Score Four Lab 4 × 4 × 4 · gravity · 76 lines

Click or type a peg (b3) · drag to turn · ←/→ step the game
Peg verdicts for the side to move, proven by search.
W3 win in 3 plies from this peg
D best play from here draws
L this peg loses against best play
? not proven inside the time budget
a–d / 1–4 peg = letter across, digit back; beads stack 1–4 up

Position

Engine

Refutation

Moves

No beads yet. Ivory moves first.

What the engine can and cannot tell you

Every verdict on the board is a proof: the engine searched the game tree from that peg until every reply was resolved. A ? means the proof did not finish in the time budget, and it is never replaced by a guess. Score Four is not a solved game. A 2020 effort at TU Munich ran 28 cores for 43 days (4.1 × 10¹⁴ positions) and still could not settle a 9-stone position, so early in the game expect question marks, and expect proofs to arrive once the position sharpens. The weaker engine strengths choose worse moves on purpose; they never change what the verdicts say.

Forcing play

  • Three of your beads on a line with the fourth cell open and playable is a threat; the opponent must answer it or lose at once. The board draws playable threats as rings.
  • One move that creates two threats wins: only one can be blocked. Most proven wins are threat sequences: each move forces the reply, the last one forks.
  • A threat whose cell is not yet playable is stored, and it forbids the opponent from ever playing the cell beneath it. The engine prunes those moves outright.
  • Playing under your own stored threat wastes it: the opponent blocks on top.

Where lines run

Each cell sits on a different number of the 76 lines. The counts below are per level, viewed from above (row 1 at the front). Only two counts occur: the corners of the bottom and top levels and the four inner cells of the two middle levels sit on 7 lines each; every other cell sits on 4. The engine's move ordering starts from this table.

Score Four Lab v0.2.0 Engine: exact negamax with transposition table, symmetry reduction and a forcing-sequence probe, in a Web Worker in this tab. Notation: peg b3 is second from the left, third row from the front; b3/2 is its second bead. Rules per Wikipedia: Score Four; unsolved status per TUM "Towards Solving Connect Four 3D" (2020). Privacy: nothing leaves your device. © 2026 Derek Sather, all rights reserved.