Revisiting the Algorithm That Changed Horse Race Betting

Summary

The remarkable story of Bill Benter and how he amassed a staggering $1B fortune betting on horses in Hong Kong has been extensively documented in the article, The Gambler Who Cracked the Horse-Racing Code. In 1994, Benter published an academic paper titled Computer Based Horse Race Handicapping and Wagering Systems: A Report. In it, he documents the implementation of a successful horse race betting model, which by virtue of it being published, likely meant that the model was outdated and superceded by more sophisticated models. Despite this, the paper remains an insightful read, offering a rare glimpse into the lucrative application of mathematics to an unconventional field, made even more interesting by the substantial hardware and software limitations of the time. In this post, we present an annotated version of the paper with added code blocks and blockquoted comments. The main text is all from the paper itself. Instead of building the fundamental and combined models, we’ll be highlighting interesting aspects of the paper using the public estimate, derived from the Hong Kong Jockey Club’s historical win odds. We’ll look at how the model calibration tables were generated in the original paper, assess how the public estimate has improved through the years and try our hand at fitting the adjustments factors from scratch using PyTorch. While the original paper uses data samples between 1986–1993, we’ll also be using data from the subsequent three decades (1996–2003, 2006–2013 and 2016–2023) for comparison. import pandas as pd DATA_FILE = "../data/HKJC/df_hkjc.csv" DATE_RANGES = [ ("1986-08-01", "1993-08-01"), ("1996-08-01", "2003-08-01"), ("2006-08-01", "2013-08-01"), ("2016-08-01", "2023-08-01"), ] pd.read_csv(DATA_FILE, index_col=[0, 1, 2, 3]) Table A: Historical Win Odds from Hong Kong Jockey Club date venue number horse_name place win_odds 1979-09-22 Happy Valley 1 Victorious II 1 3.4 1979-09-22 Happy Valley 1 Money First 2 16.0 1979-09-22 Happy Valley 1 Star Tro...