Connect Four was solved twice in one month

Two people, one month, the same answer

In October 1988 Connect Four stopped being an open question. James Dow Allen worked out the game's perfect result on 1 October. Victor Allis arrived at the same conclusion on 16 October, independently, and wrote his up as a thesis at the Vrije Universiteit in Amsterdam, titled A Knowledge-based Approach of Connect-Four.

Neither knew what the other was doing. After decades of the game sitting in living rooms unexamined, two people cracked it within a fortnight of each other, which says more about the state of computing in 1988 than about coincidence. The hardware had finally caught up with the problem.

Who is James Dow Allen?

James Dow Allen is the person who solved Connect Four first. He reached the result two weeks ahead of Allis, which makes him the answer to the trivia question even though Allis's thesis is the better known document, because it was published academically and set out the method in detail.

Allen kept working on the game after 1988. He wrote Expert Play in Connect-Four in 1990, and in 2010 published The Complete Book of Connect 4: History, Strategy, Puzzles, a book that covers where the game came from, how strong players think about it, and a large set of positions to solve. If you want to go deeper than the articles on this site, it is the natural next step.

Who is Victor Allis?

Victor Allis was a student at the Vrije Universiteit in Amsterdam when he solved the game, and his thesis set out nine strategic rules that between them were enough to prove the result. He went on to a doctorate on solving games, including Gomoku, which he showed to be a first player win.

The answer

With flawless play from both sides, the player who moves first wins, and only by opening in the centre column. Open in one of the two columns beside the centre and the game is a draw. Open in any of the four outer columns and the first player loses.

That is a remarkably sharp result for a game most people treat as a coin toss. The entire theoretical outcome is decided by the very first disc.

What solving a game actually means

Researchers distinguish between levels of solution, and the difference matters.

An ultra weak solution tells you the result of perfect play without telling you how to achieve it. A weak solution gives you the result plus a strategy that reaches it from the starting position. A strong solution gives you the correct move in every legal position, including positions you would only reach after mutual blunders.

Connect Four has been solved in the stronger senses, which is why a modern engine can tell you not just who should win, but exactly how many moves it should take from any position you care to set up.

The idea was 75 years old already

The proof that an answer had to exist arrived long before anybody could compute it. In 1913 the mathematician Ernst Zermelo showed that in a finite two player game with no hidden information and no element of chance, the result of perfect play is already determined. Either one side can force a win, or both can force a draw.

Zermelo was writing about chess, and chess remains unsolved because the position count is astronomically beyond reach. His argument nevertheless covers Connect Four completely. From 1913 onward it was certain that Connect Four had a definite answer. It just took until 1988 for anyone to find out what it was.

The solved games club

Connect Four has company. Qubic, the four by four by four version of noughts and crosses, fell in 1980 and is a first player win.

Draughts held out far longer. A team led by Jonathan Schaeffer at the University of Alberta ran the Chinook project from 1989 and announced in 2007 that the game had been solved. The answer, after roughly eighteen years of computation, is that perfect draughts is a draw. It remains one of the largest games ever solved.

Chess and Go are not close to being solved and will not be soon. Modern engines beat every human alive, but playing better than people is a completely different achievement from proving what the perfect result is.

How the proofs actually worked

Neither solution was brute force in the naive sense. Four and a half trillion positions was far beyond 1988 hardware, so both efforts leaned on knowledge rather than raw enumeration.

Allis in particular built his proof around a catalogue of recurring patterns, rules describing when a threat is safely claimable by one side because of how the rows will inevitably fill. Given enough of those rules, large regions of the search tree can be dismissed with an argument instead of a search, which is what brought the problem inside the reach of a machine of that era.

It is a useful reminder that solving a game is rarely about counting faster. It is about finding the structure that lets you avoid counting at all.

What changed after 1988

Very little, for players. Connect Four sold just as well the following Christmas, because knowing a perfect strategy exists is not the same as being able to execute it across a kitchen table.

What did change is that the game became a standard teaching example. It is now one of the first serious search problems handed to computer science students, precisely because it is small enough to solve on a laptop and rich enough to reward doing it well.

Does knowing spoil it

Not really. Perfect play requires calculating far beyond what a person does across a coffee table, and the moment either side deviates, the theoretical result stops applying. Knowing that the first player wins with the centre opening is useful advice, not a spoiler.

Questions about the solution