Is Gomoku Solved?
Yes — gomoku has been mathematically proven to be a first-player win. In 1993, Dutch computer scientist Victor Allis demonstrated that with perfect play, Black (the first player) can always force a win on a standard 15×15 board. But this answer comes with important nuances.
What Does "Solved" Mean?
In game theory, a "solved" game means the outcome can be determined from any position assuming perfect play. There are three levels: ultra-weakly solved (initial outcome known), weakly solved (a strategy exists from the start), and strongly solved (every position analyzed). Gomoku is weakly solved — we know Black can always win from the starting position, but not every possible board position has been fully analyzed.
The Proof
Victor Allis proved gomoku is a first-player win in his 1993 paper "Knowledge-based Approaches in Go-Moku" (ICGA Journal). His approach used threat-space search, knowledge rules derived from expert play, and extensive computer verification. He showed that Black can force a win by creating an unstoppable "double threat" — a position where Black threatens to win in two different ways simultaneously, and White can only block one.
Why This Doesn't Ruin the Game
1. The strategy is too complex for humans. Allis's proof involves a strategy tree far too complex for any human to memorize. In practice, games between skilled players are still competitive.
2. Renju adds restrictions to balance the game. Professional gomoku (Renju) forbids Black from creating double-threes, double-fours, and overlines. These restrictions make the game significantly more balanced. Learn more about Renju rules →
3. Even chess is theoretically solvable — it's a finite, perfect-information game. The fact that a game can be solved in principle doesn't diminish its practical value.
Comparison With Other Solved Games
| Game | Solved Status | Practical Impact |
|---|---|---|
| Tic-tac-toe | Strongly solved | Trivial for adults |
| Connect Four | Strongly solved | Still fun casually |
| Gomoku (standard) | Weakly solved | Still competitive |
| Checkers | Strongly solved (2007) | Still played competitively |
Frequently Asked Questions
Does "solved" mean Black always wins in real games?
No. The proof assumes perfect play by Black. In real games between humans, both players make mistakes, and White wins a significant portion of games at all skill levels.
Is Renju also solved?
No. Renju's restrictions on Black make the game much harder to analyze, and it has not been mathematically solved. This is one reason professional gomoku is played with Renju rules.