# Expected Value

> Content from Expected Value.

## Pillar topics

- [Cognitive Biases](https://expectedvalue.co.uk/category/cognitive-biases): Your brain is wired to misjudge probability. Anchoring, availability bias, the gamblers fallacy, sunk cost thinking — these mental shortcuts helped our ancestors survive but they consistently lead to poor decisions in modern life. Learn to recognise these biases in yourself and others, and discover practical techniques to counteract them.
- [Fundamentals](https://expectedvalue.co.uk/category/fundamentals): Master the building blocks of probabilistic thinking. From Bayes theorem and expected value calculations to base rates and conditional probability, these guides lay the mathematical and conceptual foundation you need to make better decisions under uncertainty. Whether you are new to probability or brushing up, start here.
- [Investing](https://expectedvalue.co.uk/category/investing): Markets are probability machines. Every investment is a bet on an uncertain future, and the best investors think in expected values, not certainties. Explore how probabilistic thinking applies to portfolio construction, risk management, index investing, and avoiding the behavioural traps that cost most investors dearly.
- [Strategy](https://expectedvalue.co.uk/category/strategy): From career choices to business decisions, strategy is applied probability. Learn decision frameworks like expected value analysis, scenario planning, pre-mortems, and Kelly criterion sizing. These practical guides help you structure complex decisions and make consistently better choices when the stakes are high.
- [Tools & Resources](https://expectedvalue.co.uk/category/tools-resources): Practical tools and resources for applying probabilistic thinking in your daily life. Calculators, spreadsheets, book recommendations, courses, and software that help you quantify uncertainty, track your predictions, and improve your calibration over time.

