Monty-Hall (classical-host) Theorem and Monty-Hall (strategist-host) Theorem

Monty-Hall (classical-host) Theorem and Monty-Hall (strategist-host) Theorem

Dr.(Prof.) Keshava Prasad Halemane,

Professor - retired from

Department of Mathematical And Computational Sciences,

National Institute of Technology Karnataka Surathkal,

Srinivasnagar, Mangaluru - 575025, India.

https://orcid.org/0000-0003-3483-3521

Independent Researcher (no funding)

SASHESHA,  8-129/12  Sowjanya Road, Naigara Hills,

Bikarnakatte, Kulshekar Post,

Mangaluru-575005. Karnataka State, India

https://www.linkedin.com/in/keshavaprasadahalemane/

k.prasad.h@gmail.com

ABSTRACT

The Monty-Hall (classical-host) Theorem is presented along with a constructive proof by solving the classical Monty-Hall Problem.  It establishes the fact that the probability of winning the prize is unaffected by a switched-choice; unlike the most prevalent and widely accepted position held by the leading subject matter experts.

A parameterized supermodel is presented, with the associated generic Monty-Hall (strategist-host) Theorem, along with a constructive proof, by solving the corresponding Monty-Hall Problem, wherein the host plays a generic parameterized strategy on the guest.  This model subsumes the Monty-Hall (classical) Problem.  It establishes the limits on the range of values for the probability of winning the prize, with or without a possible switched-choice.  Eight extreme strategies have been identified and characterized.  It is established that there does not exist any strategy, that a strategist-host may play on the guest, which would result in a situation wherein a switched-choice will always (irrespective of the placement of the prize and irrespective of the initial-choice of the guest) lead to an enhancement in the chances of winning the prize for the guest.

The clearly partitioned three-dimensional discrete event(sample)space, with the twelve mutually-exclusive together-exhaustive possible alternatives, along with the corresponding apriori probabilities, presented as the input data set, is a fail-safe framework to study, analyze & solve the problem; with no possibility of missing any relevant component terms or including any irrelevant component terms, while going through the required calculations in order to derive the desired results.

Keywords:    Monty-Hall (classical-host) Theorem;

                  Monty-Hall (strategist-host) Theorem;

                  Monty-Hall Theorems; Bayes-Price Rule; Bayes Theorem;

                  Discrete Event (Sample) Space;

                  Parameterized Strategy; Perturbation Parameters;

AMS MSC Mathematics Subject Classification:    60A99; 60C99; 62A99; 62C99.