Mathematics
Expected Value Fundamentals
Quick fact
The expected value of a fair coin flip is zero, meaning you neither gain nor lose money on average if you bet fairly.
Why this is interesting
Have you ever wondered why casinos always win in the long run? It's all about expected value—calculating what you're likely to gain or lose over time.
Read the full explanation
Understanding Expected Value Fundamentals
Expected value helps us predict the average outcome of uncertain events. Imagine flipping a coin: heads you win $1, tails you lose $1. Since each has a 50% chance, your expected value is (0.5 1) + (0.5 -1) = 0. Over many flips, you'd break even.
A deeper explanation
Expected value works by multiplying each possible outcome by its probability and summing the results. This gives a weighted average that represents what we expect to happen on average over time. It's crucial for evaluating risks and rewards in real-world scenarios like investments or gambling.