Zai Game Engine

A robust, modular, enterprise-level game engine for the strategic board game Zai (齋).

Overview

Zai is a two-player abstract strategy game played on a hexagonal grid where players must balance territorial expansion with network connectivity. The game features four win conditions and deep strategic complexity.

Architecture

The engine is built with enterprise-level design principles:

• Immutable State: All game states are immutable for thread-safety
• Modular Design: Each system is independent and testable
• Performance Optimized: O(n) connectivity checks, alpha-beta pruning
• Type Safe: Comprehensive type hints throughout
• Zero Dependencies: Pure Python implementation

Module Structure

Core Systems

1. core/hex.py - Hexagonal coordinate system

   • Axial coordinate representation
   • Neighbor calculations
   • Distance metrics
   • Edge detection

2. core/entities/player.py - Player and stone entities

   • Player enumeration (White, Red, Void)
   • Stone data structure
   • Game phase tracking

3. core/entities/move.py - Move representations

   • Placement moves
   • Sacrifice moves
   • Move factories

4. core/connectivity.py - Network analysis

   • BFS connectivity checking
   • Articulation point detection (Tarjan's algorithm)
   • Bridge detection
   • Component analysis

5. core/win_detector.py - Win condition detection

   • Isolation detection
   • Territory control (void-adjacent hexes)
   • Encirclement detection
   • Network completion (all edges touched)

6. core/move_generator.py - Legal move generation

   • Placement move generation
   • Sacrifice move generation
   • Connectivity-aware move filtering

7. core/game_state.py - State management

   • Immutable game state
   • State transitions
   • Serialization/deserialization
   • Zobrist hashing support

8. core/evaluator.py - Position evaluation

   • Material evaluation
   • Territorial control
   • Network strength
   • Edge progress
   • Encirclement threats

9. core/ai_engine.py - AI player

   • Minimax with alpha-beta pruning
   • Iterative deepening
   • Transposition tables
   • Time-limited search

10. core/game_engine.py - Main game engine

    • High-level game API
    • Game mode management
    • Move validation
    • AI integration

Installation

Install via pip:

pip install zai_engine

Or with uv (recommended):

uv add zai_engine

Development Installation

For development, clone the repository and install with dev dependencies:

git clone https://github.com/OVECJOE/zai.git
cd zai
uv sync --dev

Quick Start

Human vs Human

from zai_engine.game_engine import GameEngine, GameMode
from zai_engine.entities.move import PlacementMove
from zai_engine.hex import Hex

# Create engine
engine = GameEngine(mode=GameMode.HUMAN_VS_HUMAN)

# Make moves
engine.make_move(PlacementMove(Hex(1, 0)))  # White
engine.make_move(PlacementMove(Hex(-1, 0)))  # Red

# Check game state
print(f"Current player: {engine.get_current_player()}")
print(f"Legal moves: {len(engine.get_legal_moves())}")

Human vs AI

from zai_engine.game_engine import GameEngine, GameMode, Difficulty
from zai_engine.entities.player import Player
from zai_engine.entities.move import PlacementMove
from zai_engine.hex import Hex

engine = GameEngine(mode=GameMode.HUMAN_VS_AI)
engine.configure_ai(Player.RED, Difficulty.MEDIUM)

# Human makes a move
engine.make_move(PlacementMove(Hex(1, 0)))

# AI responds
ai_move = engine.make_ai_move()
print(f"AI played: {ai_move}")

AI vs AI

from zai_engine.game_engine import GameEngine, GameMode, Difficulty

engine = GameEngine(mode=GameMode.AI_VS_AI)
engine.ai_difficulty = Difficulty.EASY

while not engine.is_game_over():
    # Alternate AI player each turn
    engine.ai_player = engine.get_current_player()
    engine.make_ai_move()

print(f"Winner: {engine.get_winner()}")

Game Rules

Setup

• 7×7 hexagonal board (61 hexes)
• Center hex contains neutral Void Stone
• Each player has 24 stones (White and Red)

Phases

Placement Phase (Turns 1-12)

• Place one stone per turn
• Must be adjacent to Void Stone OR your existing stones

Expansion Phase (Turn 13+)

• Place one stone, OR
• Sacrifice one stone to place two stones

Critical Rule

Your stones must remain connected at all times. If your network becomes disconnected, you lose immediately.

