Chapter 3 Further Reading: Expected Value and the Bettor's Edge

The following resources deepen and extend the concepts covered in Chapter 3. They are organized by category and annotated with relevance notes to help you prioritize your reading based on your background and interests.

Gambling Mathematics and Probability

1. Epstein, Richard A. The Theory of Gambling and Statistical Logic. 2nd revised edition. Academic Press, 2009.

The definitive mathematical treatment of gambling from a probability theory perspective. Epstein covers expected value, variance, optimal strategy, and the mathematics of every major casino game and betting market. Chapters 3-5 on probability distributions and expected value are directly relevant to Chapter 3 of this textbook. The book is rigorous but accessible to readers with undergraduate-level mathematics. Essential reading for anyone who wants a deep understanding of why expected value governs all gambling outcomes.

Relevance: Core theory. Directly extends the EV and variance concepts from Chapter 3.

2. Haigh, John. Taking Chances: Winning with Probability. Oxford University Press, 2003.

An engaging, example-driven introduction to probability with extensive applications to gambling, sports, and everyday decision-making. Haigh excels at building intuition for expected value through concrete scenarios. The chapters on betting and odds are particularly well-written and include several worked examples that complement the calculations in Chapter 3. Recommended for readers who want to strengthen their probabilistic intuition without heavy formalism.

Relevance: Accessible companion. Builds intuition for EV and probability.

3. Packel, Edward W. The Mathematics of Games and Gambling. 2nd edition. Mathematical Association of America, 2006.

A concise, textbook-style introduction to the mathematics underlying games of chance and skill. Covers expected value, the gambler's ruin problem, Markov chains, and game theory. The treatment of the gambler's ruin problem is especially relevant to understanding why bankroll management is inseparable from expected value. Well-suited for self-study by readers with a solid high school or introductory college math background.

Relevance: Foundational math. Strong coverage of gambler's ruin and EV.

4. Bewersdorff, Jorg. Luck, Logic, and White Lies: The Mathematics of Games. A K Peters/CRC Press, 2004.

A comprehensive survey of the mathematics behind games of chance, combinatorial games, and strategic games. Bewersdorff provides clear derivations of expected value for a wide variety of betting scenarios and discusses the mathematical basis for the house edge. The chapter on sports betting markets is brief but insightful, connecting EV to real-world wagering. Suitable for readers who enjoy exploring mathematical concepts across a variety of game types.

Relevance: Broad mathematical context. Good for connecting EV to game theory.

Academic Papers on Betting Market Efficiency

5. Levitt, Steven D. "Why Are Gambling Markets Organised So Differently from Financial Markets?" The Economic Journal, vol. 114, no. 495, 2004, pp. 223-246.

A landmark paper examining the economics of sports betting markets. Levitt argues that sportsbooks do not simply balance their books but instead exploit systematic biases in bettor behavior, particularly the tendency to overbet favorites and popular teams. The paper's findings have direct implications for understanding how +EV opportunities arise from predictable bettor biases. Essential reading for anyone interested in market efficiency and the bettor's edge.

Relevance: Directly relevant. Explains how sportsbook pricing creates +EV opportunities for informed bettors.

6. Woodland, Linda M. and Bill M. Woodland. "Market Efficiency and the Favorite-Longshot Bias: The Baseball Betting Market." The Journal of Finance, vol. 49, no. 1, 1994, pp. 269-279.

One of the most-cited papers on the favorite-longshot bias, demonstrating that bettors systematically overvalue longshots and undervalue favorites in baseball moneyline markets. The paper tests market efficiency by examining whether simple betting strategies based on odds levels can generate positive expected value. A clear illustration of how academic research can identify exploitable inefficiencies in betting markets.

Relevance: Core academic reference on market inefficiency and EV.

7. Gandar, John, Richard Zuber, Thomas O'Brien, and Ben Russo. "Testing Rationality in the Point Spread Betting Market." The Journal of Finance, vol. 43, no. 4, 1988, pp. 995-1008.

An early and influential test of the efficient market hypothesis applied to NFL point spread betting. The authors examine whether closing spreads are unbiased predictors of game outcomes and whether simple strategies can generate +EV. Their finding that certain biases exist but are small enough to be consumed by the vig is a key lesson for bettors: the edge must exceed the vig to be profitable.

Relevance: Foundational market efficiency study. Illustrates the relationship between edge and vig.

8. Borghesi, Richard. "Price Biases in a Prediction Market: NFL Contracts on Tradesports." Applied Economics, vol. 41, no. 23, 2009, pp. 3025-3035.

Examines price biases in prediction markets for NFL games, finding evidence of both the favorite-longshot bias and other systematic mispricings. Borghesi's analysis bridges the gap between traditional sportsbook markets and prediction/exchange markets, providing insight into how expected value opportunities can differ across market structures.

Relevance: Market efficiency. Useful for understanding how different market structures affect EV.

9. Humphreys, Brad R., Paul, Rodney J., and Andrew P. Weinbach. "Consumption Benefits and Gambling: Evidence from the NCAA Basketball Betting Market." Journal of Economic Psychology, vol. 34, 2013, pp. 66-75.

This paper investigates the role of "consumption value" (entertainment utility) in betting behavior, showing that recreational bettors willingly accept -EV bets because they derive enjoyment from the act of betting. The findings help explain why inefficiencies persist in betting markets: not all participants are maximizing expected monetary value, which creates opportunities for those who are.

