Gomoku is old, widely played, and unusual among traditional games in having been completely solved. Its history explains both why the rules vary so much and why the competitive version looks the way it does.
Origins
Games of making a line on a grid appear across East Asia going back many centuries, played on go boards because go boards were what people had. The name gomoku narabe is Japanese — roughly 'five points lined up'. Chinese and Korean traditions have their own long-standing equivalents.
Because it was played casually on borrowed equipment rather than codified by an institution, local rules varied enormously. That variation persists today.
The first-player problem
It was noticed early that the first player has an advantage, and by the late nineteenth century Japanese players were experimenting with restrictions to balance it. This produced Renju, formalised around 1899, which forbids Black from making double threes, double fours and overlines.
Renju is a genuinely different competitive game with its own literature and professional players, though it shares all its tactics with free-style gomoku.
The solution
In 1993 the Dutch researcher Victor Allis proved that free-style gomoku on a 15×15 board is a win for the first player, using a technique called threat-space search. The proof matters practically as well as theoretically: it confirmed that competitive play needs either Renju restrictions or an opening protocol.
Renju itself was later shown to be a first-player win under some conditions too, which is why modern tournaments layer opening protocols on top of the restrictions.
Modern competitive play
The Renju International Federation has run world championships since 1989. Most international events now use Swap2 or a related protocol, where the opening position is set up by one player and the colours are chosen by the other, so neither side can rely on a known advantage.
The game is strongest in Japan, Estonia, Russia and China, with an active tournament circuit and published opening theory that runs deeper than most casual players would guess.
Why it survives
Three reasons. The rules fit in one sentence, so anyone can be taught instantly. The equipment is a grid and two colours of counter, which has always been easy to improvise. And the gap between knowing the rules and playing well is large enough to sustain serious study.
Related games worth a look
Connect Four is gomoku with gravity. Pente adds capturing. Both descend from the same basic idea of making a line, and both solve the balance problem differently.
The version on this board
Free-style, 15×15, overlines win, no restrictions on either colour. This is the most widely recognised casual form and the best one for learning, because every tactic transfers to Renju and every other variant.
If you want the balanced experience, take White — that single choice reproduces most of what the competitive rule sets are trying to achieve.