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Fundamentals
How Insurance Companies Use Probability to Make Money
Insurance is a negative-EV bet - for you. Here's how actuarial science, risk pooling, and the law of large numbers turn that into reliable profit.
Most read
Fundamentals
The Kelly Criterion: How to Size Your Bets Optimally
The Kelly Criterion tells you exactly how much to stake when you have an edge. Formula derivation, fractional Kelly, history, and worked examples for 2026.
Jun 2026
Fundamentals
Nassim Taleb's Ideas: Black Swan, Antifragile & More
A guide to Nassim Taleb's key ideas - Black Swans, Antifragile, Skin in the Game, fat tails, barbell strategy and the Lindy effect - and where to start.
Jul 2026
Latest
Investing
When Is Travel Insurance Worth It? The EV Case
Travel insurance is usually negative-EV, yet often the right call. The expected-value rule for when a risk is worth insuring - and when to self-insure.
Jul 2026
Investing
Sequence-of-Returns Risk: Why the Order Matters
Same average return, wildly different outcomes: why the ORDER of your returns decides how long a pension pot lasts. Sequence-of-returns risk explained.
Jul 2026
Fundamentals
Expected Value Thinking: Better Decisions Under Uncertainty
Expected value thinking: the most important concept in decision-making under uncertainty. What it is, how to calculate it, when to apply it.
Jul 2026
Tools & Resources
15 Best Decision Making Books to Change How You Think
15 best decision-making books - choice architecture, behavioural economics, frameworks, and habits. Mini-reviews, who each is for, and reading order.
Jul 2026
Cognitive Biases
Thinking, Fast and Slow: The Bias Book Worth the Hype
Kahneman's Thinking, Fast and Slow is the canonical text on cognitive bias. What it gets right, what hasn't aged well, and whether to buy it.
Jul 2026
Strategy
Thinking in Bets: Decisions Like a Poker Pro
Annie Duke's Thinking in Bets reframes every decision as a bet under uncertainty. The ideas of resulting, calibration, and decision groups.
Jul 2026
Fundamentals
12 Best Books on Probabilistic Thinking and Decision-Making
A curated reading list on probability, decision-making under uncertainty, and rational thinking - from Kahneman to practical guides for forecasters.
Jul 2026
Fundamentals
How Prediction Markets Work: Probability Meets Money
Prediction markets turn questions about the future into tradeable contracts whose prices behave like probabilities. How they work, and how to use them.
Jul 2026
Fundamentals
Probabilistic Thinking in Daily Life: 7 Practical Uses
How to apply probabilistic thinking to medical decisions, career bets, insurance, investing, dating, sports betting and travel. 7 worked examples.
Jul 2026
Cognitive Biases
Status Quo Bias: Why We Stick with Defaults
Status quo bias explained: the cognitive tendency to stick with defaults. UK financial impact: pension funds, insurance renewals, current accounts.
Jul 2026
Investing
Position Sizing: How Much to Bet When You Have an Edge
Knowing you have an edge is half the battle - sizing positions correctly is the other half. How to size bets so you don't blow up or waste your advantage.
Jul 2026
Strategy
Expected Value in Poker: Pot Odds, EV & Decisions
Expected value in poker - pot odds, implied odds, EV of bluffs and folds. Worked hand examples showing how the maths translates into better decisions.
Jul 2026
Tools & Resources
Expected Value Calculator: How to Calculate EV Step-by-Step
Learn how to calculate expected value with a clear formula, four worked examples (betting, investing, insurance, career) and the common mistakes to avoid.
Jul 2026
Fundamentals
Monte Carlo Thinking: How to Stress-Test Decisions
Monte Carlo simulation lets you stress-test decisions across thousands of scenarios. A practical guide to using it for retirement, projects and investing.
Jul 2026
Fundamentals
Expected Value Formula: Derivation and 5 Worked Examples
The expected value formula is E[X] = Σ(p × x). Full derivation and five worked examples - coin flip, lottery, insurance, poker, and stock investment.
