A Spreadsheet Simulation Of The Monty Hall Problem

Abstract

The “Monty Hall” problem or “Three Door” problem—where a person chooses one of three doors in hope of winning a valuable prize but is subsequently offered the choice of changing his or her selection—is a well known and often discussed probability problem.  In this paper, the structure, history, and ultimate solution of the Monty Hall problem are discussed. The problem solution is modeled with a spreadsheet simulation that evaluates the frequencies of the possible outcomes (win or lose) under the two choices or strategies available:  switch to the unopened door or do not switch. A Law of Large Numbers approach is also used to graphically demonstrate the long run outcome of adopting one the two available strategies. As is known, the optimal strategy is to switch to the unopened door; the spreadsheet model illustrates why this strategy is optimal. A complete discussion of the spreadsheet logic is included. Pedagogical approaches and applications of the spreadsheet simulation approach are also discussed.