3D Tic-tac-toe

Goal

The board is a 4 × 4 × 4 cube of squares, made up of four stacked levels. Players take turns placing a sphere of their colour on a free square. The first to line up four spheres wins.

The 76 lines

• On a single level: rows, columns and diagonals (40 lines).
• Through the levels: the vertical pillars (16 lines) and the diagonals that climb from one level to the next (16 lines).
• The four space diagonals that cross the cube from corner to corner.

How it works

• Amber always goes first.
• Play by tapping a square on any of the four levels drawn flat; on a computer, you can also click directly in the cube.
• Rotate the cube by dragging it, or with the keyboard arrows.
• If all 64 squares are filled with no line, the game is a draw.

About the AI

The engine keeps track, for each of the 76 lines, of the number of spheres each player has there, which makes evaluation instantaneous. It explores moves with alpha-beta pruning and a transposition table, extends the search on forced blocks and looks for wins through successive threats: each move creates a threat that the opponent must block, up to the decisive double threat.

At the Master level, the AI also rules out any move that would hand its opponent such an attack. As a fun fact, this cube was solved by computer in 1980: the first player can force a win, but the winning strategy is fearsomely complex.