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Gomoku — the overline rule, done properly

Does six in a row win? Every other free site answers that question by accident. Here all three rule sets are implemented and labelled — free-style, standard and renju — the board tells you which one you are on, and it says so out loud when your six does not count. Also free: go · shogi · chess.

Gomoku五目並べ

Five in a row on a fifteen-by-fifteen grid. You play Black and move first.

Rule set — this is the choice everyone else hides

Opening — Black is proven to win without one

Play the computer

Free. Nothing is locked.

Play a person

A private room needs no account.

OR

Both players stay anonymous. Black moves first and has the advantage — the Pro opening reduces it.

Honest about the bot: Sharp finds forced wins by consecutive fours and every one-move double threat, then searches four ply. It does not have Allis's full threat-space search over threes, so a win that has to be set up with a sequence of open threes will be missed. Club level at best.

The rules, in about a minute

Two players take turns placing a stone on any empty intersection of a 15×15 grid. Black moves first. Stones never move and are never captured. The first player to make a line of five of their own colour — horizontally, vertically or diagonally — wins. If the board fills with no five, the game is a draw.

That is the whole game, and it is why the next paragraph is the one that matters.

Does six in a row win? It depends, and almost nobody tells you

A line of six or more of the same colour is an overline. Whether it wins is the single most-botched rule in this game, and the three rule sets answer it differently. Quoting the definitions directly from L. Victor Allis's 1994 thesis, page 123:

All three are implemented here, you pick one before the game starts, and the panel beside the board names the one you are on for the whole game. And when you make an overline under standard rules, we tell you on screen that it does not count, instead of leaving you staring at six stones wondering whether the site is broken. We built that specifically because a reviewer of a rival gomoku app reported its top-level engine winning with “6 in a row” on a board that claimed exactly-five rules, and filed it under “Big errors”. When the rule is invisible, a bug and a variant look identical.

In renju every point Black is forbidden to play is marked with a cross, the same way our Go board marks illegal points. The forbidden shapes are a double three, a double four and an overline — and making five overrides all of them, so a move that completes an exact five wins even when the same stone would otherwise be a double four.

This game is solved, and we are not going to pretend we solved it

Gomoku is a first-player win. L. Victor Allis proved it in his 1994 PhD thesis Searching for Solutions in Games and Artificial Intelligence (University of Limburg, Maastricht), using two techniques he introduced for the job: threat-space search and proof-number search. His program Victoria solved free-style gomoku with 11.9 days of CPU time and standard gomoku with 15.1 days, on fifteen SPARCstations running outside office hours. The solution trees hold 138,790 and 153,284 positions; the deepest variation in both is 35 ply. His conclusion, page 153: “go-moku should be considered a solved game.”

🔴 Our engine does not reproduce that proof and nothing in a browser tab could. What our test suite actually checks is stated in the same plain terms it is run in:

What we do not reach: (6,6,5) — the smallest board that still feels like gomoku — is a published draw that follows from Hsu and Ko's solve of (8,8,5), and it is far beyond brute force here. We say so rather than asserting something smaller and letting you assume.

Black wins with perfect play. Here is what to do about it

The proof says a perfect Black wins; it does not hand anyone the strategy, which is a 138,790-position database. At human level the edge is real but survivable. Two honest ways to shrink it, both offered on the start screen:

The Pro opening restriction, quoted from the same thesis page: Black's first move must be the centre, White's first must be one of the eight squares touching it, and Black's second must be outside the 5×5 block around the centre. Renju goes further — Black loses on a double three, a double four or an overline, which removes most of the sharpest attacking shapes.

We looked at what the popular free gomoku sites do about this and the answer is essentially nothing: the ones we could inspect run plain free-style with Black first, one of them forcing the first stone to the centre and no more. The serious balancing systems — Swap2, Soosõrv-8, Taraguchi-10 — live in federation renju play and not in the browser. ⚠️ We have not built Swap2 either, and that is a real gap rather than a decision we are pleased with; Pro and renju are what is here today.

The honest limitation: the bot

Sharp does three things well. It finds forced wins by continuous fours — a VCF search roughly eight attacker moves deep, where every attacking move is a four so your reply is forced. It sees every one-move double threat: a move after which it has two separate squares that make five, which you cannot both block. And it searches four ply with a pattern evaluation for everything else.

What it does not have is the part of Allis's work that made his proof possible: a full threat-space search over threes. A win that has to be built with a sequence of open threes before any four appears is invisible to it. It also defends VCF by taking the square the attack would start on, which stops the line it found and is not a proof that no other line exists. So: it will beat someone learning the game reliably, it will lose to a serious gomoku player, and it is not the reason to use this page.

We are saying this here rather than in a footnote because the reason people search for this game is usually to play a computer, and finding out after twenty minutes would be worse than reading it now.

What we do not have that the big sites do

No clocks, no tournaments, no game archive, and no Swap2. Live play is a private room with a four-letter code and anonymous matchmaking; there is no rated ladder specific to gomoku beyond the site-wide one. What we do not have, we have not hidden.