Hostname: page-component-7dd5485656-7jgsp Total loading time: 0 Render date: 2025-10-31T02:57:10.269Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal strategies for the progressive Monty Hall problem

Published online by Cambridge University Press:  01 August 2016

Stephen K. Lucas  and
Jason Rosenhouse
Stephen K. Lucas
Affiliation:
Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807, USA e-mails: lucassk@jmu.edu; rosenhjd@jmu.edu
Jason Rosenhouse
Affiliation:
Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807, USA e-mails: lucassk@jmu.edu; rosenhjd@jmu.edu
Get access Rights & Permissions [Opens in a new window]

Extract

In the classical Monty Hall problem you are a contestant on a game show confronted with three identical doors. One of them conceals a car while the other two conceal goats. You choose a door, but do not open it. The host, Monty Hall, now opens one of the other two doors, careful always to choose one he knows to conceal a goat. You are then given the options either of sticking with your original door, or switching to the other unopened door. What should you do to maximise your chances of winning the car?

Information

Type
Articles
Information
The Mathematical Gazette , Volume 93 , Issue 528 , November 2009 , pp. 410 - 419
Copyright
Copyright © The Mathematical Association 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Isaac, Richard, The pleasures of probability, Springer-Verlag, New York (1995).10.1007/978-1-4612-0819-8CrossRefGoogle Scholar
2. Bapeswara Rao, V. V. and Bhaskara Rao, M., A three-door game show and some of its variants, Mathematical Scientist, 17 (2) (1992) pp. 89–94.Google Scholar
3. Lucas, S. K., Rosenhouse, J. and Schepler, A., The Monty Hall problem, reconsidered, to appear in Maths. Mag. (December 2009).10.4169/002557009X478355CrossRefGoogle Scholar
4. Paradis, J., Viader, P., Bibiloni, L., A mathematical excursion: from the three-door problem to a Cantor-type set, Amer. Math. Monthly, 106 (3) (1999) pp. 241–251.Google Scholar
5. Weisstein, E. W., Derangement, from Math World, A Wolfram Web Resource, http://mathworld.wolfram.com/Derangement.html Google Scholar
6. Efron, B. and Tibshirani, R., An introduction to the bootstrap, Chapman and Hall, New York (1993).10.1007/978-1-4899-4541-9CrossRefGoogle Scholar
7. Havil, J., Gamma, Princeton University Press, Princeton and Oxford (2003).Google Scholar
8. Witte, H.-J., A unification of some approaches to Poisson approximation, Journal of Applied Probability, 27 (3) (1990) pp. 611–621.10.2307/3214545CrossRefGoogle Scholar
9. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (5th edn.), Clarendon Press (1979).Google Scholar
10. Honsberger, Ross, Ingenuity in mathematics, Mathematical Association of America (1970).10.5948/UPO9780883859384CrossRefGoogle Scholar