Chapter 25 Further Reading: Optimization Methods for Betting
The following annotated bibliography provides resources for deeper exploration of the optimization topics introduced in Chapter 25. Entries are organized by category and chosen for their relevance to sports betting applications.
Books: Optimization Foundations
1. Boyd, Stephen and Vandenberghe, Lieven. Convex Optimization. Cambridge University Press, 2004. The definitive textbook on convex optimization, freely available online. Chapters 4 (Linear Programming) and 7 (Quadratic Programming) provide the mathematical foundation for the LP and mean-variance methods in Sections 25.1 and 25.2. The treatment of duality and sensitivity analysis is especially relevant for understanding shadow prices in betting allocation. Highly recommended for readers who want a rigorous understanding of why the solvers work.
2. Luenberger, David G. and Ye, Yinyu. Linear and Nonlinear Programming. Springer, 2016 (4th edition). A classic graduate-level text on mathematical programming. The chapters on the simplex method, duality theory, and sensitivity analysis provide deeper coverage of the LP concepts from Section 25.1. The nonlinear programming chapters are relevant to the constrained Kelly formulation in Section 25.4, particularly the KKT conditions and sequential quadratic programming.
3. Cornuejols, Gerard and Tutuncu, Reha. Optimization Methods in Finance. Cambridge University Press, 2007 (2nd edition). Bridges the gap between optimization theory and financial applications, including portfolio optimization, risk management, and asset allocation. While focused on finance rather than betting, the mathematical formulations translate directly. Chapters on mean-variance optimization and the efficient frontier are the most relevant.
Books: Portfolio Theory
4. Markowitz, Harry M. Portfolio Selection: Efficient Diversification of Investments. Yale University Press, 1959 (reprinted by Wiley, 1991). The original monograph establishing modern portfolio theory. Markowitz's insight that correlations between assets determine portfolio risk, not just individual asset risks, is the foundation of Section 25.2. While the financial context differs from betting, the mathematical framework transfers directly. Essential historical reading for understanding the intellectual origins of portfolio optimization.
5. Elton, Edwin J., Gruber, Martin J., Brown, Stephen J., and Goetzmann, William N. Modern Portfolio Theory and Investment Analysis. Wiley, 2014 (9th edition). A comprehensive textbook covering portfolio theory from Markowitz through modern extensions. The chapters on the efficient frontier, the Capital Asset Pricing Model, and multi-factor models provide context for adapting portfolio theory to betting. The practical discussions of estimation error and robust portfolio construction are directly applicable to the challenges of betting portfolio optimization.
Books: Kelly Criterion and Bet Sizing
6. Poundstone, William. Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street. Hill and Wang, 2005. An accessible narrative history of the Kelly criterion, from Claude Shannon and John Kelly at Bell Labs through its application in blackjack, horse racing, and financial markets. While not mathematically rigorous, it provides essential context for understanding why Kelly optimization matters and how it has been applied in practice. The discussions of Kelly's limitations and practical modifications are directly relevant to Section 25.4.
7. MacLean, Leonard C., Thorp, Edward O., and Ziemba, William T., eds. The Kelly Capital Growth Investment Criterion: Theory and Practice. World Scientific, 2011. The definitive collection of papers on the Kelly criterion, including Kelly's original 1956 paper, Thorp's extensions to blackjack and financial markets, and modern treatments of multi-asset Kelly. Part IV on "Extensions of the Kelly Criterion" contains papers on constrained Kelly optimization that directly inform Section 25.4. Essential reading for anyone implementing Kelly-based bet sizing.
8. Thorp, Edward O. A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market. Random House, 2017. Thorp's autobiography provides practical insights into applying Kelly criterion in real betting and investing contexts. His discussions of fractional Kelly, bankroll management, and the gap between theoretical optimality and practical execution are directly relevant to the constraints and modifications discussed in Section 25.4.
Academic Papers
9. Kelly, John L. Jr. "A New Interpretation of Information Rate." Bell System Technical Journal, 35(4), 1956, pp. 917-926. The foundational paper establishing the Kelly criterion. Kelly showed that maximizing the expected logarithm of wealth is equivalent to maximizing the long-run growth rate. The paper's information-theoretic framework provides the mathematical justification for log-growth optimization used in Section 25.4. Short, elegant, and still the primary theoretical reference for Kelly-based bet sizing.
10. Markowitz, Harry M. "Portfolio Selection." The Journal of Finance, 7(1), 1952, pp. 77-91. The seminal paper introducing mean-variance portfolio optimization. Markowitz formalized the trade-off between expected return and risk (variance) and introduced the concept of the efficient frontier. This 12-page paper launched modern portfolio theory and remains the intellectual foundation for Section 25.2. Required reading for any quantitative bettor.