Jul 2026
Strategy
Fractional Kelly: Why Half Kelly Is the Smart Default
Full Kelly is mathematically optimal but emotionally brutal. Why half Kelly is the practical default, when to scale up or down, and how the pros use it.
Jul 2026
Cognitive Biases
The Gambler's Fallacy: Why You're Wrong About 'Due' Outcomes
The Gambler's Fallacy: why we wrongly believe random outcomes are 'due'. The cognitive trap, where it costs you, and how to think clearly under randomness.
Jul 2026
Fundamentals
Expected Value vs Expected Utility: When EV Isn't Enough
Pure expected value can lead to ruinous decisions. Here's why expected utility, risk aversion, and the St Petersburg paradox matter for real-life choices.
Jul 2026
Cognitive Biases
12 Cognitive Biases That Wreck Probability Estimates
The 12 cognitive biases that most consistently distort probability judgements - what each one does and how to defend against it.
Jul 2026
Strategy
Decision Trees: A Visual Framework for Complex Choices
Decision trees turn tangled choices into a diagram you can actually solve. Build one in five steps, work through three examples, and avoid common traps.
Jul 2026
Cognitive Biases
Hindsight Bias: Why Everything Looks Obvious After the Fact
Hindsight bias makes the past feel inevitable. Here's why it distorts post-mortems, juries and investing - and how to fight it.
Jul 2026
Fundamentals
Ergodicity Explained: Why Time Averages Matter Most
Ergodicity separates sensible bets from catastrophic ones. The difference between ensemble averages and time averages - and why ignoring it can ruin you.
Jul 2026
Fundamentals
Conditional Probability Explained Simply, With Examples
Conditional probability is the chance one event happens given another already has. Worked examples in medical testing, weather, and the Monty Hall problem.
Jul 2026
Cognitive Biases
Loss Aversion: Why Losses Hurt Twice as Much
Loss aversion: why losses hurt twice as much as equivalent gains feel good. The Kahneman/Tversky research, where it warps decisions, and how to counter it.
Jul 2026
Cognitive Biases
The Prosecutor's Fallacy: How Courts Get Statistics Wrong
Confusing P(evidence | innocent) with P(innocent | evidence) sends innocent people to prison. The Sally Clark case and how to spot the trap.
Jul 2026
Cognitive Biases
The Dunning-Kruger Effect: Why We Overestimate Our Abilities
The Dunning-Kruger effect: the gap between how good people think they are and how good they actually are. The real research is more useful than the chart.
Jul 2026
Cognitive Biases
Bayesian Thinking for Everyday Decisions
Bayesian thinking - the art of changing your mind rationally. How to update beliefs with evidence, with examples from interviews, medicine, and investing.
Jul 2026
Fundamentals
Risk vs Uncertainty: The Distinction That Matters
Risk is measurable; uncertainty is not. Confusing the two produces overconfident forecasts and brittle portfolios. Here's how to tell them apart.
Jul 2026
Fundamentals
The Law of Large Numbers: Why Casinos Always Win
The Law of Large Numbers explains why a single bet is wildly volatile but casinos profit reliably - the maths behind insurance and long-run averages.
Jul 2026
Cognitive Biases
Anchoring Bias: How First Numbers Hijack Judgement
Anchoring bias: why the first number you hear silently warps every estimate that follows - with research, examples, and debiasing strategies that work.
Jul 2026
Cognitive Biases
Base Rate Neglect: Why Your Intuitions Are Wrong
Base rate neglect is one of the most costly cognitive biases. Why most positive medical tests are wrong, and how to train yourself to think in base rates.
Jul 2026
Fundamentals
Decision Making Under Uncertainty Frameworks
Decision making under uncertainty frameworks: minimax regret, expected utility, satisficing, maximax compared. When each applies.
Jul 2026
Cognitive Biases
Mental Accounting Fallacy Explained
Mental accounting fallacy: separating money into psychological 'buckets' distorts financial decisions; budgeting + investment implications.
