Blaise Pascal was 17th century genius who invented the mechanical calculator. Pierre de Fermat is famous for a theorem that took three hundred years to prove. What could bring these two minds together? A washed up gambler, down on his luck.

Once upon a time there was a French nobleman named Antoine Gombaud. He lived in the 1600s, before it was possible to accidentally post nude photos on twitter, and so he had to find a different way to destroy himself. After some consideration, he chose gambling. And he chose a particular form of gambling. He calculated the odds of a certain outcome, and bet huge sums based on those odds. This was his game.

Roll a single die four times. What are the odds of getting a six? Well, each roll has a single chance out of six, so four rolls should give us a four out of six chance to roll a six. Good so far.

Now roll two dice twenty-four times. What are the odds of getting a double six? Well, on each roll each die has a one out of six chance to roll a six, but because we have to roll a double six, those two chances have to be multiplied. So each toss of the dice has a one out of thirty-six chance to roll a double six. Roll twenty-four times, and your odds of getting a double six should be twenty-four out of thirty-six, which reduces to four out of six.

Those two outcomes are equally likely, Gombaud thought, and so he set games up based on those odds. After he lost a huge amount of money, it occurred to him that he might have made a little mistake. Did he give up? No. Did he turn to ordinary math students? No. He went to no less a mind than Blaise Pascal.

Pascal was one of those people in history who are annoying accomplished. He was a physician and an inventor who, in his spare time, wrote works of philosophy and clarified physics concepts like the idea of a vacuum. But when it came to Gombaud's little gambling problem, even he was stumped. He kicked the problem over to Pierre de Fermat, presumably sometime before Fermat's Last Theorem.

The two scientists worked the problem over while the gambler fretted. At last they clarified the problem by simply calculating the odds of not rolling a six or a double six.