We implement a traditional Monte-Carlo Tree Search (MCTS) and a bayesian variant inspired by the paper Bayesian Inference in Monte-Carlo Tree Search by Gerald Tesauro, VT Rajan, and Richard Segal. Our implementation is focused on the game chess, and is designed with flexibility in mind, allowing different strategies to be used in the rollout phase.

Installation

To set up the project, follow these steps:

Install Dependencies:

Ensure that Python 3.11+ is installed on your machine.

Install Python dependencies with:
```
pip install -r requirements.txt
```
Download Chess Engines

Download stockfish and unpack it to /stockfish. Download lc0 and unpack it to /lc0.

Optionally, if you also want to set up the lichess bot, follow these steps:

Install local python package

Install the code in chesspp as a local package, so we can use it in the lichess bot:
```
pip install -e .
```
Set the API Key

Get an API key from lichess. And set the token in lichess_bot/config.yml to this API key.
Install Lichess specific Dependencies:

Install the Python dependencies of the lichess bot by executing in the folder /lichess_bot:
```
pip install -r requirements.txt
```

Main Functionalities

Engine Matches

Let two engines play against each other and collect statistics.

python main.py --e1 BayesianMCTS --s1 Stockfish --e2 ClassicMCTS --s2 Stockfish -n 24 --proc 12 --time=1

You can customize with the following command-line arguments:

--e1:
- Engine 1.
- Possible Values:
  - ClassicMCTS: Our MCTS implementation .
  - BayesianMCTS: Our bayesian MCTS implementation.
  - Random: Plays completely random.
  - Stockfish: Plays with stockfish.
  - Lc0: Plays with Lc0.
--e2:
- Engine 2.
- Possible Values: The same ones as Engine 1.
--s1:
- Strategy that Engine 1 uses for the rollout, when set to ClassicMCTS or BayesianMCTS.
- Possible Values:
  - Random: Plays the rollout randomly. Evaluates the terminal state with a simple board evaluation by Tomasz Michniewski.
  - Stockfish: Plays the rollout with stockfish. Evaluates the terminal state with stockfish.
  - Lc0: Plays the rollout with lc0. Evaluates the terminal state with lc0.
  - RandomStockfish: Plays the rollout randomly. Evaluates the terminal state with stockfish.
  - PESTO: Plays the rollout according to PESTOs board evaluation. Evaluates the terminal state with PESTOs board evaluation.
--s2:
- Strategy for Engine 2 for the rollout.
- Possible Values: The same ones as Strategy 1.
-n:
- Number of games to play.
--proc:
- Number of processor cores to use.
--time:
- Amount of second each engine has foreach turn.
--nodes:
- Number of nodes each engine can compute each turn.
--stockfish_elo:
- Elo for stockfish engine.
- Default is 1500.
--stockfish_path:
- Path for the stockfish engine executable.
- Default is /stockfish.
--lc0_path:
- Path for the lc0 engine executable.
- Default is /lc0.
-h:
- Show the help message.

Web Interface

A web interface for watching two chess engines play against each other.

python web.py --e1 BayesianMCTS --s1 Stockfish --e2 ClassicMCTS --s2 Stockfish

You can customize with the same command-line arguments as main.py.

Lichess Bot

A bot you can play against on the website lichess.

The code for the bot is contained in /lichess_bot, and uses the repository from lichess-bot as a basis. Our bot implementation is defined in /lichess_bot/lib/strategies.py.

Start the bot by running the following in /lichess_bot:

python lichess-bot.py

The bot should then be up and running. For more information look at the GitHub from the lichess-bot.

Interactive Geogebra File

A Geogebra file Mean_max.gbb for exploring how to get the minimum and maximum of two gaussian distributions.

These two papers have been quite helpful for this part:

Exact Distribution of the Max/Min of Two Gaussian Random Variables by Saralees Nadarajah and Samuel Kotz
Speeding up Computation of the max/min of a set of Gaussians for Statistical Timing Analysis and Optimization by Kuruvilla et al.

Credits

Lukas Kuess, Stefan Steiniger, Theo Haslinger, Lukas Wieser