scholarly journals A Spreadsheet Simulation Of The Monty Hall Problem

2010 ◽  
Vol 3 (2) ◽  
pp. 1-24
Author(s):  
Mike C. Patterson ◽  
Bob Harmel ◽  
Dan Friesen
Keyword(s):  
Law Of Large Numbers ◽  
Problem Solution ◽  
Simulation Approach ◽  
Spreadsheet Model ◽  
Long Run ◽  
Large Numbers ◽  
Complete Discussion ◽  
Monty Hall ◽  
Monty Hall Problem ◽  
Pedagogical Approaches

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.

scholarly journals A Bridge from Monty Hall to the Hot Hand: The Principle of Restricted Choice

2019 ◽  
Vol 33 (3) ◽  
pp. 144-162 ◽  
Author(s):  
Joshua B. Miller ◽  
Adam Sanjurjo
Keyword(s):  
Conditional Probability ◽  
Selection Bias ◽  
Experimental Subject ◽  
Card Game ◽  
Hot Hand ◽  
Monty Hall ◽  
Monty Hall Problem ◽  
Available Information ◽  
Inferential Rule

We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the recently discovered hot hand selection bias. We explain the connection by way of the principle of restricted choice, an intuitive inferential rule from the card game bridge, which we show is naturally quantified as the updating factor in the odds form of Bayes’s rule. We illustrate how, just as the experimental subject fails to use available information to update correctly when choosing a door in the Monty Hall problem, researchers may neglect analogous information when designing experiments, analyzing data, and interpreting results.

scholarly journals The Monty Hall Problem as a Bayesian Game

Games ◽  
2017 ◽  
Vol 8 (3) ◽  
pp. 31
Author(s):  
Mark Whitmeyer
Keyword(s):  
Bayesian Game ◽  
Monty Hall ◽  
Monty Hall Problem
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