Game rules
The 24 axioms (A1–A24) and 15 theorems (T1–T15) that define 3Chess — board, pieces, turn order, win conditions.
Overview
The game-rules system is the foundation. It defines the board’s geometry, the piece set, the turn order, when a player is eliminated, and how the game ends. Every other 3Chess system derives from this one or from positions it produces.
Scope: A1–A24 are axioms (the rules) · T1–T15 are theorems (derived facts). Current version is v2.2. Earlier versions are listed in the changelog; v2.2 cut the move-rule from 50 to 20 based on the NP1 proof.
What the system covers
- Board — the 127-cell regular hexagon, axial coordinates
(q, r), three 120°-rotationally-symmetric territories. - Pieces — 15 per player (1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, 7 pawns), hex-adjusted geometry.
- Movement — king (12 directions), queen (8 directions on hex grid), bishop (locked to one of three colour classes), knight (12 distance-3 offsets), pawn (player-dependent forward + flanking captures).
- Turn order — White → Black → Red, cyclic.
- Elimination — A player whose king is checkmated or captured stays on the board as inert obstacles (A14).
- Win conditions — Last player standing, including via cascading checkmate; or territory scoring when the game reaches a draw condition.
- Draw conditions — Threefold repetition, 20-move rule (A20.2), insufficient material, two-player stalemate — all resolved by territory scoring.
Status
Locked at v2.2 since the NP1 proof. No open questions remain at the rules layer; the next round of changes will only happen if real-game play surfaces an edge case the current axioms don’t resolve.
Coming soon — the full A1–A24 listing with derivations is being prepared for publication.