Talk:Monty Hall problem/Sources

Morgan et al

Morgan, J. P., Chaganty, N. R., Dahiya, R. C., & Doviak, M. J. (1991). "Let's make a deal: The player's dilemma," American Statistician 45: 284-287.

Problem formulation

In what Morgan refer to as the vos Savant scenario the host always reveals a goat. Although not explicitly stated the assumption implicit in the calculations (and confirmed by a later remark) is that the car is initially placed uniformly at random

Points made

• The question is asked after Monty has opened a door to reveal a goat.
• The solutions of vos Savant and Mosteller are false.
• In general we cannot answer the question 'What is the probability of winning if I switch given that I have been shown a goat behind door 3. This probability can be expressed as 1/(1+q) where q is the probability that the host opens door 3 when the car is behind door 1.
• The problem asked (by Whitaker) has to be solved by calculating conditional probabilities.

Rosenthal

Monty Hall, Monty Fall, Monty Crawl

Problem statement

A car is equally likely to be behind any one of three doors. You select one of the three doors (say, Door #1). The host then reveals one non-selected door (say, Door #3) which does not contain the car. At this point, you choose whether to stick with your original choice (i.e. Door #1), or switch to the remaining door (i.e. Door #2). What are the probabilities that you will win the car if you stick, versus if you switch?

Also many problem variants

Points made

• Unconditional solution is, 'correct, but I consider it "shaky" because it fails for slight variants of the problem'.

Eisenhauer

The Monty Hall Matrix

• 'Without making some assumptions, at least implicitly, about the host's behaviour, even the basic three-door problem would be insoluble'.
• If Monty randomly reveals a goat, the probability of the car being behind door 1 is independent of the door opened by the host
• The 'no news' argument relies at best on an unstated assumption (They do not say what this is, presumably that the host chooses a random goat door)
• Vos Savant's answer was unconvincing and misleading.

Lucas, Rosenhouse, and Schepler

The Monty Hall Problem, Reconsidered

Selvin

Selvin has special status amongst sources as being the originator of the problem in a letter to the American Statistician and the originator of the name 'Monty Hall problem' in a second letter to the same journal.

Problem statement

Selvin originally states the problem in the form of a dialogue.

Points made

• In his original letter Selvin provides a clearly unconditional solution, in that the two possible doors that the host might open are considired together.
• In his second letter Selvin makes clear that the host chooses between goat doors at random.
• In his second letter Selvin gives an alternative conditional solution to show that his original answer was correct.
• Selvin does not say that the unconditional solution is wrong or incomplete.