# **Game Design Document: “Crystal Grid”** --- ## 1. Concept Paragraph “**Crystal Grid**” is a deterministic, turn-based strategy duel in which two mystic architects compete to align charged crystals on a sacred 3×3 energy grid. Each player channels a unique elemental charge—Solar (Player 1) or Lunar (Player 2)—and infuses crystals into empty nodes. The goal is to align three of one’s crystals horizontally, vertically, or diagonally to create a stable energy conduit. The available actions consist solely of placing a crystal at a chosen grid coordinate. This design is entirely unrelated to any negotiation or trading game; it’s a pure positional alignment challenge grounded in an original magical circuit theme. --- ## 2. Roles and Win Condition - **Players**: - Player 1: **Solar Architect** (mark → `S`) - Player 2: **Lunar Architect** (mark → `L`) - **Objective**: Align three of one’s crystals (`S` or `L`) in a row, column, or diagonal. - **Win Condition**: - A player **wins** if after their turn, three of their marks form an unbroken line. - The opposing player **loses** immediately. - If all nine nodes are filled and no line is formed, the outcome is a **draw**. Decision rules: 1. Check alignment after every placement. 2. If both align simultaneously (impossible under alternation), the current mover’s alignment takes precedence. 3. Draw declared if maximum turns (9) are reached without a win. --- ## 3. Turn Structure and Determinism - Players alternate strictly (`Solar → Lunar → Solar → ...`). - The first mover (Solar) always begins. - The environment is **fully deterministic**. - Random seeding affects only which player may go first if configured optionally; otherwise fixed for reproducibility via explicit seed. - Turn limit: **9** turns maximum. - All outcomes reproducible with identical initial seed and move sequence. --- ## 4. Action Grammar (Machine-Parseable) **Allowed Action Tokens**: Each player may perform: ``` [Place: ,] ``` where: - `` and `` ∈ `{1,2,3}` - Positions are 1-indexed (top-left is 1,1; bottom-right is 3,3) - No repetition; cannot place where a crystal already exists. **Formal Pattern (regex)**: ``` ^\[Place:\s*([1-3]),\s*([1-3])\]$ ``` **Example valid action**: ``` [Place: 2,3] ``` Reason valid: Correct token keyword, valid 1–3 coordinates, comma-separated. **Example invalid action #1**: ``` [Place: 0,3] ``` Reason invalid: Row out of allowed range (must be 1–3). **Example invalid action #2**: ``` [Play: 2,3] ``` Reason invalid: Token keyword incorrect (‘Play’ not recognized). In actual play, players will respond with `\boxed{{[Place: 2,3]}}` formatting, but the validation operates on the unboxed content. --- ## 5. Game State Schema Example runtime structure: ```json { "turn_count": 4, "current_player": "Solar", "grid": [ ["S", "L", null], [null, "S", null], [null, null, "L"] ], "available_cells": [[1,3],[2,1],[2,3],[3,1],[3,2]], "winner": null, "is_terminal": false, "observations": { "Solar": "Previous move: [Place: 1,2] by Lunar.", "Lunar": "Your opponent placed [Place: 1,2]." }, "history": [ "Solar → [Place: 1,1]", "Lunar → [Place: 1,2]", "Solar → [Place: 2,2]", "Lunar → [Place: 3,3]" ], "seed": 42, "score": { "Solar": 0, "Lunar": 0 } } ``` --- ## 6. Initialization Rules - The grid initializes to all `null` (empty). - `current_player` set to `"Solar"` unless overridden by seed-based first mover rule. - `winner` set to `null`, `turn_count = 0`. - The `seed` controls any shuffle variation for first turn but not the grid generation. - Initial observations describe the empty grid and player symbols: ``` The Crystal Grid is empty. You are Solar Architect (symbol ‘S’). Your charge begins first. ``` --- ## 7. Validation and Error Handling **Invalid move triggers**: 1. **Pattern mismatch** — doesn’t match regex → “Action format not recognized.” 2. **Cell out of range** — row/col outside 1–3 → “Coordinates must be between 1 and 3.” 3. **Cell occupied** — attempted placement on non-null grid cell → “That node already holds a crystal.” 4. **Not your turn** — action attempted by the wrong player → “It is not your turn.” When detected, environment returns `set_invalid_move(player_id, reason)`. --- ## 8. Terminal Conditions and Scoring **Check each turn**: 1. After placement, verify if that player occupies any of the 8 winning lines: - Rows: (1,2,3)*(each same row) - Columns: (1,2,3)*(each same column) - Diagonals: `(1,1)-(2,2)-(3,3)` and `(1,3)-(2,2)-(3,1)` 2. If true → `is_terminal = True`, `winner = current_player`. 3. If `turn_count == 9` and no winner → `is_terminal = True`, `winner = "draw"`. **Scoring convention**: - Win → +1 score for winner, 0 for loser. - Draw → 0.5 each. **Tie-break**: - None required beyond draw detection. --- ## 9. Player Prompt Specification When `_generate_player_prompt` runs, it assembles a structured text like below: **Prompt Outline:** - Identity blurb: “You are a mystic architect competing on the Crystal Grid. Align three of your charged crystals before your opponent does.” - Display current board in a human-readable format with coordinates. - List allowed actions summary: ``` Allowed Action: [Place: row,col] where row and col are integers in {1,2,3}. ``` - Explain win conditions and turn rules. - Example response instructions, including final boxed action. **Example snippets shown in prompt:** ``` Example valid response: I will charge the central node for structural balance. \boxed{{[Place: 2,2]}} ``` If an invalid attempt occurs: ``` Invalid example (do not use): \boxed{{[Play: 2,2]}} <-- token must be [Place: ...] ``` **Response format reminder**: “At the end of your message, put your final answer within \boxed{{}} using one allowed action.” --- ## 10. API Mapping Plan **reset()** - Clears grid and logs, initializes player identifiers and seed. - Returns initial `game_state`, first `observations`, and references to legal actions. - No winner or score yet. **step(player_action)** - Extracts action via `_extract_answer_content()`. - Validates syntax and legality. - If valid: updates grid, increments turn count, checks for winner/draw. - Updates `observations` to include transcript of both players’ actions. - Returns updated `game_state`, new observation for next player, and completion flag. **_generate_player_prompt(player_id)** - Constructs full textual prompt described above with player perspective. - Reads `game_state`: grid, turn count, player symbols, etc. - Inserts few-shot examples of valid/invalid moves. - Ends with explicit directive to produce `\boxed{{[Place: ,]}}`. --- ## 11. Copy-Check Against the Example All entities, vocabulary, and schema in “**Crystal Grid**” are fully original: - Theme: mystical crystal alignment, not trading, negotiation, or pricing. - Roles: Solar and Lunar Architects, not merchants or diplomats. - Objective: spatial pattern alignment, not bargaining success. - Keys (`grid`, `available_cells`, `seed`, `history`, etc.) are unique to this design. - Actions: `[Place: row,col]` tokens, entirely distinct from any negotiation-style `[Offer]` or `[Accept]`. This confirms full conceptual independence from the previous example while preserving structure needed for deterministic, turn-based API implementation.