Counterintuitive Facts (44): Why You Should Never Trust 'Average Returns'

I. Let's play a game: Russian Roulette. Gun has 6 chambers, 1 bullet. You fire once. If you don't die, you get $10 million. If you die, game over.

II. If 1000 people play this game (ensemble probability): About 833 walk away with money. 167 die. Ensemble average return is: (833 × $10M + 167 × 0) / 1000 = $8.33M. Positive return! And very high! So economists will tell you: this game is worth playing. Expected value is positive.

III. But what if you alone play 1000 times (time probability)? First shot, you might win. Second shot, might also win. But as long as you keep playing, by law of large numbers, your probability of hitting that bullet approaches 100%. Once that bullet appears, your return isn't 0. It's negative infinity. All previous $10 millions become meaningless. You're dead.

IV.