In 1994, we celebrate the 500th anniversary of the printing of the oldest known problem in the theory of probability, namely, the problem of points which appeared in the book “Summa de Arithmetica, Geometria, Proportioni e Proportionalita” by Lucas Pacioli in Venice in 1494. The problem of points is of considerable interest and had great influence on the evolution of probability theory. The paper traces the historical development of the problem, studies the pioneering solutions of Pierre de Fermat and Blaise Pascal in 1654, and puts in proper perspective the various methods and results achieved in the past 500 years.