AlphaPawnwars

Fitting the AlphaZero model with some tweaks to the chess variant game Pawn Wars.

Overview

AlphaPawnwars is an implementation of the AlphaZero algorithm tailored to the Pawn Wars variant of chess. The project explores various techniques to improve the model's performance, including incentivized self-play and competitive games against Stockfish.

Goal of Pawn Wars

The primary objective in Pawn Wars is to advance one of your pawns to the other side of the board. This variant emphasizes pawn strategy and positioning over traditional chess tactics.

Results

First Decent Results

• White's Strategy: Induced to play more king moves (2000 games).
• Black's Strategy: Pure self-play (2000 games).

Second Decent Results

• Extended Training: Built upon the initial White model with an additional 8000 self-play games, resulting in a total of 10000 games.
• Emergent Strategy: The model employs the "Fox in the Chicken Coop" strategy.

Technical Details

State Representation

The state of the game is represented using a 3D array with the dimensions (10, 8, 8). Each plane in the array captures specific information about the board configuration and potential moves.

• Dimensions: The state is encoded into a 3D array of size (10, 8, 8).
  • The first dimension (10) represents different channels or planes.
  • The second and third dimensions (8, 8) represent the chessboard with 8 rows and 8 columns.

Planes Description

1. White Pawns: Plane 0
   • Represents the positions of white pawns on the board.
2. White Kings: Plane 1
   • Represents the positions of white kings on the board.
3. Black Pawns: Plane 2
   • Represents the positions of black pawns on the board.
4. Black Kings: Plane 3
   • Represents the positions of black kings on the board.
5. White King Moves and Captures: Plane 4
   • Indicates squares to which the white king can move or capture.
6. Black King Moves and Captures: Plane 5
   • Indicates squares to which the black king can move or capture.
7. White Potential Captures: Plane 6
   • Marks columns where white pieces can potentially capture.
8. Black Potential Captures: Plane 7
   • Marks columns where black pieces can potentially capture.
9. Passed Pawns (White): Plane 8
   • Indicates columns with passed white pawns.
10. Passed Pawns (Black): Plane 9

• Indicates columns with passed black pawns.

Move Probability Changes

The move probability adjustment is designed to incentivize certain strategic behaviors based on the state of the game. Here are the key aspects of these adjustments:

King Movement

• Direction-Based Multiplier:

  • Forward Movement: Highest priority with a multiplier of 5.
  • Sideways Movement: Medium priority with a multiplier of 3.
  • Backward Movement: Lowest priority with a multiplier of 2.

• Player Perspective:

  • The multipliers are adjusted based on whether the player is White or Black to account for the different perspectives.

Number of Pawns

The number of pawns on the board further influences the multipliers:

• Fewer or Equal to 4 Pawns: Multiplier is reduced to 0.25.
• Between 5 to 6 Pawns: Multiplier is reduced to 0.5.
• Between 7 to 8 Pawns: Multiplier is reduced to 0.66.

Example Adjustments

Here is an example of how the move probabilities are adjusted:

• If the White King moves forward and there are 3 pawns:

  • Base multiplier: 5
  • Adjustment for pawns: 0.25
  • Final multiplier: 5 * 0.25 = 1.25

• If the Black King moves sideways and there are 6 pawns:

  • Base multiplier: 3
  • Adjustment for pawns: 0.5
  • Final multiplier: 3 * 0.5 = 1.5

Conclusion

AlphaPawnwars demonstrates the potential of tailored modifications to the AlphaZero algorithm for specific chess variants. By adjusting state representation and move probabilities, the model can develop unique strategies and improve its performance in Pawn Wars.

Feel free to explore the code and experiment with further adjustments to enhance the model's capabilities!