Renju forbidden moves

What are Renju's forbidden moves?

In Renju, forbidden moves apply to Black only. A double-three (one move creating open threes in two different directions), a double-four (one move creating two or more fours), and an overline (six or more stones in a row) are all illegal for Black — Black simply cannot play there. White has no forbidden moves and wins with five or more in a row.

However, if a move completes a five at the same time as it would otherwise form a forbidden shape, the five always takes precedence — the move simply wins. The six examples below walk through each rule.

Double-three

Playing Black at the marked point creates an open three both horizontally and vertically at once. Because the same move produces threes in two different directions, it's a double-three — forbidden, and Black may not play there.

Black at h8 would create an open three in both the row and the column at once — a double-three, forbidden.

Double-four

Playing Black at the marked point creates two separate fours on the same row. Two or more fours from a single move is a double-four — forbidden, and Black may not play there.

Black at h8 creates two distinct fours — one completed at d8-h8, another at h8-l8 — a double-four, forbidden.

Overline

Playing Black at the marked point makes six stones in a row in that direction. Six or more — not exactly five — is an overline, forbidden for Black in Renju.

Black at h8 would connect six stones from e8 to j8 — an overline, forbidden.

False three

When a move looks like it creates threes in two directions, but the point that would complete one of them is itself already forbidden, that apparent three doesn't count — it's a "false three". In the example below, the row's apparent three is false because its completing point would create an overline (itself forbidden); only the column's genuine three remains, so this is not a double-three and the move is legal.

h8 is legal. Completing the row's three (e8-f8-h8) would need g8 — but g8 would make the g-column six in a row (g6 through g11), which is already forbidden as an overline. So the row's three is false; only the column's three (h8-h9-h10) is genuine, so this move is not a double-three.

Four-three is allowed

Making one four and one open three at the same time — a "four-three" — is not forbidden in Renju. Only a five automatically escapes the forbidden-move rules on its own, but a single four plus a single three is neither a double-four nor a double-three, so it's legal by itself.

Black at h8 makes a straight four on the row (e8-f8-g8-h8) and an open three on the column (h8-h9-h10) at the same time — a four-three, which is legal.

Five takes precedence

When a move completes a five, forbidden-move checks are skipped entirely even if the same move also looks like it creates a double-three or an overline in another direction — completing the five wins outright.

Black at h8 completes an exactly-five on the row (d8 through h8) and wins immediately. It also happens to create three-like shapes in the column and diagonal, but five takes precedence over any forbidden-move check.