In the old game show “Let’s Make a Deal,” contestants chose one of three curtains, behind which were either fabulous prizes or nothing, or worse (sometimes “booby prizes” would be behind a curtain). First, a contestant chose a curtain, numbered 1, 2, or 3. Then the host, Monty Hall, would open one of the remaining curtains to show that it did not contain the grand prize. Finally, the contestant was offered the opportunity to switch to the remaining unopened curtain and take whatever was behind it, or to stay with the original curtain chosen and take whatever was behind that one. Despite the emotions involved and whatever is behind the curtain that is shown (which will never be the grand prize), the question actually just boils down to whether the contestant should stay with the original door or switch.

Create a Monte Carlo simulation of the game in Excel that compares the two strategies (stay and switch). Run the game for 1000 rounds, with 2 players each round, a “Stayer” and a “Switcher.” Put the trial numbers in column A. Label column B “Prize,” and label column C “Choice.” Both columns B and C should use the formula =RANDBETWEEN(1,3). This represents both a random door for the prize and a random choice for the player. Then label columns D, E, F, and G “Stayer’s Choice,” “Stayer Correct?”, “Switcher’s Choice,” “Switcher Correct?,” respectively. The Stayer’s Choice would simply cell-reference column C. The Switcher’s Choice would simply cell-reference column B. (Note that if the Switcher were originally incorrect, then he or she will receive the grand prize after switching because the other incorrect door will have already been opened.) For columns E and G, you can use an IF function to insert a 1 if the choice matches the prize and a 0 if it does not. (Thus, in each round either the Stayer will have a 1 and the Switcher will have a 0, or vice versa.) Calculate the percent correct at the bottom of the spreadsheet. How often is the Stayer correct, and how often is the Switcher correct?