On the Monty Hall Dilemma and Some Related Variations
DOI:
https://doi.org/10.26713/cma.v7i2.444Keywords:
Game theory, Monty Hall problem, Random number, Decision makingAbstract
The current paper refers to the probabilistic problem posed by Monty Hall dilemma. The classical variation was considered along with two proposed variations on this two round chance game. Random number generators were used to obtain samples for individual games in order to assess the outcome, depending on the strategy employed by the player. An assumption was made and confirmed numerically, that if the decision in the second round is made randomly, the odds become \(1/2\) both ways whereas if the player uses an "always switch” approach, they increase their winning chances - confirming vos Savant's hypothesis. Hence the main conclusions are that there is no mandatory chronological order for the two decision stages and that "stick-or-switch” choice refers to the choice to play the original or the converse game. The dilemma has a wide range of applications from social psychology to other fields of science such as quantum mechanics.Downloads
References
S. Selvin, A problem in probability, Amer. Stat. 29 (1975), 67.
B.D. Kluger and S.B. Wyatt, Are judgment errors reflected in market prices and allocations? Experimental evidence based on the Monty hall problem, The Journal of Finance 59 (3) (June 2004), 969-998.
D. Granberg and T.A. Brown, The Monty Hall dilemma, Personality and Social Psychology Bulletin 21 (7) (July 1995), 711–723, http://dx.doi.org/10.1177/0146167295217006.
S. Krauss and X.T. Stefan, The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser, Journal of Experimental Psychology: General 132 (1) (March 2003), 3–22 http://dx.doi.org/10.1037/0096-3445.132.1.3
A.P. Flitney, P. Adrian and D. Abbott, Quantum version of the Monty Hall problem, Physical Review A 65 (2002).
M. vos Savant, The Power of Logical Thinking, St. Martin's Press, New York (1996).
R. Williams, Course Notes, Appendix D: The Monty Hall Controversy (2004).
Wolfram Inc., http://mathworld.wolfram.com/MontyHallProblem.html, accessed on 01±12/2015.
B.D. McCullough and B. Wilson (2005), On the accuracy of statistical procedures in Microsoft Excel, Computational Statistics & Data Analysis (CSDA) 49 (2003), 1244–1252.
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