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 to get involved …without much luck. Galileo, for example, did such an analysis (without any interest) only because his employer, the Grand Duke of Tuscany, hoped to benefit in his games via Galileo’s findings!

Then came the Chevalier de Mere, a French nobleman/mathematician/gambler, who coaxed Blaise Pascal and Fermat (of the Last Theorem fame) to try and find a solution to the puzzle of balla that had still not been solved 2 centuries after it had been posed. The two Frenchmen solved the problem, and ended up inventing probability theory along the way!

Whoever said gambling can’t lead to good things?

Comments

  1. KumarMay 4, 2011 at 7:16 PM

    Interesting!

    Do people know that the probability idea coming from Pascal and Fermat and the probability idea that is the backbone of quantum mechanics are at variance at a very, very fundamental level? The quantum mechanics probability is far more intriguing and virtually psychedelic!

    ReplyDelete

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