11. Grant, Andrew, Johnstone, David, and Kwon, Oh Kang. "Optimal Betting Strategies for Simultaneous Games." Decision Analysis, 5(1), 2008, pp. 10-18. One of the few academic papers that directly addresses the multi-bet Kelly criterion for sports betting. The authors derive the optimal allocation for simultaneous bets with binary outcomes and discuss the computational challenges of exact optimization as the number of bets increases. The paper's numerical examples directly complement the implementation in Section 25.4.
12. Busseti, Enzo, Ryu, Ernest K., and Boyd, Stephen. "Risk-Constrained Kelly Gambling." Journal of Investing, 25(3), 2016, pp. 118-134. Extends the Kelly criterion with explicit risk constraints, including maximum drawdown, Value at Risk, and Conditional Value at Risk constraints. The authors formulate risk-constrained Kelly as a convex optimization problem that can be solved efficiently with cvxpy. This paper provides the theoretical foundation for the constrained Kelly implementation in Section 25.4.
13. Hausch, Donald B. and Ziemba, William T. "Efficiency of the Market for Racetrack Betting." Management Science, 27(12), 1981, pp. 1435-1452. A classic paper applying optimization methods to horse racing betting markets. Demonstrates that systematic biases in racetrack odds can be exploited with an optimization-based staking strategy. The paper's Dr. Z system, which uses Kelly-based optimization with constraints, was one of the first practical applications of mathematical optimization to sports betting.
14. Miettinen, Kaisa. "Nonlinear Multiobjective Optimization." Springer, 1999. The standard reference on multi-objective optimization methods, including the weighted-sum method, epsilon-constraint method, and evolutionary approaches. While mathematically oriented, the methods described are directly applicable to the multi-objective betting optimization in Section 25.5. The chapter on the Pareto frontier and solution characterization is especially relevant.
Applied Tutorials and Resources
15. cvxpy Documentation (cvxpy.org). The official documentation for cvxpy, the Python library used for convex optimization throughout Chapter 25. Includes tutorials on linear programming, quadratic programming, and portfolio optimization that directly correspond to the implementations in Sections 25.1 and 25.2. The "Examples" section contains portfolio optimization implementations that complement the textbook code.
16. PuLP Documentation (coin-or.github.io/pulp/). Documentation for the PuLP Python library used for linear programming in Section 25.1. PuLP provides a high-level interface to LP solvers and is the recommended tool for pure LP problems. The tutorials on LP formulation and sensitivity analysis are directly relevant.
17. Pinnacle Sports. "Pinnacle Betting Resources." Pinnacle's educational content includes articles on arbitrage detection, Kelly criterion application, and betting market efficiency. As a sportsbook known for sharp lines and high limits, Pinnacle's perspective on these topics provides practical context for the optimization methods in Chapter 25. Their articles on why they welcome arbitrage bettors offer insight into market microstructure.
Software and Tools
18. scipy.optimize Documentation (docs.scipy.org/doc/scipy/reference/optimize.html).
Documentation for SciPy's optimization module, which provides the minimize function used for constrained Kelly optimization in Section 25.4. The SLSQP solver (Sequential Least Squares Programming) is the default choice for constrained nonlinear optimization with bound and inequality constraints. Understanding the solver options and convergence criteria is essential for reliable optimization.
19. OddsJam / OddsShopper / RebelBetting. Commercial arbitrage detection and odds comparison tools that implement many of the concepts from Section 25.3. While the textbook provides the algorithmic foundation, these tools offer real-time odds data, automated scanning, and execution support. Evaluating these tools against the textbook's framework provides practical context for the arbitrage detection system.
Data Sources
20. The Odds API (the-odds-api.com). A data service providing real-time and historical odds from multiple sportsbooks via a REST API. This data source enables practical implementation of the arbitrage detection system from Section 25.3 and the portfolio optimization framework from Section 25.2. The free tier provides sufficient data for learning and experimentation; the paid tiers support production-level scanning.
How to Use This Reading List
For readers working through this textbook sequentially, the following prioritization is suggested:
- Start with: Boyd and Vandenberghe (entry 1) for the optimization theory, or Poundstone (entry 6) for accessible narrative context on Kelly criterion.
- Go deeper on portfolio theory: Markowitz (entry 4) and Elton et al. (entry 5) for the financial portfolio framework that Section 25.2 adapts.
- For Kelly expertise: MacLean, Thorp, and Ziemba (entry 7) is the definitive collection, and Busseti, Ryu, and Boyd (entry 12) provide the modern constrained formulation.
- For implementation: cvxpy docs (entry 15) and scipy.optimize docs (entry 18) for hands-on coding guidance.
- For practical deployment: The Odds API (entry 20) and the commercial tools (entry 19) to connect textbook methods to real-world data.
- For mathematical rigor: Luenberger and Ye (entry 2) and Miettinen (entry 14) for the complete optimization theory.
These resources will be referenced again in later chapters as optimization methods are combined with practical implementation (Chapter 26) and long-term strategy design (Part VIII).