Jul 2026
Cognitive Biases
The Availability Heuristic: Why Vivid Examples Mislead
Why we judge risk by what comes to mind first - fear of flying, market news, terrorism - and the practical techniques to debias your thinking.
Jul 2026
Fundamentals
Negative Expected Value: Why Lottery Tickets Always Lose
Why every lottery ticket, roulette spin and slot pull is mathematically a loss in expectation. The maths behind why the house always wins.
Jul 2026
Strategy
A Probabilistic Framework for Career Decisions
Use expected value, scenario planning and Kelly-style sizing to evaluate job offers, career pivots and salary negotiations honestly.
Jul 2026
Fundamentals
Probability vs Odds: The Difference and Why It Matters
Probability and odds describe the same uncertainty differently - and confusing them costs people money. How each works, conversions, and bookmaker tricks.
Jul 2026
Tools & Resources
Kelly Criterion Calculator: Betting, Investing, Poker
Step-by-step Kelly Criterion calculator with worked examples for sports betting, investing and poker. Convert odds to stake percentages instantly.
Jul 2026
Fundamentals
The False Positive Paradox: Why Positive Tests Mislead
When a test for a rare condition comes back positive, it's often more likely wrong than right. The false positive paradox, explained with real numbers.
Jul 2026
Investing
What Investment Platform Fees Really Cost Over 20 Years
A 0.35% platform fee sounds tiny. Compounded over 25 years it can cost £30,000+. The maths of fee drag, and where flat fees beat percentages.
Jul 2026
Fundamentals
Probability Weighted Utility for Decisions
Probability weighted utility for high-stakes decisions: combining probabilities and personal values for better choices.
Jul 2026
Fundamentals
Bayesian Updating in Everyday Life UK 2026
Bayesian updating UK 2026: practical examples of updating beliefs with new evidence in investment, health, and career decisions.
Jul 2026
Cognitive Biases
Conjunction Fallacy in Business Decisions
Conjunction fallacy in business: how compound probability errors distort startup planning, investment scenarios, project timelines.
Jul 2026
Cognitive Biases
Sunk Cost Fallacy: When to Quit and When to Persist
The sunk cost fallacy: why we keep investing in losing decisions. The bias, the psychology, and a clear test for when to quit and when to persist.
Jul 2026
Cognitive Biases
Risk Aversion vs Loss Aversion Explained
Risk aversion vs loss aversion: the behavioural distinction; investment + portfolio implications; how each affects decisions.
Jul 2026
Tools & Resources
Second-Order Thinking: How to See Around Corners
Most decisions are made on first-order effects, but second-order consequences are where the surprises live. A framework for seeing past the obvious.
Jul 2026
Strategy
Expected Value in Poker Tournaments
EV in poker tournaments: ICM considerations, bubble dynamics, when raw chip-EV diverges from actual tournament-EV.
Jul 2026
Strategy
Black Swan Events: How to Prepare for the Unpredictable
Black swan events explained: Taleb's definition, examples (2008, COVID, AI surge), and the barbell strategy + antifragility approach.
Jul 2026
Cognitive Biases
Thinking in Probabilities: Why Your Brain Is Bad at Risk
Your brain systematically misjudges probability. Learn the cognitive biases that distort risk perception and how to calibrate better.
Jul 2026
Fundamentals
Correlation vs Causation: A Probabilistic Thinking Guide
Correlation is not causation - the most-quoted line in statistics, and the most misunderstood. What it really means, and how to think clearly about cause.
Jul 2026
Strategy
Probability Calibration: Predict Like a Superforecaster
Learn probability calibration like a superforecaster - Brier scores, drills, and free tools to sharpen your forecasts. Based on Philip Tetlock's research.
Jul 2026
Strategy
UK FIRE Movement 2026: The Complete Roadmap
A UK FIRE roadmap for 2026: the 4% rule, your real number, the tax-wrapper order, and the ISA bridge to pension access age. Honest maths, no hype.
