Start here · Essential guide
Probability Basics for Casino Games
Learn what outcomes, events and sample spaces are, and how to calculate simple chances for dice, cards and roulette with clear, hand-checked examples.
The Math
The Probability Toolkit
The core math ideas behind every casino game, explained step by step.
Combinations and Permutations in Card Games
Understand the counting methods behind card hand probabilities: permutations, combinations and the 2,598,960 possible five-card poker hands.
Converting Odds Between Fractions, Decimals and Percentages
Learn how to translate a chance between fractions, decimals, percentages and 'X to Y' odds, with worked examples and a quick reference table.
Expected Value Explained With Simple Examples
See how expected value is calculated as the average result per bet, with hypothetical coin, die and roulette examples that are checked step by step.
Hit Rate, Payout Ratio and Break-Even Probability
Learn how hit rate and payout ratio combine to set the break-even probability of a bet, with checked examples from roulette, blackjack and a hypothetical game.
Independent and Dependent Events in Games
Contrast independent events like roulette spins and dice rolls with dependent events like card draws without replacement, using checked probability examples.
Monte Carlo Simulation: How Designers Test Games
How repeated virtual play estimates a game's return and volatility, why accuracy improves with more trials, and where simulation falls short.
Risk of Ruin: How Likely Is a Bankroll to Run Out
Understand risk of ruin, the chance a bankroll is fully depleted, and why it is higher than intuition suggests when the edge is against the player.
Standard Deviation as a Measure of Swings
A plain-language look at standard deviation as the typical spread of results around the average, with checked roulette examples for 1, 100 and 10,000 bets.
The Law of Large Numbers and Why It Favors the House
Why averages settle over many trials while single sessions stay unpredictable, and why that steadiness benefits a venue but not an individual player.
Why Small Samples Mislead
See how short runs of spins, flips or hands can look very different from long-run averages, with checked examples and tips for reading streaks honestly.
Related topics
More in the math
Odds and House Edge How the built-in house edge, odds and probability shape every casino game. Slots Roulette and Baccarat The mechanics and math of individual casino games. Blackjack Math The mathematics, strategy and limits of blackjack. Variance and Volatility Why short-term results swing and what that does to the player experience. Bet Types and Game Comparisons Side bets, even-money bets and how to compare games on equal terms.