Is Your Game Rigged? Unpacking When 'A Game is Said to be Fair'

Ever wonder what makes a game *fair*? It's more than just following the rules! In probability, 'a game is said to be fair if' your expected winnings are zero. Sounds complicated? Let's break it down.

Imagine flipping a coin. You win $1 if it's heads, lose $1 if it's tails. There's a 50/50 chance of each outcome. Your expected value is (0.5 * $1) + (0.5 * -$1) = $0. That's a fair game! Neither you nor the 'house' has an advantage over the long run.

However, if the payouts were skewed – say you win $2 for heads but still lose $1 for tails – the expected value would be positive for you (0.5 * $2) + (0.5 * -$1) = $0.50. That's *not* a fair game; you'd expect to win money over time.

Fairness doesn't mean you'll win *every* time, it means that, on average, neither player nor the house has a statistical edge. So, next time you're playing, consider the probabilities – and ask yourself, is this game *really* fair?