Further Reading: Chapter 10 — Expected Value

Essential Reading

1. Thinking in Bets: Making Smarter Decisions When You Don't Have All the Facts Annie Duke (Portfolio/Penguin, 2018)

Annie Duke spent years as a professional poker player and World Series of Poker champion before becoming a decision-science consultant and educator. This book is the most accessible introduction to EV-based decision-making available. Duke's central argument — that good decisions are about process quality, not outcome quality — maps directly to the poker framework Dr. Yuki introduces in this chapter. Her treatment of "resulting" (evaluating decisions by their outcomes, which maps to what this chapter calls outcome bias) is particularly sharp. Highly recommended for all readers; it reads like a conversation, not a textbook.

Best chapters for this topic: "Resulting" (Ch. 1–2), "Poker Thinking" (Ch. 3), "Wanna Bet?" (Ch. 4)

2. Against the Gods: The Remarkable Story of Risk Peter L. Bernstein (Wiley, 1996)

The definitive popular history of how human beings learned to think about probability, risk, and expected value — from ancient dice games through the development of modern finance. Bernstein covers Bernoulli's utility theory (relevant to the St. Petersburg paradox), the development of actuarial science (the foundation of insurance pricing), and the long intellectual journey from "luck is divine will" to "luck is a calculable distribution." Beautifully written and genuinely thrilling as intellectual history. Accessible to strong high school readers; essential for college students interested in the history of ideas.

Best chapters for this topic: "The Remarkable Bernoullis" (Ch. 6), "The Search for Moral Certainty" (Ch. 7)

3. The Kelly Capital Growth Investment Criterion Edited by Leonard MacLean, Edward Thorp, and William Ziemba (World Scientific, 2011)

This is the technical reference — a collection of academic papers on Kelly Criterion theory and application. The opening papers, including Kelly's original 1956 Bell System Technical Journal article ("A New Interpretation of Information Rate"), are freely available online and are worth reading even if you skip the rest of the volume. Kelly's original argument is surprisingly readable for a mathematical paper and reveals the elegant connection between information theory (Shannon's entropy) and optimal bet sizing. For advanced readers interested in the mathematical foundations.

Kelly's original paper is available: via Google Scholar or the Bell Labs technical archives. Search "Kelly 1956 New Interpretation Information Rate."

4. Misbehaving: The Making of Behavioral Economics Richard Thaler (W.W. Norton, 2015)

Thaler won the Nobel Prize in Economics in 2017 for his work integrating psychology into economic theory — much of which involves showing how real humans systematically deviate from the rational EV maximization that classical economics assumes. His work on mental accounting, sunk cost fallacy, and "nudge" theory is directly relevant to understanding why people make insurance decisions that seem irrational (but aren't) and investment decisions that seem rational (but aren't). More accessible and entertaining than most economics texts.

Best chapters for this topic: "Mental Accounting Matters" (Ch. 3–4), "Buckets and Budgets" (Ch. 6)

5. Judgment Under Uncertainty: Heuristics and Biases Edited by Daniel Kahneman, Paul Slovic, and Amos Tversky (Cambridge University Press, 1982)

The foundational academic text for behavioral decision theory. This edited volume collects the landmark papers from Kahneman and Tversky's research program, including the original prospect theory paper (Kahneman and Tversky, 1979) that explains why utility is not linear in outcomes — the mathematical basis for why insurance is rationally purchased. Also includes papers on probability calibration, overconfidence, and the availability heuristic. Dense but rewarding. Individual papers are available through Google Scholar for readers who want primary sources without committing to the whole volume.

Most relevant papers: Kahneman and Tversky (1979) "Prospect Theory: An Analysis of Decision Under Risk," Tversky and Kahneman (1974) "Judgment Under Uncertainty: Heuristics and Biases."

6. The Drunkard's Walk: How Randomness Rules Our Lives Leonard Mlodinow (Pantheon, 2008)

A physicist's tour through probability and randomness, with excellent chapters on expected value and why our intuitions fail. Mlodinow's treatment of how randomness creates the illusion of skill in short-run outcomes is particularly relevant to the outcome bias problem. His coverage of the St. Petersburg paradox and Bernoulli's utility theory is clear and non-technical. Good complement to Bernstein's Against the Gods — shorter, more focused on randomness, and very readable.

Best chapters for this topic: "The Drunkard's Walk" (Ch. 1), "The Laws of Large Numbers" (Ch. 5), "Muddling Through" (Ch. 9)

7. "Pascal's Mugging" — Nick Bostrom (2009) Published in Analysis, Volume 69, Issue 3

The original philosophical paper introducing the Pascal's Mugging thought experiment (covered in Case Study 10-1). Bostrom's paper is short (eight pages), clearly written, and directly engages the problem of low-probability, high-magnitude outcomes in expected utility theory. The paper proposes several potential solutions, including the complexity discount. Freely available online through Nick Bostrom's website at the Future of Humanity Institute. Essential reading for anyone interested in the philosophical limits of EV theory.

Available at: nickbostrom.com or via Google Scholar (search "Pascal's Mugging Bostrom 2009")

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

A compelling narrative account of how Claude Shannon, John Kelly Jr., and Edward Thorp applied information theory to gambling and financial markets — culminating in the Kelly Criterion's rise to prominence and its eventual adoption (and controversy) in quantitative finance. The book is part biography, part history of ideas, and part thriller, following Thorp's application of Kelly to blackjack and eventually to the hedge fund industry. The clearest popular account of where Kelly Criterion comes from and what it actually means in practice. Highly recommended.

Best chapters for this topic: "The Fundamental Theorem of Gambling" (Ch. 6–8), "Kelly's Formula" (Ch. 9)

9. Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets Nassim Nicholas Taleb (Random House, 2001; updated 2004)

Taleb's first book in what became the "Incerto" series is, in many ways, about the limits of EV thinking — specifically the danger of assuming that past distributions predict future ones (the "turkey problem"), the systematic underestimation of tail risks, and the cognitive errors that come from observing success without observing the survivors. His argument that EV calculations are often built on "silent evidence" (the unseen distribution of failures) connects directly to the survivorship bias of Chapter 9 and the Pascal's Mugging problem of Case Study 10-1. More opinionated and argumentative than most books on this list, but productively so.

Best chapters for this topic: "If You're So Rich, Why Aren't You Smart?" (Ch. 1), "A Bizarre Accounting Method" (Ch. 4), "Skewness and Asymmetry" (Ch. 7)

Online Resources

EV Calculator Tools: - GTO Wizard (for poker-specific EV practice): gtowizard.com - Decision Matrix Builder (general): Many versions available via Google Sheets templates; search "expected value decision matrix template"

Academic Papers: - Kahneman and Tversky (1979) Prospect Theory: Available via JSTOR (free with library access) or Google Scholar - Baron and Hershey (1988) "Outcome Bias in Decision Evaluation": Journal of Personality and Social Psychology, 54(4). Available via Google Scholar.

Video Explanations: - "Expected Value — Introduction" — Khan Academy (khanacademy.org): Clear, interactive treatment of basic EV with practice problems - "The Kelly Criterion" — Numberphile (YouTube): Accessible explanation of Kelly with good visual examples - "Thinking in Bets" — Annie Duke TED Talk and various interviews available on YouTube

All books listed are available through major libraries and most university library systems. Digital versions are available through services including Libby/OverDrive (free with library card) and most university library ebook portals.