Mathematics
Expected Value
Quick fact
In a fair coin flip, the expected value of winning $1 for heads and losing $1 for tails is $0—the game is 'fair' because the long-run average is exactly zero.
Why this is interesting
Imagine you’re offered a coin flip: heads you win $100, tails you lose $50. Would you play? Intuition might say yes, but the real answer lies in a simple calculation that reveals the 'expected' payoff—and it might surprise you.