Analyzing Winning Chances in the Candidates Tournament: A Deep Dive into ELO Calculations and Game Simulations
The recent episode of the Perpetual Chess podcast sparked a discussion on the winning chances for the Candidates Tournament, as calculated by Chess By the Numbers. The calculations were based on Monte Carlo simulations of the full tournament, using the players’ live ELO ratings at the start of the event.
Chess By the Numbers mentioned running 5000 simulations for the tournament, but some critics felt that this number was insufficient to reduce statistical noise. Intrigued by this, one individual decided to write their own code to perform a similar calculation.
The ELO formula predicts the expected number of points each player will earn in a game, with the total points typically summing up to 1. This includes points for a win (1 point) or a draw (0.5 points). However, a separate model is needed to determine draw probabilities, as more than 50% of games at the highest levels of chess end in draws.
One approach to calculating draw probabilities involves considering the difference in ELO ratings between players and the sum of their ELO ratings. Another factor to consider is the advantage of playing as white, which is estimated to be approximately 35 points in ELO rating due to the first-move advantage.
Two formulas for ELO-based win probability were discussed – a normal formula and an exponential formula. The exponential formula was favored for its simplicity in dealing with ELO differences and its consideration of extraordinary events that may occur during a game.
To further explore these calculations, the individual wrote Python code to simulate chess games based on player ELO ratings. The code factored in ELO advantages for white players, draw odds, and calculated win probabilities for each player.
Overall, the discussion on ELO-based win probabilities and the simulation code provided a deeper insight into the complexities of predicting outcomes in chess tournaments. The exploration of different models and formulas shed light on the nuances of chess strategy and probability.