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Monty Hall

Now I first came across this as a postgraduate. Astrofizz. I was on a night out with Leeds University Maths postgrads. I grokked it first off. I really did and I knew why. The mathematicians (and bear in mind this is the second biggest school after Cambridge in the country) were going up the fucking wall. Many beer mats were scribbled upon especially after a mere computational astrophysical fluid dynamicist nailed it straight off and gave the reason. And bear in mind here that Leeds University was the toppest place in the World for mathematical logic. We had PhD students in da logic who had said “fuck you” to Oxford, Harvard and the Sorbonne and they went absolutely mental over a mere trifle to a physicist and a poker player.

So knock yourself out over the Monty Hall Problem…

BTW the best explanation of the Monty Hall problem I ever read is in “The Curious Incident of the Dog in the Night-Time”.

13 Comments

  1. RAB says:

    I thought you despised Deal or No Deal? :-)

  2. NickM says:

    One is mathematics at it’s purest and the other is Noel Edmonds. The word “cunt” does not suffice for him. But he is an iridium-plated cunt of the first water. To first approx.

  3. NickM says:

    Anyway RAB, what I think about “Deal or no Deal” utterly pales into nonesuch compared to “Geordie Shore” which is epic wank. Let me speak boldly now! I took my gf (now my missus) for a walk many years ago- it’s not far from the house I grew-up in – to the house Mr George Stephenson (like on the fiver) lived in in Wylam. That is a true Geordie. An engineer and a gentleman. Not a collection of fuckwits. Some write Viz, some read it and others it is about. And I have met my share of fat slags. I generally tended to thank the goddess Nike for my running ability. Generally.

  4. dcardno says:

    Funny…
    I am just preparing an in-house training seminar or risk analysis, and solving the Monty Hall problem by way of Bayesian analysis is the capstone. I’ll just have to hope no one sees this blog.
    Oh well – then that’s that taken care of, I guess…
    :)

    Dean

  5. dcardno says:

    or risk analysis” s/b on risk analysis…

  6. NickM says:

    Bayes is good Dean. Truly a scholar and a gentleman. You torture them with Monty! I have seen it reduce PhD pure maths types to tears. Obviously not astrophysicists. We are built of sterner stuff… We know the iron in our very blood is made in the stellar furnace of a dying star. We have seen things they would not believe. And we have dreamed of more.

  7. RAB says:

    I’m feeling playful, so we twp Law Graduates, whose maths is pretty basic (do you know the exam in the Law Society Pt 2 that budding Solicitors fail most first time and have to retake? The Accountancy paper) ask why it isn’t 50% when the first door is opened to reveal the goat?

    It may be 33% when the choice is between 3, but when you are down to two it is a completely different situation surely? And you could have been right all along so always swapping doesn’t seem to make any sense. ;-)

  8. David Gillies says:

    I wrote a Monte (Monty?) Carlo simulation of this to convince Doubting Thomases. It’s in bog-standard ANSI C for a POSIX-compliant system. Source code available on request. A reasonably good random number library is helpful to have (most system-supplied RNGs are awful).

    As a straightforward problem in Bayesian analysis, the probability of winning if we always switch is (1 . 1/3)/(1/2) = 2/3, and the probability if we never switch is (1/2 1/3)/(1/2) = 1/3. If we choose to switch with probability p, then our probability of winning is (1 + p)/3

    The analysis is not hard, just label the doors 1,2,3 (the problem is symmetric under a permutation of doors {1,2,3}) and look at the joint probabilities if the prize is, and is not, behind the initially chosen door. Monty can choose either of the other two doors in the former case, but he has to choose the single door that is neither the original choice nor the one concealing the prize in the latter case. Since the a priori chance of picking the correct door is 1/3, it makes sense to always switch.

  9. dcardno says:

    David – when I first ran into the Monty Hall problem I also ran a simulation (in @Risk, an Excel add-in) since the explanation that came along with the solution was so poor. I got the impression that the guy explaining it to me was just repeating something he had been told (or read), but didn’t really understand; that never makes for a convincing answer. The one in the linked clip is much better.

  10. Michael says:

    I encountered this problem for the first time during a test in part of my Masters Degree. The issue is that people “think” about probability rather than the mathematics. Most people when presented with the problem assume the probability has actually changed to 50:50 when, of course, it has not! Ian Stewart has a nice analysis in “The Magical Maze” and if I remember correctly, used it in the Royal Institute Christmas Lecture.

  11. NickM says:

    David, nice take. Now I have a thingie. And it is in QBasic. Can you crack it? I bet nobody can. I just have to write it.

    Michael, I am currently reading that book oddly enough.

    RAB, the point is Monty has prior knowledge. This queers the pitch. He knows where the car is. And the goats.

  12. RAB says:

    Monty’s queered the pitch has he? So what is all this Maths, Probability theory about then?

    Nick and David, if you’d like to drop in for a game of Roulette some time, my wheel has a powerful magnet under the Double zero. Shirts will be worn, temporarily :-)

  13. Roue le Jour says:

    Monty not only knows where the car is, he also has discretion in offering the swap, which means the problem is 100% psychology and 0% probability.

    You are not playing random chance, you are playing a skilled adversary who doesn’t want to lose the car and will only offer you the swap if he perceives it to be in his interest.

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