8 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.