Chapter 14 Further Reading: Advanced Bankroll and Staking Strategies

The following annotated bibliography provides resources for deeper exploration of the topics introduced in Chapter 14. Entries are organized by category and chosen for their relevance to the Kelly criterion, portfolio theory for betting, drawdown management, and multi-account bankroll strategies.

Books: Kelly Criterion and Growth-Optimal Strategies

1. 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. The autobiography of the mathematician who first applied the Kelly criterion to blackjack and later to financial markets. Thorp provides firsthand accounts of how Kelly-optimal strategies perform in practice, including the psychological challenges of sustaining them during drawdowns. Essential context for understanding why the Kelly criterion matters and how it was validated through decades of real-world application.

2. 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 highly readable narrative history of the Kelly criterion, covering its development by John Kelly at Bell Labs, its application by Edward Thorp in blackjack and financial markets, and the philosophical debate between Kelly proponents and Paul Samuelson's utility-theoretic critics. This book makes the mathematical foundations of Chapter 14 accessible to a general audience.

3. MacLean, Leonard C., Edward O. Thorp, and William T. Ziemba, eds. The Kelly Capital Growth Investment Criterion: Theory and Practice. World Scientific, 2011. The definitive academic collection on the Kelly criterion. Contains the original Kelly paper (1956), Thorp's extensions, and dozens of subsequent papers on geometric growth rate maximization, fractional Kelly strategies, and applications to finance and gambling. This is the primary reference for the mathematical derivations in Section 14.1.

4. Ziemba, William T., and Donald B. Hausch. Betting at the Racetrack. Dr. Z Investments, 1985. Although focused on horse racing, this book provides some of the earliest practical applications of the Kelly criterion and portfolio theory to betting markets. The treatment of simultaneous bets, correlated outcomes, and bankroll sizing directly informs the portfolio approach developed in Section 14.2.

Books: Portfolio Theory and Risk Management

5. Markowitz, Harry M. Portfolio Selection: Efficient Diversification of Investments. John Wiley & Sons, 1959. The foundational text on modern portfolio theory. While written for financial markets, Markowitz's framework for mean-variance optimization, diversification, and the efficient frontier transfers directly to betting portfolios. Understanding this book provides the theoretical underpinning for Section 14.2's adaptation of MPT to sports betting.

6. Bernstein, Peter L. Against the Gods: The Remarkable Story of Risk. John Wiley & Sons, 1996. A sweeping history of how humans have learned to understand, measure, and manage risk. Chapters on probability theory, decision under uncertainty, and portfolio theory provide essential context for the risk management frameworks in Chapter 14. Particularly relevant for understanding why logarithmic utility (the basis of Kelly) is a natural choice for sequential decision-making.

7. Taleb, Nassim Nicholas. Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets. Random House, 2004. Taleb's exploration of how humans systematically misinterpret randomness is directly relevant to the drawdown management framework in Section 14.4. His discussion of survivorship bias, the ludic fallacy, and the difference between being "lucky" and being "skilled" should inform every bettor's approach to interpreting their own results.

Academic Papers: Kelly Criterion Extensions

8. Kelly, John L., Jr. "A New Interpretation of Information Rate." Bell System Technical Journal, 35(4), 1956, pp. 917-926. The original paper that introduced the Kelly criterion. Kelly derived the optimal bet fraction as a consequence of information theory, connecting the growth rate of a gambler's capital to the channel capacity of a communication system. While the paper is technically dense, reading it provides insight into the deep mathematical structure underlying the "simple" Kelly formula.

9. Thorp, Edward O. "The Kelly Criterion in Blackjack Sports Betting, and the Stock Market." Handbook of Asset and Liability Management, 2006. Thorp's comprehensive review of Kelly applications across gambling and finance. Covers the multi-asset Kelly criterion, fractional Kelly, and practical considerations including estimation error and transaction costs. This paper directly informs the fractional Kelly analysis in Section 14.1 and the portfolio extensions in Section 14.2.

10. Breiman, Leo. "Optimal Gambling Systems for Favorable Games." Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1961, pp. 65-78. A rigorous mathematical proof that the Kelly strategy maximizes the asymptotic growth rate of capital almost surely. Breiman's result is the formal justification for the claim that Kelly is "asymptotically optimal," which is stated informally in Section 14.1.

11. Cover, Thomas M., and Joy A. Thomas. "Elements of Information Theory." Chapter 6: "Gambling and Data Compression." Wiley, 2006. The relationship between Kelly gambling, entropy, and data compression is one of the most beautiful results in information theory. This chapter formalizes the connection between the growth rate of a Kelly bettor and the Shannon entropy of the underlying probability distribution.

