Talk:Monty Hall problem/Introduction

This page is intended to help newcomers get up to speed on the issues being discussed on the Monty Hall problem talk page. It is not intended to control the discussion in any way; its purpose is to prevent endless arguments caused by misunderstandings.

The background to the problem is given in the article itself. It is suggested that editors read this before entering into any discussion on the subject.

'''Please do not post arguments or anything contentious here, use the [Talk page] or the [Arguments page]

The Parade statement
The most well known statement of the problem comes from a question asked in the magazine 'Parade'(Krauss and Wang call the Parade statement the standard version).

Several other statements exist including the show on which the problem is based (Let's make a deal), which could be regarded by some as a statement of the problem. In discussions it is important to know what statement of the problem is being referred to.

It is generally presumed that the objective of a player is to win a car.

Problem formulations
For any given statement of the problem it is necessary to decide exactly what the words are to be taken to mean. For most statements of the problem there are some ambiguities over the exact intended meaning.

It could be asked whether the Parade statement is to be taken to state what happens every time or is it just an example of what has happened on one particular occasion. for example, does the host alway open a door, does he always offer the swap, does he alway reveal a goat, how does he choose which door to open when he has a choice?

Some formulations are:

vos Savant's (vS) formulation of the Parade version
This is vos Savant's stated understanding of the the Parade statement of the problem, in which: the goats and cars are initially placed randomly, the host always opens a door that he knows will reveal a goat, he chooses randomly between goat doors when he has a choice, he always offers the swap. As vos Savant put it, 'Pure probability is the paradigm, and we have published no significant reason to view the host as anything more than an agent of chance...'.

Morgan's formulation
Morgan et al carried out a comprehensive analysis of the problem in which they consider the effect of everything that, in their opinion, is not defined with absolute certainty in the question.

One formulation that they mention is the same as vS except that the host does not open a goat door randomly when he has a choice.

Numerical Answers
These are numerical answers to a given problem formulation. For example, in the vS formulation, players who switch have has a 2/3 chance of wining a car.

Solutions
A solution is the process used to determine the probability of a particular outcome. It is possible that a solution could be invalid but still happen to come up with the correct numerical answer.

General agreement
Some things are generally agreed amongst experts and regular editors here.

The answer to the vS problem is that you have a 2/3 chance of winning if you swap and a 1/3 chance of winning if you stick

Disagreements
Items under debate include

Is the vS formulation the 'real' Monty Hall problem?

Is it necessary to use conditional probability for a solution to the vS formulation?