Jul 2026
Investing
Are Extended Warranties Ever Worth It? The Expected Value
Warranty maths retailers hope you never do: premium vs failure odds x repair cost. Why most UK cover is -EV, and the one case where it isn't.
Jul 2026
Investing
Voluntary Excess: How to Choose the Level That Pays Off
Raising your voluntary excess cuts your premium but raises claim costs. Use expected value to find the excess level that actually pays off.
Jul 2026
Investing
Premium Bonds: What's the Real Expected Value?
Premium Bonds advertise 3.8%, but that average hides a skewed reality. Here's the real expected (and typical) return for £1k, £10k and £50k holdings.
Jun 2026
Strategy
Where Can You Actually Find Positive Expected Value?
Almost every bet is negative-EV by design. Here are the few places an ordinary person can genuinely find positive expected value.
Jun 2026
Investing
Stocks and Shares ISA Limit 2026: Rules and 2027 Changes
The 2026/27 stocks and shares ISA limit is £20,000. Here's how the allowance works, what the April 2027 cash ISA cut means, and how to use it.
Jun 2026
Fundamentals
Bayes Theorem Explained: Formula and 5 Worked Examples
Bayes theorem explained from the formula up: derivation, intuitive examples (medical tests, spam filters), and the base-rate trap that fools experts.
Jun 2026
Cognitive Biases
Framing Effect: Why How You Hear It Changes Your Choice
The framing effect: identical numbers presented differently produce opposite decisions. Asian Disease Problem, gain vs loss framing, defences.
Jun 2026
Cognitive Biases
Availability Cascade in Markets
Availability cascade in markets: how compounding information cascades amplify trends, create bubbles, and drive systematic mispricing.
Jun 2026
Fundamentals
The Monty Hall Problem: Why You Should Always Switch
The Monty Hall problem looks 50/50 and isn't - switching doors wins two-thirds of the time. Here's why, with five proofs and the famous controversy.
Jun 2026
Fundamentals
Bayesian vs Frequentist Statistics: What's the Difference?
Bayesian vs frequentist statistics - the philosophical split that decides whether you get p-values or posteriors, and when each one actually wins.
Jun 2026
Cognitive Biases
Recency Bias in Investing and Sports Predictions
Recency bias: why investors chase last quarter's winners and bettors back the form team. The mechanics, the cost, and the four tools that defuse it.
Jun 2026
Cognitive Biases
Survivorship Bias: The Hidden Data That Changes Everything
Survivorship bias hides the failures behind every success story - from WWII bombers to mutual funds. How to spot the missing data and decide better.
Jun 2026
Cognitive Biases
Overconfidence Bias: Why Active Traders Underperform
Overconfidence bias is investing's most expensive cognitive error. How overestimation, the planning fallacy and overprecision hide it, and what fixes it.
Jun 2026
Cognitive Biases
Confirmation Bias in Investing: Fight Your Own Brain
Confirmation bias quietly destroys investment returns. Here's how it works in markets - and the three techniques that actually neutralise it.
Jun 2026
Fundamentals
Regression to the Mean: Why Extremes Don't Last
Why extreme performance - sporting peaks, market gains, viral hits - almost always reverts to average. Galton's discovery, examples, and how to spot it.
Jun 2026
Strategy
The Pre-Mortem - Imagine Your Decision Already Failed
The pre-mortem flips the post-mortem on its head: imagine the decision has already failed, then work backwards to find what optimism hides.
Jun 2026
Cognitive Biases
Endowment Effect Explained: Why You Overvalue What You Own
The endowment effect makes you value the things you own more highly than identical things you do not. Here is why it happens, with worked examples.
Jun 2026
Strategy
Decision Journals: Track Your Thinking to Improve It
A decision journal is the only honest record of how well you actually think. What to record, when to review, and the mistakes that ruin the practice.
Jun 2026
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