What are the Odds?
The development of probability theory has interesting origins: it’s all connected to gambling! Born in 1445, Luca Paccioli, a Franciscan monk, posed the problem that came to be called the puzzle of the points: A and B are playing a game of balla. The first person to win 6 rounds wins. But the game has to be stopped when A had won 5 rounds and B has won 3 rounds. How should the money be divided in such an uncompleted game? Finding a way to solve this problem had implications far beyond gambling. After all, this question involves factoring what may happen in the future. To put it differently, what are the chances that B catches up and overtakes A if the game continued? Gamblers were always interested in this kind of question: which numbers show up more often in a throw of the dice? What are the odds of a particular number showing up when two dice are involved instead of one? Like all smart people, the gamblers didn’t just do such analysis themselves. They even tried asking mathematicians...