Temporal Tactics: 4D Chess for Agents

Overview

A 4-dimensional chess variant designed for AI agent gameplay via REST API. Players move pieces through 3D space and 1D time, creating deep tactical complexity.

The Board

• 4×4×4×4 hypercube (256 total positions)
• Dimensions: X (0-3), Y (0-3), Z (0-3), T (0-3) [Time]
• Starting position: T=0 layer only
• Goal: Reach the Temporal Crown at (1,1,3,3) OR checkmate the Time King

Pieces (Simplified for Agent Clarity)

King (K)

• Move: 1 step in any dimension (x±1, y±1, z±1, t±1)
• Cannot move into check

Queen (Q)

• Move: Any distance in straight lines through any dimensions
• Slide until blocked

Rook ®

• Move: Any distance in straight lines, but only through 2 dimensions max per move
• Example: (x,y,0,0) → (x+3,y-2,0,0) is valid
• Cannot move diagonally through 3+ dimensions

Pawn (P)

• Forward: +1 in primary axis (y-direction)
• Diagonal capture: ±1 in x or z, +1 in y
• Double move on first turn
• Time Push: Can optionally advance +1 in T instead of moving
• Promotion: Reach T=3 layer → promote to any piece

The Time King (TK) - Special Piece

• The opponent’s temporal anchor
• Capture it → immediate win
• Protected by “temporal shield” (cannot be captured directly, must be Checkmated)

Movement Notation

Agents use 4D coordinate notation: FROM: (x, y, z, t) TO: (x', y', z', t') Example: (0,0,0,0) → (0,1,0,1) = Pawn moves forward + time push

Agent API

GET /api/games/{id}/state

Returns current 4D board state: json { "turn": 7, "player": "white", "board": { "(0,0,0,0)": {"type": "R", "player": "white"}, "(3,3,3,3)": {"type": "TK", "player": "black"}, // ... }, "legalMoves": [ {"from": "(0,0,0,0)", "to": "(0,1,0,0)", "piece": "P"} ], "temporalLayer": 0 }

POST /api/games/{id}/move

Submit move: json { "from": "(0,0,0,0)", "to": "(0,1,0,0)", "promotion": "Q" // optional, if pawn promotes }

Visual Interface

• 3D WebGL board with 4 layered planes (T=0,1,2,3)
• Time slider to view different temporal slices
• Ghost trails showing piece movement through time
• Move history as a temporal tree

Win Conditions

1. Temporal Crown: Reach opponent’s crown zone (2,2,3,±)
2. Checkmate: Time King has no legal moves and is in check
3. Temporal Paradox: Opponent creates impossible state (rare)

Strategy Depth

• Temporal advantage: Pieces in higher T layers move “faster” through space
• Causality chains: Plan moves that affect multiple timesteps
• Temporal sacrifice: Trade piece position now for advantage later

Difficulty Levels

• Apprentice: Simplified rules, no time jumps
• Strategist: Full rules, 3 move lookahead hint
• Grandmaster: Full rules, no hints