## Guides and articles

- [Black Swan Events: How to Prepare for the Unpredictable](https://expectedvalue.co.uk/blog/black-swan-events)
- [Base Rate Neglect: Why Your Intuitions Are Wrong](https://expectedvalue.co.uk/blog/base-rate-neglect)
- [Loss Aversion: Why Losses Hurt Twice as Much](https://expectedvalue.co.uk/blog/loss-aversion)
- [Status Quo Bias: Why We Stick with Defaults](https://expectedvalue.co.uk/blog/status-quo-bias)
- [How Prediction Markets Work: Probability Meets Money](https://expectedvalue.co.uk/blog/how-prediction-markets-work)
- [Thinking, Fast and Slow: The Bias Book Worth the Hype](https://expectedvalue.co.uk/blog/thinking-fast-and-slow-kahneman)
- [How Insurance Companies Use Probability to Make Money](https://expectedvalue.co.uk/blog/how-insurance-companies-use-probability)
- [When Is Travel Insurance Worth It? The EV Case](https://expectedvalue.co.uk/blog/travel-insurance-expected-value)
- [Sequence-of-Returns Risk: Why the Order Matters](https://expectedvalue.co.uk/blog/sequence-of-returns-risk)
- [Expected Value Thinking: Better Decisions Under Uncertainty](https://expectedvalue.co.uk/blog/expected-value-explained)
- [15 Best Decision Making Books to Change How You Think](https://expectedvalue.co.uk/blog/best-decision-making-books)
- [Nassim Taleb's Ideas: Black Swan, Antifragile & More](https://expectedvalue.co.uk/blog/nassim-taleb-ideas-explained)
- [Thinking in Bets: Decisions Like a Poker Pro](https://expectedvalue.co.uk/blog/thinking-in-bets-annie-duke)
- [12 Best Books on Probabilistic Thinking and Decision-Making](https://expectedvalue.co.uk/blog/best-books-probabilistic-thinking-decision-making)
- [Probabilistic Thinking in Daily Life: 7 Practical Uses](https://expectedvalue.co.uk/blog/probabilistic-thinking-everyday-life)
- [Position Sizing: How Much to Bet When You Have an Edge](https://expectedvalue.co.uk/blog/position-sizing-kelly-criterion)
- [Expected Value in Poker: Pot Odds, EV & Decisions](https://expectedvalue.co.uk/blog/expected-value-poker)
- [Expected Value Calculator: How to Calculate EV Step-by-Step](https://expectedvalue.co.uk/blog/expected-value-calculator)
- [Monte Carlo Thinking: How to Stress-Test Decisions](https://expectedvalue.co.uk/blog/monte-carlo-thinking)
- [Expected Value Formula: Derivation and 5 Worked Examples](https://expectedvalue.co.uk/blog/expected-value-formula)
- [Fractional Kelly: Why Half Kelly Is the Smart Default](https://expectedvalue.co.uk/blog/fractional-kelly)
- [The Gambler's Fallacy: Why You're Wrong About 'Due' Outcomes](https://expectedvalue.co.uk/blog/gamblers-fallacy)
- [Expected Value vs Expected Utility: When EV Isn't Enough](https://expectedvalue.co.uk/blog/expected-value-vs-expected-utility)
- [12 Cognitive Biases That Wreck Probability Estimates](https://expectedvalue.co.uk/blog/cognitive-biases-probability)
- [Decision Trees: A Visual Framework for Complex Choices](https://expectedvalue.co.uk/blog/decision-trees-visual-framework)
- [Hindsight Bias: Why Everything Looks Obvious After the Fact](https://expectedvalue.co.uk/blog/hindsight-bias)
- [Ergodicity Explained: Why Time Averages Matter Most](https://expectedvalue.co.uk/blog/ergodicity-explained)
- [Conditional Probability Explained Simply, With Examples](https://expectedvalue.co.uk/blog/conditional-probability-explained)
- [The Prosecutor's Fallacy: How Courts Get Statistics Wrong](https://expectedvalue.co.uk/blog/prosecutors-fallacy)
- [The Dunning-Kruger Effect: Why We Overestimate Our Abilities](https://expectedvalue.co.uk/blog/dunning-kruger-effect)
- [Bayesian Thinking for Everyday Decisions](https://expectedvalue.co.uk/blog/bayesian-thinking-everyday-decisions)
- [Risk vs Uncertainty: The Distinction That Matters](https://expectedvalue.co.uk/blog/risk-vs-uncertainty)
- [The Law of Large Numbers: Why Casinos Always Win](https://expectedvalue.co.uk/blog/law-of-large-numbers)
- [Anchoring Bias: How First Numbers Hijack Judgement](https://expectedvalue.co.uk/blog/anchoring-bias)
- [Decision Making Under Uncertainty Frameworks](https://expectedvalue.co.uk/blog/decision-making-uncertainty-frameworks)
- [Mental Accounting Fallacy Explained](https://expectedvalue.co.uk/blog/mental-accounting-fallacy-explained)
- [The Availability Heuristic: Why Vivid Examples Mislead](https://expectedvalue.co.uk/blog/availability-heuristic)
- [Negative Expected Value: Why Lottery Tickets Always Lose](https://expectedvalue.co.uk/blog/negative-expected-value)
- [A Probabilistic Framework for Career Decisions](https://expectedvalue.co.uk/blog/probabilistic-framework-career-decisions)
- [Probability vs Odds: The Difference and Why It Matters](https://expectedvalue.co.uk/blog/probability-vs-odds)
- [Kelly Criterion Calculator: Betting, Investing, Poker](https://expectedvalue.co.uk/blog/kelly-criterion-calculator)
- [The False Positive Paradox: Why Positive Tests Mislead](https://expectedvalue.co.uk/blog/false-positive-paradox)
- [What Investment Platform Fees Really Cost Over 20 Years](https://expectedvalue.co.uk/blog/investment-platform-fees-long-term-cost)
- [Probability Weighted Utility for Decisions](https://expectedvalue.co.uk/blog/probability-weighted-utility-decisions)
- [Bayesian Updating in Everyday Life UK 2026](https://expectedvalue.co.uk/blog/bayesian-updating-everyday-life-uk-2026)
- [Conjunction Fallacy in Business Decisions](https://expectedvalue.co.uk/blog/conjunction-fallacy-business-decisions)
- [Sunk Cost Fallacy: When to Quit and When to Persist](https://expectedvalue.co.uk/blog/sunk-cost-fallacy)
- [Risk Aversion vs Loss Aversion Explained](https://expectedvalue.co.uk/blog/risk-aversion-vs-loss-aversion-explained)
- [Second-Order Thinking: How to See Around Corners](https://expectedvalue.co.uk/blog/second-order-thinking)
- [Expected Value in Poker Tournaments](https://expectedvalue.co.uk/blog/expected-value-poker-tournaments)
- [Thinking in Probabilities: Why Your Brain Is Bad at Risk](https://expectedvalue.co.uk/blog/thinking-in-probabilities)
- [Correlation vs Causation: A Probabilistic Thinking Guide](https://expectedvalue.co.uk/blog/correlation-vs-causation)
- [Probability Calibration: Predict Like a Superforecaster](https://expectedvalue.co.uk/blog/probability-calibration-training)
- [UK FIRE Movement 2026: The Complete Roadmap](https://expectedvalue.co.uk/blog/uk-fire-movement-2026)
- [Are Extended Warranties Ever Worth It? The Expected Value](https://expectedvalue.co.uk/blog/extended-warranties-expected-value)
- [Voluntary Excess: How to Choose the Level That Pays Off](https://expectedvalue.co.uk/blog/insurance-excess-expected-value)
- [The Kelly Criterion: How to Size Your Bets Optimally](https://expectedvalue.co.uk/blog/kelly-criterion-optimal-bet-sizing)
- [Premium Bonds: What's the Real Expected Value?](https://expectedvalue.co.uk/blog/premium-bonds-expected-value)
- [Where Can You Actually Find Positive Expected Value?](https://expectedvalue.co.uk/blog/where-to-find-positive-expected-value)
- [Stocks and Shares ISA Limit 2026: Rules and 2027 Changes](https://expectedvalue.co.uk/blog/stocks-and-shares-isa-limit-2026)
- [Bayes Theorem Explained: Formula and 5 Worked Examples](https://expectedvalue.co.uk/blog/bayes-theorem-explained)
- [Framing Effect: Why How You Hear It Changes Your Choice](https://expectedvalue.co.uk/blog/framing-effect-bias)
- [Availability Cascade in Markets](https://expectedvalue.co.uk/blog/availability-cascade-in-markets)
- [The Monty Hall Problem: Why You Should Always Switch](https://expectedvalue.co.uk/blog/monty-hall-problem-explained)
- [Bayesian vs Frequentist Statistics: What's the Difference?](https://expectedvalue.co.uk/blog/bayesian-vs-frequentist)
- [Recency Bias in Investing and Sports Predictions](https://expectedvalue.co.uk/blog/recency-bias)
- [Survivorship Bias: The Hidden Data That Changes Everything](https://expectedvalue.co.uk/blog/survivorship-bias)
- [Overconfidence Bias: Why Active Traders Underperform](https://expectedvalue.co.uk/blog/overconfidence-bias)
- [Confirmation Bias in Investing: Fight Your Own Brain](https://expectedvalue.co.uk/blog/confirmation-bias-investing)
- [Regression to the Mean: Why Extremes Don't Last](https://expectedvalue.co.uk/blog/regression-to-the-mean)
- [The Pre-Mortem - Imagine Your Decision Already Failed](https://expectedvalue.co.uk/blog/pre-mortem-decision-making)
- [Endowment Effect Explained: Why You Overvalue What You Own](https://expectedvalue.co.uk/blog/endowment-effect)
- [Decision Journals: Track Your Thinking to Improve It](https://expectedvalue.co.uk/blog/decision-journals)

