Monty-Hall (parameterized strategist-host) Theorem

The Monty-Hall (parameterized strategist-host) Theorem along with a constructive proof is presented, by solving the corresponding Monty-Hall Problem, wherein the host plays a parameterized strategy on the guest.  It establishes the limits on the range of values for the probability of winning the prize.  Eight extreme strategies that have been identified and characterized.  It is shown that there does not exist any strategy 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.  The classical Monty-Hall Problem is a special case with zero-value for each of the three perturbation parameters. This is a refutation of the position held by the leading subject matter experts, that a switched-choice always provides an enhancement on the probability of winning the prize in the classical case. The clearly partitioned three-dimensional discrete event(sample)space along with the corresponding apriori probabilities presented as the input data set is a fail-safe framework to study, analyze and solve the problem; with no possibility of missing any relevant component terms or including any irrelevant ones, while going through the required calculations in order to derive the desired results.