All topics
Every guide on the site, grouped by topic. 146 articles and counting.
Foundations
The core ideas of chance and the errors people make about it.
Probability Basics
- Probability Theory for Gamers: A Primer
- Complement Rule: Finding the Chance Something Does Not Happen
- Essential Probability Concepts for Gamers
- From Chance to Probability: A Gaming Primer
- Key Concepts in Gaming Probability
- Math in Gaming: Understanding Probability
- Mental Math for Gaming: Probability Tricks
- Monte Carlo Methods for Gaming Probability
- Number Crunching: Using Probability in Gaming
- Probability Distributions in Plain Language
- Probability in Action: Real-World Gaming Examples
- The Binomial Distribution with Dice and Coins
Myths and Fallacies
- 10 Common Gaming Fallacies Debunked
- Avoiding Common Mistakes in Gaming Probability
- Common Probability Misconceptions in Gaming
- Debunking the Hot Hand Fallacy in Sports Games
- Gaming Probability: Separating Fact from Fiction
- Misconceptions About Probability in Gaming
- Myths and Legends of Gaming Probability
- Probability Mistakes to Avoid in Gaming
- The Birthday Coincidence Instinct and Other Coincidence Myths
Puzzles and Paradoxes
- Classic Probability Puzzles and Why They Trick Us
- Bertrand Box Paradox
- Non-Transitive Dice Explained
- Penneys Game: Why Some Coin Sequences Beat Others
- Simpsons Paradox in Game and Sports Statistics
- The Birthday Problem: Why 23 People Is Enough
- The Boy or Girl Born on a Tuesday Puzzle
- The Monty Hall Problem Explained Step by Step
- The Secretary Problem and Optimal Stopping
- The St Petersburg Paradox and Infinite Expectations
- The Two Child Problem and Why Wording Matters
Probability by Game
How chance works in cards, casinos, video games and sport.
Cards and Poker
Casino Maths
Video Games
- Probability in Video Games: A Guide
- Adapting to Probability in Real-Time Strategy Games
- Critical Hit Chances and How They Stack
- Exploiting Probability in Multiplayer Games
- Game Theory and Probability in Competitive Gaming
- How to Calculate Probability in Video Games
- Optimizing Probability in Multiplayer Games
- Probability in Online Gaming: A Guide
- Procedural Generation and Seeded Randomness
Sports and Esports
Dice and Coins
- Dice Probability Explained: Every Roll from One Die to Many
- Advantage and Disadvantage Rolls Explained
- Coin Toss Probability and Runs of Heads
- Expected Number of Rolls to See Every Face
- How Fair Is a Real Coin Flip
- Loaded Dice and How to Test a Die for Bias
- Polyhedral Dice in Tabletop Games: d4 to d20
- The Chance of Rolling at Least One Six
- The Chevalier de Mere Dice Problem
- Why Seven Is the Most Common Total with Two Dice
- Yahtzee Odds: Chances of Five of a Kind
Design and Decisions
Using probability to build games and make clearer choices.
Game Design
Better Decisions
Variance and Bankroll Maths
- Variance and Standard Deviation in Games of Chance
- Bankroll Maths as a Concept, Not a Strategy
- Confidence Intervals for Win Rates
- Gamblers Ruin: Why a Finite Bankroll Runs Out
- Short Run Versus Long Run Results
- Streaks and Clusters in Random Sequences
- The Kelly Criterion as a Mathematical Idea
- The Law of Large Numbers Explained
- The Normal Distribution and Bell Curves
- Volatility in Games: High and Low Variance Design
Methods and Tools
Counting, Bayes and simulation techniques for working out chances by hand and by code.
Counting and Combinatorics
- Counting Principles Every Probability Learner Needs
- Counting Possible Passwords and Combination Locks
- Derangements and the Hat Check Problem
- Factorials Explained with Shuffled Decks
- How Many Five Card Poker Hands Are There
- Inclusion-Exclusion for Overlapping Events
- Pascals Triangle and Binomial Coefficients
- Permutations Versus Combinations: When Order Matters
- The Pigeonhole Principle in Games
- The Stars and Bars Method
Conditional Probability and Bayes
- Bayes Theorem Explained with Everyday Examples
- Base Rate Neglect and Why It Misleads
- False Positives in Screening Tests
- Independent Versus Dependent Events
- Natural Frequencies: An Easier Way to Think About Risk
- Probability Trees for Multi-Step Events
- Reading Hidden Information in Card Games with Bayes
- The Law of Total Probability
- The Prosecutors Fallacy
- Updating Beliefs About a Possibly Biased Coin
Simulating Chance
- Simulating Probability with Simple Code
- Checking the Monty Hall Answer with a Simulation
- How Many Trials Does a Simulation Need
- Pseudo-Random Number Generators Explained
- Shuffling Cards Fairly with the Fisher-Yates Algorithm
- Simulating a Random Walk
- Simulating Dice Rolls in Python
- Simulating Loot Drops and Pity Timers
- Spreadsheet Simulations Without Coding
- Visualising Results with Histograms
Chance Beyond Games
Lotteries, statistics in the news and staying safe around gambling.
Lotteries and Long Odds
- How Lottery Odds Work and Why They Are So Long
- Annuity Versus Lump Sum: The Time Value of Money
- Do Lucky Numbers Change Lottery Chances
- Expected Value of a Lottery Ticket
- Picturing One in Fourteen Million
- Raffles and Prize Draws: Calculating Your Chances
- Scratch Cards and How Prize Pools Work
- Shared Jackpots and Popular Number Choices
- Why Lottery Winners Seem to Come in Clusters
- Why Syndicates Do Not Improve Value
Statistics Literacy
- Statistics Literacy for Sports and Esports Fans
- Averages Versus Medians in Player Stats
- Cherry-Picked Statistics and How to Spot Them
- Correlation Is Not Causation
- Expected Goals and Other Model-Based Stats
- Reading Elo Ratings and Matchmaking Numbers
- Regression to the Mean in Sport
- Small Sample Sizes and Misleading Records
- Survivorship Bias in Success Stories
- Understanding Percentages and Percentage Points
Gambling Harm and Safer Play
- Recognising Problem Gambling: Signs and Support
- Cognitive Biases That Fuel Gambling Harm
- Gambling and Debt: Why Borrowing to Play Is Dangerous
- How Near Misses and Variable Rewards Keep People Playing
- Loot Boxes, Gambling and Young Players
- Setting Limits on Time and Money Spent Gaming
- Social Casino Games and Free-to-Play Spending
- Talking to Someone About Their Gambling
- The Illusion of Control in Games of Chance
- Why the House Always Has the Long-Run Advantage