Beyond Expected Value

Expected value tells you whether a bet is worth taking, but not how much to stake. A game with positive EV can still ruin you if you bet too big and hit a bad streak. The Kelly criterion, derived by Bell Labs mathematician John Kelly in 1956, gives the fraction of your bankroll to wager: f = (bp − q) / b, where b is the odds, p is the probability of winning, and q is the probability of losing.

The lesson is simple: never bet so much that one bad outcome ends the game. EV answers "should I take this bet?" — Kelly answers "how much should I stake?"