Does Gomoku Have a Solved Strategy
Free-style gomoku was proved a first-player win in 1993, so the question of whether gomoku is solved has a real answer. Here is what the proof covers, why it does not hand you an unbeatable line, and what still decides your games.
Is gomoku solved? Yes, with one word doing most of the work. Free-style gomoku on a 15x15 board, no forbidden moves and no opening restrictions, was proved a first-player win by Victor Allis in 1993: black can force five in a row against any defence. Most people assume the game sits somewhere between tic-tac-toe and chess. It does not. It sits on the solved side of the line, and the distance between that fact and how you actually play is where the interesting part lives.
What solved means for a gomoku solved game
A solved game has a known outcome when both sides play perfectly from the start, usually with a method for reaching it. Strongly solved means every legal position has a computed win, draw or loss. Weakly solved means you know the result from the opening position and can play toward it, without a table for every branch. Allis produced the second kind: he proved black wins, using threat-space search rather than brute force over the whole tree.
The 1993 proof, in plain terms
Threat-space search does not walk every move. Allis tracked forcing lines instead: a live three that must be answered, an open four that must be blocked, and eventually a double threat with no answer at all. Gomoku suits this approach because threats accumulate. A stone dropped between two of your own often creates two problems at once, and the defender gets one move per turn. The first-player win grows out of that pile-up. It is not a statistical edge observed over many games.
Perfect play exists, and you cannot memorise it
Knowing gomoku perfect play exists and producing it are different things. Allis proved the win is there; the line itself runs through dozens of moves, branches on how white answers, and keeps the burden on black the whole way. Nobody hands you a fifteen-move script to recite over breakfast. Strong human players lose the thread three or four moves in, which is why the proof changed how the rules get written rather than how club players open their games.
Why renju added forbidden moves
- Black wins under free rules, so competitive play restricted black: double threes and double fours lose, and overlines do not count
- Opening rules went further. In renju, black's first three moves follow a protocol that lets white swap sides, which pushes the advantage back toward even
- A renju-like game without those opening rules was claimed solved by Janos Wagner and Istvan Virag in 2001, also as a first-player win
- So the honest answer to whether gomoku is solved depends on your rule set. Free-style: yes. Renju with the full opening protocol: not settled the same way
What this changes about how you play
- Take the opening seriously. If black has a forced win in the free game, most club games are decided inside the first six moves
- Count your opponent's forcing moves before admiring your own shape. A live three on the far side of the board is worth more than the pattern you were building
- Do not assume the opponent plays perfectly. Perfect play settles the theoretical result; your games are settled by whoever finds the double threat first
- People hunt for an unbeatable gomoku line the way they hunt for a perfect chess opening. What transfers instead are the habits the search relies on
How YiBoard handles the first-move problem
YiBoard plays free-style gomoku with a server-side referee, and the engine gets a fixed 500ms budget per move. That budget is deliberate: the opponent is strong enough to punish a missed block and weak enough that a well-built attack still lands. If both sides played perfectly the game would be over on move one, and nobody would come back for a second round. The first move covers where to put the first stone, double threes and double fours covers the forks the proof leans on, and defence first covers the other half.
FAQ
Is gomoku solved on every board size?
The 1993 result covers free-style rules on the standard 15x15 board. Bigger boards make the first-player win easier rather than harder, since there is more room to build threats, but that is not the same as a published proof for every size and every rule combination you might invent.
Does that mean black always wins online?
No. The proof assumes both sides play perfectly from move one. People do not, engines under a time budget do not, and the win is only forced for whoever holds the advantage and keeps holding it.
Can I look up the winning line and use it?
Not in any practical way. It is not a short sequence you can memorise. What carries over are the habits the search depends on: build double threats, answer forcing moves, and check the far side of the board before you commit.
What is the difference between gomoku and renju here?
Renju bans double threes, double fours and overlines for black, and adds an opening protocol with a swap option. Those rules exist because the free game is a first-player win.
Every game on yiboardgame.com runs the same referee, and the play page opens one in your browser with no sign-up. Ranked games feed the rating described in How Ratings Work: Starting at 1200, and Evaluation Functions explains what the engine counts when it cannot search to the end.