Talk:Monty Hall problem/Archive 24

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Canonical assumptions

Instead of the text from K & W, I suggest using the more structured assumptions from Rosenhouse p. 156:

1. The doors were initially equiprobable.
2. Monty never opens the door you initially chose, and he reveals a goat with probability 1.
3. Monty chooses his door randomly whenever he has more than one option.

(It's an actual quote). Tijfo098 (talk) 13:48, 10 April 2011 (UTC)

I think that's a good idea, moreover as long as we focus on the mathematical aspects/ambiguity of the problem citing a math source is more appropriate.--Kmhkmh (talk) 15:36, 10 April 2011 (UTC)

I think 1 is rather vague, we all know what it means but it is not clear. In this subject it is best to make things crystal clear. There is no reason that we cannot state the assumptions in our own words provided that they are all unequivocally supported by reliable sources. Martin Hogbin (talk) 15:34, 10 April 2011 (UTC)

An equivalent formulation of a source content would be fine as long as the editors agree on it.--Kmhkmh (talk) 15:39, 10 April 2011 (UTC)

Yes, 1 could use some clarification. I'll see if I can dig a better source (possibly some other page in Rosenhouse). My WP:OR is that (1) means (1b) the player initially picks the door hiding the car with [equal] probability 1/3. Neither the car placement nor the player's first door choice need to be actually random, as long as (1b) is met. Tijfo098 (talk) 16:46, 10 April 2011 (UTC)

Why not take 1 literally? To wit: every door may hide the car with equal probability. This is a neutral statement that applies regardless of whether it is read as (a) a rule of the game (i.e. a constraint on where the car may be placed before the game is played), (b) the state of knowledge of the player prior to making a choice, (c) the strategy used by the player to make his initial choice (d) (perversely, IMHO) as a long-run frequency of car placements over many games, (e) ...? I may be misinterpreting Rosenhouse here, but I suspect that he chose that form of the statement exactly because it elegantly avoids unnecessary considerations of strategy or, worse, interpretations of probability. glopk (talk) 18:57, 10 April 2011 (UTC)

If you say that the doors are intially equally likely to hide the car, and that Monty is equally likely to open either door when he has a choice, you are being strictly neutral with regard to probability interpretation, but you are already biased to solutions which require full probability assumptions "host side". Many people solve MHP without these assumptions at all, they only assume that their own initial choice was random. Please note that "chooses randomly" is ambiguous, I suppose Rosenhouse (who is not a probabilist or a statistician) means "completely randomly". Anyway "chooses (completely) randomly" biases the reader to the frequentist interpretation. For the subjectivist, the uncertainty is in the mind of the player, not in the brain or action of the host. Richard Gill (talk) 07:47, 11 April 2011 (UTC)

PS, stating assumptions is fine, but do not call them THE assumptions. They are a commonly made set of assumptions, but not unversally made. The simple solutions don't even use all of these assumptions, which means that they are stronger (in the sense of being more widely applicable). Richard Gill (talk) 07:51, 11 April 2011 (UTC)