Monte Carlo Simulation Basics: Using Random Sampling to Solve Hard Problems
Monte Carlo methods use repeated random sampling to estimate complex quantities that are hard to compute directly.
Count the chances, not the feeling
Welcome to Fair Count, your educational guide to the mathematics of chance. We explore the principles of probability to help you understand the world of uncertainty.
One example, one conclusion
Dice, coins, and cards are only there to see probability. This is not advice to play games of chance.
Watch one way to practice counting
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Permutations vs Combinations: Why Order Changes Everything in Probability
Learn the difference between permutations and combinations with clear examples. Understand how order-dependent and order-independent counting shape probability.
The Binomial Distribution Explained: Success and Failure in Repeated Trials
Break down the binomial distribution, its formula, assumptions, mean, variance, and examples for repeated success/failure trials.
The Gambler’s Fallacy Explained: Probability and Why the Past Does Not Control the Next Independent Event
See why past random events do not affect future outcomes, how independent trials work, and where probability really comes from.
Tracing the Origins of Probability Theory from Gambling Problems to Rigorous Mathematics
The origins of probability theory lie in gambling questions, yet centuries of work turned them into a rigorous mathematics of uncertainty.
The Law of Large Numbers: Why Averages Stabilize Over Many Trials
The law of large numbers explains why average results stabilize over many trials, even when single outcomes vary wildly.