## Reviews

- [The Signal and the Noise Review (Nate Silver, 2012)](https://expectedvalue.co.uk/review/signal-and-noise-silver-review): Research-led review of Nate Silver's The Signal and the Noise (2012). Bayesian reasoning, domain-by-domain forecastability, the 2016 misfire.
- [Fooled by Randomness Review (Nassim Taleb, 2001)](https://expectedvalue.co.uk/review/fooled-by-randomness-taleb-review): Research-led review of Taleb's Fooled by Randomness (2001) - the foundational Incerto book on survivorship bias and the role of luck in success.
- [Superforecasting Review (Tetlock & Gardner, 2015)](https://expectedvalue.co.uk/review/superforecasting-tetlock-gardner-review): Research-led review of Tetlock & Gardner's Superforecasting (2015). Good Judgment Project + the 10-commandment framework + an honest read of the limits.

## Comparisons

- [Thinking, Fast and Slow vs Thinking in Bets](https://expectedvalue.co.uk/compare/thinking-fast-and-slow-vs-thinking-in-bets)
- [Best SIPP UK 2026: 10 Providers Compared](https://expectedvalue.co.uk/compare/best-sipp-uk-2026)
- [Vanguard vs InvestEngine: UK 2026 Comparison](https://expectedvalue.co.uk/compare/vanguard-vs-investengine-uk-2026)
- [Trading 212 vs eToro: UK 2026 Comparison](https://expectedvalue.co.uk/compare/trading-212-vs-etoro-uk-2026)
- [Kalshi vs Polymarket vs Manifold (UK & US 2026)](https://expectedvalue.co.uk/compare/kalshi-vs-polymarket-vs-manifold)

## Products

- [Superforecasting: The Art and Science of Prediction](https://expectedvalue.co.uk/product/superforecasting-tetlock-gardner): Philip Tetlock + Dan Gardner's 2015 book on Good Judgment Project research into what makes forecasters more accurate. Foundational text.
- [Fooled by Randomness: The Hidden Role of Chance](https://expectedvalue.co.uk/product/fooled-by-randomness-taleb): Nassim Taleb's 2001 book on luck in success and how survivorship bias distorts judgment of skill in finance + business. First Incerto text.
- [The Signal and the Noise: Why Predictions Fail](https://expectedvalue.co.uk/product/signal-and-noise-nate-silver): Nate Silver's 2012 book on probabilistic forecasting across weather, sports, poker, economics, politics. Builds the case for Bayesian reasoning.

## Reference

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