Solving the Problem of Points with a Recursion

In a companion note in this issue of the Journal, Gary Skoog and James Ciecka explain their recursive method for finding probability mass functions for future years of labor market activity. Computational parsimony and simplicity are the main benefits of this method. Recursions solve the problem of searching the huge number of labor force activity/inactivity/death paths that can occur throughout a person’s life. Recursive methods have a long history in probability theory dating to Blaise Pascal (1623–1662) in his treatment of the Problem of Points. Pascal learned about the Problem of Points from Antoine Gombaud, chevalier de Mere (1607–1684) and initiated a correspondence with Pierre de Fermat (1601–1665) in 1654 on the problem. Their correspondence marks the beginning of modern-day mathematical probability theory. This note is about a recursive solution proposed by Pascal which has been described as ‘‘of the greatest importance to the development of probability theory because in it Pascal introduces the notation of expectation.’’ (Edwards 1982).