10 articles
The 2.70% house edge and 5.26% house edge both sound small. Across thousands of spins the difference is anything but, here is the exact math.
Ask most people how many people fit in a room before two share a birthday. They say 183. The correct answer is 23. Here is the exact math explaining why.
Flip a coin 10 times and you might get 70% heads. Flip it 1,000,000 times and you will be within 0.05% of 50%. The law of large numbers guarantees this convergence.
Heights, measurement errors, stock returns, IQ scores. Why does the bell curve keep appearing? The Central Limit Theorem is the answer, and it is arguably the most important theorem in statistics.
Standard deviation is not just a formula, it is a measure of how wrong your average is. Understanding it changes how you read every statistic you encounter.
In 1898, a statistician counted soldiers kicked to death by horses. The data followed a distribution that now models everything from earthquakes to Amazon server requests.
A gambler with finite wealth faces a casino with infinite wealth. Even with a fair coin, the gambler is mathematically certain to go broke. The proof is exact and merciless.
A random walk is the sum of random steps. It describes particle diffusion, genetic drift, and, according to the Efficient Market Hypothesis, stock price movements.
Modern slot machines are not mechanical, they are software running random number generators. Understanding the math explains why they are the most profitable machines in any casino.
Conditional probability is where human intuition fails most dramatically. The Monty Hall problem, medical tests, and the prosecutor's fallacy all trace back to one misunderstood concept.