Elocator: Chess Complexity Calculator

Enter the FEN youd like to analyze below.

What is this? How does it work?

Elocator is a tool that calculates the complexity of a given chess position. It does this by analyzing the position and assigning a score from 1 to 10, with 1 being the least complex and 10 being the most complex.

How can we define the complexity of a chess position? There are many ways to do this, but I have chosen to define complexity as the expected change in Win % after a move is made. Imagine a position where white has a +1 advantage from Stockfish. That implies a 59% win rate for white. Assuming Stockfish is perfect, a human can only play a move that is as good or worse than Stockfish (i.e., a move that does not increase the win rate for white). We know that after the next move is played, white will have a 59% or lower chance of winning.

Depending on the position a grandmaster may find the best move, or maybe it is a really difficult position to find the best move. Over a large enough dataset, we can make correlations between the state of the board, and how much we expect the win % to go down after a move is made. As an example, over 20,000 moves, my data shows that a GM is expected to lose 1.4% win rate after a move is made in a position with a queen on the board, compared to 1.3% if there is no queen. So positions are about 7% more complex when there is a queen (1.4/1.3).

I created a dataset of FENs mapped to the loss in Win % from a GM that made a move in that position (classical OTB games only). Underlying this tool is a neural network (AI, deep learning, yada yada) that has been trained on 100,000 chess moves made by grandmasters. The model has learned to predict the complexity of a position by learning the expected change in Win % after a move is made, as measured by Stockfish 16 at depth 20.

The model is then used to predict the complexity of a given position. The model is not perfect, but it is a good starting point for understanding the complexity of a position. I look forward to making it better over time. Soon, I will publish some analytics around model performance.

Some example FENs:

Low Complexity: r1bqkbnr/pppp1ppp/2n5/4p3/2B1P3/5N2/PPPP1PPP/RNBQK2R b KQkq - 3 3

Medium Complexity: 4rk2/ppp1qppp/3p2R1/8/4P3/2Q1R2P/PPP2PP1/6K1 b - - 0 1

High Complexity: 2kr3r/ppqb4/3p1b1p/2pPnpp1/NPP1p1nP/6PB/PB2PPN1/2RQ1RK1 w - - 0 1

In the immediate future, I have a few goals:

1. Make the complexity model much better (incorporate a larger training dataset, a better NN structure, e.g. HalfKA)

2. Find a mechanism to turn the complexity score into game evaluations

3. Find a mechanism to turn a series of games into a tournament score.

4. Find a mechanism to identify outliers beyond some percentile (e.g., to identify cheating).

Longer term, I view this as an opportunity for the chess community to develop open source cheating detection, among other things.

You can learn more about the model and the dataset by visiting the Elocator GitHub repository.