Relevance: Behavioral economics of betting. Explains why +EV opportunities persist.

10. Snowberg, Erik and Justin Wolfers. "Explaining the Favorite-Longshot Bias: Is It Risk-Love or Misperceptions?" Journal of Political Economy, vol. 118, no. 4, 2010, pp. 723-746.

A rigorous investigation of whether the favorite-longshot bias is driven by risk-seeking preferences or by systematic probability misperceptions. The authors use data from horse racing and sports betting to argue that misperception of small probabilities (overweighting longshots) is the primary driver. Critical reading for understanding the behavioral basis of market inefficiency and how it creates +EV edges.

Relevance: Behavioral bias. Explains the psychological mechanisms behind mispricing.

11. Shin, Hyun Song. "Prices of State Contingent Claims with Insider Traders, and the Favourite-Longshot Bias." The Economic Journal, vol. 102, no. 411, 1992, pp. 426-435.

A theoretical paper showing that the presence of insider traders (bettors with superior information) causes bookmakers to distort their odds in a way that produces the favorite-longshot bias. Shin's model provides a supply-side explanation for why sportsbooks price longshots with higher margins. Understanding this pricing structure is essential for bettors analyzing where the vig is highest and where +EV is most likely to be found.

Relevance: Theoretical foundation. Explains why vig varies across odds levels.

Expected Value and Decision Theory

12. Kelly, J. L. "A New Interpretation of Information Rate." Bell System Technical Journal, vol. 35, no. 4, 1956, pp. 917-934.

The original paper introducing what is now known as the Kelly Criterion. Kelly showed that a bettor (or information channel) maximizes the long-run geometric growth rate of capital by sizing bets proportionally to their edge divided by the odds. The Kelly Criterion is the optimal solution to the question "Given a +EV bet, how much should I wager?" and represents the natural extension of the EV framework covered in Chapter 3. The paper is technical but the core result is accessible.

Relevance: Essential. The Kelly Criterion is the bridge between Chapter 3 (EV) and Chapter 4 (bankroll management).

13. Poundstone, William. Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street. Hill and Wang, 2005.

A popular account of the Kelly Criterion's history, from Claude Shannon's information theory lab to Ed Thorp's blackjack exploits and the quantitative revolution on Wall Street. Poundstone makes the mathematical concepts highly accessible and tells a compelling narrative about how expected value and optimal bet sizing have been applied across gambling and finance. Excellent companion reading for Chapters 3 and 4.

Relevance: Highly readable. Connects EV theory to real-world application and history.

14. Thorp, Edward O. "The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market." In Handbook of Asset and Liability Management, edited by S.A. Zenios and W.T. Ziemba, North Holland, 2006.

A comprehensive survey by one of the pioneers of quantitative gambling. Thorp covers the derivation, application, and practical limitations of the Kelly Criterion across multiple domains. His discussion of fractional Kelly and the trade-off between growth rate and drawdown risk is particularly valuable. This paper connects the abstract EV calculations of Chapter 3 to concrete decision-making about bet sizing.

Relevance: Advanced practical application. Essential for the EV-to-bet-sizing pipeline.

Professional Gambler Memoirs and Accounts

15. Walters, Billy (with Armen Keteyian). Gambler: Secrets from a Life at Risk. Avid Reader Press, 2023.

The memoir of Billy Walters, widely considered the most successful sports bettor in American history. Walters reportedly won over $1 billion in sports wagers over four decades. His account provides rare insight into how a professional bettor identifies +EV opportunities at scale, manages enormous variance, navigates sportsbook restrictions, and maintains discipline through inevitable downswings. While not a technical manual, the book vividly illustrates the practical reality of living by expected value.

Relevance: Real-world perspective. Shows how EV principles operate at the highest level of professional betting.

16. Konik, Michael. The Smart Money: How the World's Best Sports Bettors Beat the Bookies Out of Millions. Simon and Schuster, 2006.

An insider account of the world of professional sports betting, following several high-stakes bettors and syndicates. Konik describes the operational details of professional betting: line shopping, closing line value, steam moves, and the constant search for +EV. The book provides context for understanding why the concepts in Chapter 3 matter in practice and how professionals systematically apply them.

Relevance: Practical context. Illustrates professional application of EV concepts.

17. Manteris, Art (with Rick Talley). SuperBookie: Inside Las Vegas Sports Gambling. Contemporary Books, 1991.

A sportsbook manager's perspective on the business of sports betting. Manteris explains how lines are set, how the vig is managed, and how the sportsbook uses the Law of Large Numbers to ensure profitability. Reading the game from the sportsbook's side provides valuable insight into why the default EV environment is negative for bettors and how the house protects its edge.

Relevance: Sportsbook perspective. Understanding the house's EV advantage.

Applied Statistics and Quantitative Methods

18. Silver, Nate. The Signal and the Noise: Why So Many Predictions Fail -- but Some Don't. Penguin Press, 2012.

While not exclusively about sports betting, Silver's book is one of the best introductions to probabilistic thinking and prediction. Several chapters address sports forecasting directly, including the challenges of calibrating probability estimates, the difference between noise and signal in data, and the role of Bayesian updating. The core message -- that better probability estimates lead to better expected value -- is the foundation of the bettor's edge discussed in Chapter 3.

Relevance: Probabilistic thinking. Essential context for building the probability estimates that drive EV calculations.

How to Use This Reading List