The world around us is a capricious and often difficult place. But as we have developed our mathematical tools with increased sophistication, we have in turn improved our ability to understand the world around us.
And one of the seemingly simple places where this occurs is in the relationship between luck and skill. We have little trouble recognizing that a chess grandmaster’s victory over a novice is skill, as well as assuming that Paul the octopus’s ability to predict World Cup games is due to chance. But what about everything else?