Picture a bettor with a real edge who is down after a hundred wagers. Bad luck, or a bad process? Betting variance is how you tell the difference. The lesson takes a 55 percent even-money example, finds the expected gain, then derives the standard deviation of total profit over N bets. You see how wide the swings can run even when the math favors you. It also challenges the habit of treating bets as independent, since wagers on one game or one player tend to move together, and it covers how errors in your own probability estimate widen the picture further. Finish with a paper simulation you can run yourself, so a rough stretch reads as noise or as a warning instead of panic.
Learning objectives
Separate process quality from short-run results, quantify standard deviations for repeated binary outcomes, and recognize correlated-risk and estimation hazards.
