The Remarkable Story of Math's Most Contentious Brain Teaser
This is the first book to provide a comprehensive treatment of the Monty Hall Problem, one of the most famous brainteasers in mathematics. Its deceptive simplicity has fooled countless mathematicians. In addition to a thorough mathematical discussion of the problem, this book surveys the professional literature in a variety of disciplines.
Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.
PREFACE; ACKNOWLEDGMENTS; 1. Ancestral Monty; 2. Classical Monty; 3. Bayesian Monty; 4. Progressive Monty; 5. Miscellaneous Monty; 6. Cognitive Monty; 7. Philosophical Monty; 8. Final Monty; APPENDIX: A GALLERY OF VARIATIONS; BIBLIOGRAPHY; INDEX