes agree.

The key is the opening: the center column

Not every first move is enough. The outcome depends on the column where the first player starts:

What "the first player wins" means in practice

The theory saying the first player wins guarantees nothing if your opponent plays well: the advantage is real, but it demands precision. Still, moving first gives you two concrete things. The first is the initiative: you move first, and your opponent usually has to answer your threats. The second is parity, a widely taught rule of thumb among players: since the board has 6 rows, an even number, and players alternate turns, the squares on odd rows (1, 3 and 5, counting from the bottom) tend to end up with the player who started, and those on even rows with the second player. That is why a threat on an odd row is usually more valuable to the first player.

Why the center is worth so much

Pieces in the center column take part in more possible lines than pieces in any other column. From the center you can build four in a row horizontally, vertically and on both diagonals in many different combinations; a piece on the edge serves only one or two directions. That is why strong programs order their moves from the center outward, and why opening books start with column 4.

The practical rule for you is simple: when you have no clearly better move, pick a column near the center. And if your opponent takes the center first, don't panic: the neighboring columns are still very good.

Tips to win more games against people

• If you go first, open in the center column. It is the only opening that wins with perfect play.
• Look for double threats: two lines of three with the finishing square available at the same time. Your opponent can only block one. It is the most common way to beat humans.
• Think about threats "in the air": a line of three whose last square cannot be reached yet because a piece is missing underneath. If that square sits on a row that favors you by parity, sooner or later your opponent has to play below it and hand it to you.
• Before dropping a piece, look at which square becomes available right above it. If you give your opponent a square that completes a line, you have lost.
• Block open-ended threes before they form: they are a guaranteed loss. Anticipate one turn ahead.
• In the endgame what matters is who runs out of safe moves first, so protect the columns you can still play without danger.
• If you go second, aim for the squares on even rows and calmly block every threat on odd rows: it is your best path to a draw, or to your opponent slipping up.

So can the computer not lose?

A program that played perfectly from the very beginning and moved first would never lose, but that is a statement about the theoretical solution of the game, not about any given program. Solving the whole game from the starting position takes a huge amount of computation, and in a browser, with only about a second and a half per move, that is out of reach.

That is why the "Unbeatable" level of our Connect Four is presented as what it is: the strongest level. It uses alpha-beta search with iterative deepening, a table that remembers positions already seen, a column order that starts from the center, and a very short opening book. It looks many moves ahead and rarely lets a mistake slip by, but we do not promise it is impossible to beat. If you manage to win, you really earned it.

How to practice

A good way to improve is to play against the computer on Hard and then on the strongest level, taking turns going first. When you lose, review the game and find the turn where the double threat appeared: it can almost always be traced back to a quiet earlier move. It is also worth trying the variants, such as the larger board or PopOut mode, which force you to think differently and train your board vision.

Frequently asked questions