de Méré's problem

De Méré's problem is a question posed in the mid-seventeenth century to Blaise Pascal by a French nobleman and inveterate gambler, the Chevalier de Méré, which marked the birth of probability theory. One of de Méré's favorite bets was that at least one six would appear during a total of four rolls of a die. From past experience, he knew that this gamble paid off more often than not. Then, for a change, he started betting that he would get a double-six on 24 rolls of two dice. However, he soon realized that his old approach to the game was more profitable. He asked his friend Pascal why. Pascal showed that the probability of getting at least one six in four rolls of a die is 1 - (5/6)4 ~ 0.5177, which is slightly higher than the probability of at least one double-six in 24 throws of two dice, 1 - (35/36)24 ~ 0.4914.


This problem and others posed by de Méré are thought to have been the original inspiration for a fruitful exchange of letters on probability between Pascal and Pierre de Fermat. To tackle these problems, Fermat used combinatorial analysis (finding the number of possible outcomes in ideal games of chance by computing permutation and combination numbers), while Pascal reasoned by recursion (an iterative process that determines the result of the next case by the present case). Their combined work laid the foundations for probability theory as we know it today.