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The Negamax algorithm is a simplified implementation of Minimax that takes into account the zero-sum nature of Chess: however good a move is for you, that's how bad it is for your opponent and vice versa.
The bot traverses a tree, whose nodes are board-states and whose edges are moves. The value of a player's move to that player is equivalent to how 'bad' the resulting state of the board is for their opponent. Leaf nodes are evaluated by considering material advantage, and to a lesser extent development, doubled pawns and castling. These evaluations are then propagated to each non-leaf node by negating the highest of its children's evaluations. The logic behind this is that the players will choose the best move for them, which will be negated for the opposition. Eventually, a value is propagated to the root node and then the bot can select the most valuable child. However, the depth of the tree remains to be chosen i.e. how many nodes do we look ahead before first evaluating the goodness of a move? Choosing a single value is risky, as it may take far too long for high depth or be highly inaccurate for low depth. To avoid any risk, we start at a conservative depth of 2 and increase the depth by 1 until we run out of time (the bot has a 5-second time limit). The time required is exponential in the depth, so not much time is wasted in this incremental search.
In the above image, the bot has reached a depth of 7 within the time-limit, deciding to promote to a Knight and force the King back, instead of promoting to a Queen which is then traded with the Rook.
One issue with the above method is that the evaluation function might miss something that is about to happen. For example if we just promoted to a Queen, the resulting state might look very strong, but if the Queen is instantly captured on the next move, this would not be the case. The issue is that we evaluated an unstable node, one where the evaluation is likely to change on subsequent moves. The solution is quiescence search, where instead of evaluating leaf nodes, we perform an additional search of all potential captures or promotions, to ensure we only evaluate 'quiet' nodes, where the evaluation function is accurate.
Naive Negamax is very costly: it's exponential in the search depth with a high branching factor of ~35, producing approximately 2 billion leaf-nodes when looking 6 moves ahead. Alpha beta pruning reduces the search space by ignoring branches that can't affect the final result. One case in which this can happen is if we have found checkmate at some node, in which case we can ignore all sibling nodes (and therefore their subtrees) as these must be worse.
A second optimisation uses the fact that most board states can be reached through several sequences of moves, for example by playing the same moves in a different order. Transposition tables use memoization to avoid re-evaluating all such boards, further reducing the total number of evaluations. This method is particularly effective in the endgame, where the branching factor is small due to mostly pawns being present.
The program allows for several game modes, based on which side(s) are automated. Additionally, I've added a training mode which lets you take moves back, evaluate potential moves and sub the bot in to make moves for you. This mode also prints out the expected sequence of moves predicted by the Negamax traversal:
This project uses the LibGDX game engine to render and process user input. This allows the program to be packaged in several ways.
The most convenient of these is via my Github Pages. Unfortunately, this page run much slower for me than running locally, meaning the search depth is lower and the bot is not very good. You can instead run the program via the .jar file, with:
java -jar ChessBot.jar
or on Mac:
java -jar -XstartOnFirstThread ChessBot.jar
If you don't have Java, you can find self-contained executables on my
Google Drive,
which were packaged using packr.
Just download the relevant folder and run either the .app on Mac or
the .exe on Windows. You may need to change your permissions on Mac with
chmod +x ChessBot.app/Contents/MacOS/ChessBot
If you wish to play around with the source code you can just clone this repo and open it in Intellij.
Gradle will automatically prepare dependencies, and you can then compile and run the
program through the main method in desktop/src/com.chessbot/DesktopLauncher.java. If
you're on a Mac you will need to modify the run configuration to include the flag
-XstartOnFirstThread under VM options.