Is Gomoku Solved?

Yes — standard gomoku (15×15, no special rules) is a solved game. Black, the first player, can force a win with perfect play. This was proven in 1993 by Dutch computer scientist Victor Allis. But "solved" means something specific in game theory, and the practical impact on whether gomoku is worth playing is much smaller than you'd think.

What "Solved" Actually Means in Game Theory

When someone says a game is "solved," they could mean three very different things. Game theorists use a three-tier classification, and the differences between the tiers are not academic hair-splitting — they determine whether the solution matters for real play.

• Ultra-weakly solved: We know the outcome from the starting position (win/loss/draw), but not how to achieve it. You know the answer but not the method. Example: we're nearly certain that chess is either a White win or a draw from the starting position, but we don't know which, and we definitely can't describe the optimal strategy.
• Weakly solved: We have a concrete strategy that the winning player can follow from the start of the game to guarantee the proven outcome. Gomoku sits at this level — we know Black can force a win, and we have a strategy (albeit one no human can execute).
• Strongly solved: We know the optimal move from every possible board position, not just the starting position. Tic-tac-toe and Connect Four are at this level. No matter how badly you've misplayed the opening, a strongly solved game can tell you the best move from wherever you are right now.

Gomoku is weakly solved. We know Black can win from the starting position, and we have a strategy for it. But we haven't analyzed every possible board state — there are far too many. This means the solution only helps you if you're starting from move 1 with a clean board. If you make a single mistake — one non-optimal move — the proof's strategy tree no longer applies from that position. You're on your own, just like every human player always has been.

How Victor Allis Proved It

Victor Allis published his proof in 1993 in the ICGA Journal (then called the ICCA Journal) with his paper "Knowledge-based Approaches in Go-Moku." The paper wasn't just a theoretical argument — it described a program that actually played through the winning strategy, move by move, against every possible White defense.

Allis's approach combined three ingredients:

1. Threat-space search. Instead of brute-forcing every possible move (the game tree is astronomical), Allis's program focused on "threats" — moves that force the opponent to respond immediately. A threat is a move where, if the opponent doesn't block, you win on your next turn. The key insight: if you can create two threats at once (a double threat), the opponent can only block one. You convert the other into a win. This dramatically reduces the search space, because most moves that aren't threats can be pruned — they don't force a response, so they don't constrain the opponent's options.
2. Knowledge rules from expert play. Allis didn't start from scratch. He encoded patterns that experienced gomoku players have known for decades — things like "an open-four (4 in a row with both ends empty) is unblockable" and "a double-three (two open-threes created simultaneously) wins if the opponent hasn't already blocked both." These patterns acted as shortcuts, letting the program skip vast regions of the search tree that no experienced player would ever enter.
3. Exhaustive computer verification. The program systematically explored the game tree, pruning non-threatening branches and verifying that Black's winning strategy holds under all possible White responses. This wasn't a heuristic argument — it was a proof by exhaustive search within a constrained threat space. The program checked every line of play that White could try within that space, and verified that Black has a counter to each one.

The key finding: Black wins by creating an unstoppable double threat. The strategy relies on Black controlling the center of the board and building pressure in multiple directions simultaneously. White can block one threat line, but not both — and that's checkmate, gomoku-style.

The Strategy Is Real. The Strategy Is Also Useless (For Humans).

This is the part that confuses people. If we know Black wins, why doesn't Black always win? Because "we" — the game theory community, the computer programs — know the strategy. Individual human players do not.

Allis's proof involves a strategy tree with millions of positions. It maps out what Black should play in response to every possible White move within the threat space. No human can memorize this tree, and no human can mentally simulate it in real-time during a game. The computational cost of executing the winning strategy is simply beyond what a brain can do at the table.

Here's an analogy: we know the optimal strategy for tic-tac-toe because the game tree is small enough to hold in your head. Now imagine a tic-tac-toe game tree that's a million times larger. The logic works the same way — there's an optimal move at every point — but you can't fit it in your head anymore. That's gomoku. The strategy exists. It's proven. And it's irrelevant to human play because we can't execute it.

Three Reasons This Doesn't Ruin the Game

1. Between humans, games are genuinely competitive

Black has a statistical advantage — Black wins more often than White between human players. But "more often" is not "always." Tournament statistics from RIF events show Black winning roughly 55–60% of games between players of equal rating. That's a meaningful edge, but it's a far cry from guaranteed victory. In any individual game, the outcome depends on who makes better moves — which is the whole point of playing a strategy game.

2. Renju fixes the imbalance

Professional gomoku is played with Renju rules, which forbid Black from creating double-threes, double-fours, and overlines (lines of 6 or more). These restrictions directly target the mechanisms that make Black's winning strategy work. Many of the positions that Allis's program uses to force a win are illegal for Black under Renju. This makes the game significantly more balanced — so much so that Renju has not been solved. The RIF world championship uses Renju rules specifically because of this. The "broken" game and the competitive game are not the same game.

3. Checkers was solved harder, and nobody stopped playing

Checkers was strongly solved by Jonathan Schaeffer's Chinook project in 2007, after 18 years of computation. This is a much stronger result than gomoku's — every possible checkers position has been analyzed, not just the opening. With perfect play from both sides, checkers is a draw. And yet checkers tournaments still happen, and the World Checkers/Draughts Championship still draws competitors. Why? Because the solution exists in a supercomputer's database, not in a human's brain. The solved status matters for AI research and game theory. It barely matters for people playing against each other.

Comparison With Other Solved Games

Notice the pattern: the more positions a game has, the less the "solved" label matters for human play. Tic-tac-toe's solution is trivial. Connect Four's solution can be learned. Gomoku and checkers have solutions that exist only in databases no person can hold in their head. The game-theoretic outcome becomes increasingly abstract as complexity grows.

What About Renju? (The Unsolved Version)

Renju — competitive gomoku with forbidden moves for Black — has not been solved. Not even weakly. The forbidden-move rules (double-three, double-four, overline) fundamentally change the game tree. Black can't simply charge toward a double threat because many of the positions that create double threats are now illegal for Black — but not for White. This asymmetry adds a layer of complexity that makes the game much harder to analyze computationally.

This is why the RIF world championship uses Renju rules. The forbidden moves aren't just a house rule or a handicap system — they're the structural difference between a game that's theoretically broken and one that's still an open problem. If you care about competitive fairness, Renju is the version that matters. If you're playing casually on a website or with a friend, the standard rules are fine — the first-player advantage is real but small enough that it rarely decides individual games between humans of similar skill.

What This Means For You As a Player

If you're deciding whether to learn gomoku, "is it solved?" is the wrong question. The right questions are: "Can I play competitively against other humans?" (Yes.) "Does the better player usually win?" (Yes.) "Is there room to improve over months and years?" (Absolutely.)

The proof that Black can force a win is a beautiful piece of game theory. It tells us something deep about the structure of gomoku. But it has about as much practical impact on your games as knowing the exact chemical composition of a basketball has on your free throw. The knowledge is real. It just operates at a level that doesn't touch the experience of playing. Start learning real gomoku strategy →

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