Academic Papers: Drawdown Analysis

12. Grossman, Sanford J., and Zhongquan Zhou. "Optimal Investment Strategies for Controlling Drawdowns." Mathematical Finance, 3(3), 1993, pp. 241-276. A rigorous treatment of portfolio strategies that limit maximum drawdown. The authors derive optimal policies under drawdown constraints that are directly applicable to the bankroll management problem. Their key insight -- that drawdown constraints are equivalent to proportional portfolio insurance -- informs the drawdown policy framework in Section 14.4.

13. Magdon-Ismail, Malik, and Amir F. Atiya. "Maximum Drawdown." Risk Magazine, October 2004. Derives analytical approximations for the expected maximum drawdown of a random walk with drift, which is the model underlying the drawdown analysis in Section 14.4. The paper provides the formula used to approximate $E[D_{\max}]$ and validates it against Monte Carlo simulations.

14. Chekhlov, Alexei, Stanislav Uryasev, and Michael Zabarankin. "Drawdown Measure in Portfolio Optimization." International Journal of Theoretical and Applied Finance, 8(1), 2005, pp. 13-58. Develops portfolio optimization frameworks that use drawdown as the risk measure instead of variance. This approach is more natural for bankroll management than traditional mean-variance optimization because bettors care more about drawdown severity than return volatility per se.

Practical Resources: Bankroll Management

15. Miller, Ed, and Matthew Davidow. The Logic of Sports Betting. Ed Miller, 2019. A practitioner-oriented book that covers bankroll management, staking strategies, and the business of sports betting from the bettor's perspective. The chapters on account management, line shopping economics, and the practical challenges of multi-book betting complement the theoretical frameworks in Chapter 14.

16. Buchdahl, Joseph. Squares and Sharps, Suckers and Sharks. Oldcastle Books, 2016. Includes extensive discussion of staking strategies, comparing flat staking, proportional staking, and Kelly-based approaches using historical sports betting data. Buchdahl's empirical analysis confirms the theoretical advantages of proportional staking discussed in Chapter 14.

17. Pinnacle Sports Blog: "Staking Methods" Series (pinnacle.com/betting-resources) Pinnacle's multi-part series on staking methods provides accessible explanations of flat betting, percentage betting, Kelly criterion, and their variants. Written for a practitioner audience, it bridges the gap between the mathematical theory in Chapter 14 and real-world implementation.

Online Resources and Tools

18. Wizard of Odds: Kelly Criterion Calculator (wizardofodds.com) Michael Shackleford's online Kelly calculator handles various odds formats and provides instant Kelly fraction calculations. A useful quick-reference tool for the formulas derived in Section 14.1.

19. Unabated (unabated.com): Bankroll Management Tools Professional-grade bankroll tracking, bet sizing calculators, and portfolio analysis tools. Their Kelly calculator handles simultaneous bets and provides drawdown projections consistent with the methods discussed in Chapter 14.

20. Haghani, Victor, and Richard Dewey. "Rational Decision-Making Under Uncertainty: Observed Betting Behavior on the Outcome of Random Events." Working paper, 2016. A remarkable experiment where finance professionals were given a coin biased 60-40 in their favor and $25 to bet with. Despite the clear positive edge, most participants made serious bankroll management errors (over-betting, under-betting, inconsistent sizing). This paper provides vivid empirical evidence for why the staking discipline taught in Chapter 14 is so important -- even smart people with known edges frequently mismanage their bankrolls.

How to Use This Reading List

For readers working through this textbook sequentially, the following prioritization is suggested:

Start with: Poundstone (entry 2) for accessible history, and Thorp (entry 9) for practical Kelly applications.
Go deeper on Kelly theory: MacLean et al. (entry 3) and Cover and Thomas (entry 11) for the mathematical foundations.
Go deeper on portfolio theory: Markowitz (entry 5) and the adaptation to betting in Ziemba and Hausch (entry 4).
Go deeper on drawdowns: Magdon-Ismail and Atiya (entry 13) for analytical formulas, and Grossman and Zhou (entry 12) for optimal drawdown-constrained strategies.
For practical implementation: Miller and Davidow (entry 15) and the Pinnacle blog (entry 17) for translating theory into practice.

These resources will be referenced again in Part IV as we apply the bankroll management framework to sport-specific models in Chapters 15-18.