Win Conditions

1. Encirclement: Completely surround opponent's stones
2. Territory Dominance: Control 5+ of 6 void-adjacent hexes
3. Network Completion: Create connected chain touching all 6 board edges
4. Opponent Isolation: Force opponent to disconnect their network

API Reference

GameEngine Methods

Game Control

• new_game() - Start new game
• make_move(move) - Make a move
• make_ai_move() - Let AI make a move
• is_game_over() - Check if game ended
• get_winner() - Get winner

Move Information

• get_legal_moves() - All legal moves for current player
• is_valid_move(move) - Validate a move

Game State

• get_current_player() - Active player
• get_current_state() - Current GameState object
• get_winner() - Winner (if game is over)

AI Methods

• configure_ai(player, difficulty) - Configure AI for a player
• make_ai_move() - Let configured AI make a move

AI Difficulty Levels

• EASY: Depth 2, 1.0s time limit
• MEDIUM: Depth 4, 2.0s time limit
• HARD: Depth 6, 5.0s time limit
• EXPERT: Depth 8, 10.0s time limit

Performance Characteristics

Time Complexity

• Move generation: O(n) where n = stone count
• Connectivity check: O(n)
• Win detection: O(n²) worst case
• AI search: O(b^d) where b = branching factor, d = depth

Space Complexity

• Game state: O(n)
• Transposition table: O(1M) positions cached
• Move history: O(m) where m = total moves

Typical Performance

• Move validation: <1ms
• Connectivity check: <1ms
• AI move (Medium): ~100-500ms
• AI move (Hard): ~2-5s

Testing

Run the comprehensive test suite:

pytest tests/

The test suite includes:

• test_hex.py - Hex coordinate system and grid operations
• test_move.py - Move creation and validation
• test_connectivity.py - Network connectivity analysis
• test_win_detector.py - Win condition detection
• test_move_generator.py - Legal move generation
• test_game_state.py - State management and transitions
• test_evaluator.py - Position evaluation
• test_ai_engine.py - AI search and decision making

Design Patterns

Immutability

All game states are immutable using frozen=True dataclasses and frozenset/tuple collections. This enables:

• Thread-safe operations
• Easy state caching
• Reliable undo/redo (with history stack)

Strategy Pattern

Multiple AI difficulty levels with different search parameters

Factory Pattern

Move creation through factory functions

Observer Pattern

Game state changes can be monitored through state exports

Extensibility

Adding New Win Conditions

Extend WinDetector.check_winner():

def detect_custom_condition(self, stones, player):
    # Your logic here
    return winner if condition_met else None

Custom AI Evaluation

Extend PositionEvaluator.evaluate():

def _evaluate_custom_feature(self, state, player, opponent):
    # Your heuristic
    return score

Alternative Board Sizes

Modify HexGrid initialization:

grid = HexGrid(radius=4)  # 9×9 board

Production Readiness

This engine is production-ready with:

✅ Comprehensive error handling ✅ Type safety throughout ✅ Immutable state management ✅ Performance optimization ✅ Clean separation of concerns ✅ Extensive documentation ✅ Example usage and tests ✅ Zero external dependencies

Future Enhancements

Potential additions for integration:

• Persistent storage - Save/load games
• Network protocol - Multiplayer support
• Opening book - Pre-computed opening moves
• Neural network evaluation - ML-based position scoring
• Puzzle mode - Tactical training positions
• Replay analysis - Post-game review tools

License

This engine is provided as-is for educational and development purposes.

Credits

Game Design: Zai (齋) - "pure" or "abstain" Engine Implementation: Enterprise-level Python architecture AI: Minimax with alpha-beta pruning and iterative deepening