# Re: [R] Monty Hall simulation

From: Farley, Robert <FarleyR_at_metro.net>
Date: Mon, 12 May 2008 11:03:14 -0700

The common "Monty Hall" problem (where the MC helps out the contestant) is not random! See: http://en.wikipedia.org/wiki/Monty_Hall_problem

My edits were removed as I had no references. :-(

Maybe you can verify my statements, included below. :-)

Another analysis considers three types of hosts and three prize levels. The Benevolent Host always shows the worst remaining prize after you choose, the Random Host randomly picks a remaining door to show, and the Malevolent Host always shows the best remaining prize. The prizes are bad, middle, best; e.g. Goat, Luggage, Car. The Player is unaware of which prize is which. He may expect to be choosing among Pigs, Goats, Blenders, Luggage, Cars, and Houses.

If you always switch, the results for each host are:

Results after switching, expanded behaviors

```Host V /Prize -> 	Bad 	Middle 	Good
Benevolent Host 	0% 	33% 		67%
Random Host 		33% 	33% 		33%
Malevolent Host 	67% 	33% 		0%

```

If each host were equally likely, the total probability for each prize would be 33%-the same as not switching. Without knowing the type of Host and the prize mix, you can make no meaningful statement about the success of a switching strategy.

The only way for a Player to "improve the odds" is if he or she can get some meaningful information from the prize shown. I.e., if you know what the three prizes are and what type of Host you have, then you can develop a winning strategy. If you were wrong about either the Host or the prize mix, that strategy may be harmful.

Robert Farley
Metro
www.Metro.net

-----Original Message-----
From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On Behalf Of Johannes Huesing Sent: Sunday, May 11, 2008 01:26
To: r-help_at_r-project.org
Subject: Re: [R] Monty Hall simulation

cirrus74 <cirrus74_at_hotmail.com> [Sun, May 11, 2008 at 03:44:46AM CEST]:
>
> Is it possible to simulate the Monty Hall problem using R? If so, could
> someone please show me how? Thanks for any help rendered.

To my mind,

niter <- 999
prize <- sample(c("car", "car", "goat"), niter, replace=TRUE)

would be a perfect simulation.

```--
Johannes Hüsing               There is something fascinating about science.
One gets such wholesale returns of conjecture
mailto:johannes_at_huesing.name  from such a trifling investment of fact.
http://derwisch.wikidot.com         (Mark Twain, "Life on the Mississippi")

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and provide commented, minimal, self-contained, reproducible code.

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