What does it mean for something to be random? An event is called
... • a 999,999 in 1,000,000 chance of losing $1 and a 1 in a 1,000,000 chance of winning $1,000,000.
In all three of these bets the expected value is 0, but the outcomes are very different. A lot of
information about these bets is lost by considering only the expected values of the bets. In each