A comparative study of three AI approaches for playing 2048: Expectimax, Monte Carlo, and NEAT. This project explores which algorithmic strategy achieves the highest scores in this stochastic puzzle game.
Note: This was my first foray into Game AI (a learning project comparing search-based and evolutionary approaches)
The goal of this project was to determine which algorithmic approach yields the highest scores and most consistent wins in the stochastic environment of 2048.
I implemented three distinct agents:
- Expectimax Search
- Monte Carlo Simulation
- NEAT (Pure & Hybrid with Expectimax)
Probabilistic tree search modeling tile spawn randomness (90% twos, 10% fours). Uses dynamic depth (2-8 levels), corner bias, monotonicity, smoothness heuristics, and memoization for efficiency.
Executes 25-50 random playouts per move, selecting actions with highest average outcomes. Numba JIT-compiled for performance.
Evolves neural networks over 500 generations with 24-input features (board state, max tile, empty cells, monotonicity, smoothness). Tested both pure neural control and hybrid neural-guided Expectimax.
To ensure statistically significant comparisons, I conducted a rigorous benchmark:
- Sample Size: Each algorithm played 100 full games to completion (or timeout)
- Metrics Tracked:
- Success rate (reaching 2048 tile)
- Final score (average, median, standard deviation)
- Maximum tile achieved
- Execution time per game
- Moves executed before termination
- Hardware: All tests run on identical hardware to ensure fair comparison
| Algorithm | Success Rate | Avg Score | Avg Max Tile | Avg Time | Avg Moves |
|---|---|---|---|---|---|
| Expectimax | 79% | 47,694 | 2,880 | 48.38s | 2,276 |
| Monte Carlo | 15% | 13,445 | 989 | 42.00s | 783 |
| NEAT + Expectimax | 10% | 11,279 | 829 | 13.82s | 680 |
| NEAT Pure | 0% | 2,433 | 185 | 1.92s | 1,000 |
Expectimax's dominance (79% success) demonstrates that explicit probabilistic search with tuned heuristics significantly outperforms other approaches in this environment. Its computational cost (48s/game) translates directly into superior strategic planning.
Monte Carlo achieved moderate success (15%) with lower computational overhead, proving effective for opportunistic play but lacking deterministic long-term strategy.
Hybrid NEAT underperformed expectations (10%), suggesting that evolved evaluation functions didn't effectively complement the search algorithm. Pure NEAT completely failed (0%), indicating neural networks alone lack sufficient strategic depth for complex board states despite being 25x faster.
Key insight: In 2048, computational investment in search depth and heuristic quality directly correlates with performance.
pip install pygame neat-python matplotlib numpy numba# Expectimax
python expectimax_2048.py
# Monte Carlo
python mcts_2048.py
# NEAT
python neat_algo/train.py && python neat_algo/play_ai.pyAs mentioned, this was my first time diving into AI for games. While I am proud of the Expectimax results, I acknowledge there is significant room for optimization:
- Heuristic optimization via genetic algorithms or Bayesian optimization
- Alpha-Beta pruning for deeper search without exponential cost increase
- Bitboard representation for faster state evaluation and Monte Carlo scaling
- Neural network architecture search for more effective hybrid approaches