By Yangqing

Is Gomoku Solved?

For 15×15 gomoku without the Renju three-three restriction, published computer-search research by Victor Allis established that Black can force a win with perfect play. The exact conclusion depends on the rule set, so it should not be applied blindly to Renju, house rules, or every online implementation. “Solved” also has a specific game-theory meaning, and its practical effect on ordinary human play is limited.

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.

What Victor Allis's Research Established

Allis and colleagues described threat-space search for Go-Moku in the early 1990s, and Allis's 1994 doctoral thesis documented a first-player win for the applicable 15×15 unrestricted setting. The result is about a precisely defined rule set; it is not evidence that every common rules page, app, or Renju event has the same outcome.

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.

Threats and double threats are central tactical ideas in gomoku. The published solving result establishes a first-player win under its stated conditions; it should not be reduced to a single opening square or a short human-play recipe.

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.

The result comes from specialized search rather than a short sequence a player can memorize. For people playing over the board or in a browser, pattern recognition, time control, and mistakes still determine most games.

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 first-move advantage in unrestricted gomoku, but it is not a guarantee in human play. Results vary with the rule set, player strength, opening procedure, and time control. Avoid treating an unsourced percentage as a universal tournament statistic; in any individual game, tactical decisions and mistakes still decide the result.

2. Renju fixes the imbalance

Competitive Renju applies Black-only forbidden-move and opening rules to address first-player advantage. Those rules make it a distinct game from the unrestricted setting in the solving result. As of this review, this site has not found a published solution that establishes the game-theoretic value of standard Renju; readers should consult the current Renju International Federation rules for tournament requirements.

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 is a separate competitive ruleset with forbidden moves for Black and formal opening procedures. This site has not found a published weak or strong solution for standard Renju, but absence of a cited solution is not proof that none can exist. The important practical point is that Renju cannot be treated as interchangeable with unrestricted Gomoku.

If competitive fairness matters, use the current RIF rules and the event's published opening procedure. For casual play, agree on the board size, overline rule, and whether any swap or forbidden-move rule applies before the first move.

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 →

Sources and Editorial Notes

• L. Victor Allis, H. J. van den Herik, and M. P. H. Huntjens, “Go-Moku and Threat-Space Search”, 1994.
• L. Victor Allis, Searching for Solutions in Games and Artificial Intelligence, doctoral thesis, 1994.
• Renju International Federation rules, consulted for the distinction between competitive Renju and unrestricted Gomoku.

Key Takeaways

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