Pascal and Fermat and the Theory of Probability

Pascal

In 1654, a French nobleman, Chevalier de Sr., challenged to solve a puzzle known at the time that the problem of points. The problem, first raised by an Italian monk in late 1400, had remained unsolved for almost 200 years (Carnap34). At issue was deciding how the stakes of a game of chance should be divided if the game is not completed for any reason. The example used in the original publication refers to a game of balla where six goals were required to win the game. If the game ended normally, the winner takes all. But what if the game stopped when a player was in the lead by five goals to three? In the search for a solution, Pascal entered into correspondence with the Pierre de Fermat.

Pierre de Fermat

Pierre de Fermat was a seventeenth-century French mathematician who made important discoveries in number theory. He also worked on optics and the theory of probability (Feller22). Fermat furthermore made some assistance to calculus. Pierre de Fermat's father was a rich merchant and the second consul of his hometown, Beaumont-de-Lomagne. Pierre began his education at the Franciscan convent of the Cordeliers in Beaumont. He then went to study with the Jesuits. After assisting the University of Toulouse, he moved to Bordeau. Fermat used Francois Viete's algebra to refurbish Apollonius of Perga's Plane loci. The work was renamed procedure for determining Maxima and Minima and Tangents to Curved Lines.

To understand the solution, we can simplify the problem to a game coin toss with two players. The game ends when the coin toss has gone out twice. We say that player 1 wins in the first instance, while player 2 wins in the second. If the game reaches its natural conclusion, whether a player or player ...