Horizon maths show

[Jojo Apollo]

Tonight BBC2 9pm

Just a reminder for maths fans. Here's a preview:http://news.bbc.co.uk/1/hi/education/7968997.stm

[Michael Wallace]

Oh god not him again.

[Ben Hunter]

Oh god not him again.

Yeah Jojo, stop posting already .

[Jojo Apollo]

Oh god not him again.

Yeah Jojo, stop posting already .

Quite interesting show it was.

[Kirk Bevins]

Quite interesting show it was.

Yeah, I haven't watched the TV for literally ages (I only ever watch Countdown and that's via 4od on the internet) so was good to sit with my housemates in the living room again for an hour watching it. Was really good. Good to see the Monty Hall problem being mentioned but I hate anything mentioned with 4 dimensions in. It's odd.

[Rosemary Roberts]

I hate anything mentioned with 4 dimensions in. It's odd.

Surely five dimensions would be odder?

[Jojo Apollo]

Quite interesting show it was.

Yeah, I haven't watched the TV for literally ages (I only ever watch Countdown and that's via 4od on the internet) so was good to sit with my housemates in the living room again for an hour watching it. Was really good. Good to see the Monty Hall problem being mentioned but I hate anything mentioned with 4 dimensions in. It's odd.

First time I've seen that particular problem, really tricky at first to get your head round why it is better to switch (well for me at least). There's a wiki page on it: http://en.wikipedia.org/wiki/Monty_Hall_problem which helps explain it more.

[Charlie Reams]

Good to see the Monty Hall problem being mentioned

Yeah, I think that's the best handling of the problem I've ever seen. I particularly liked it when Alan wouldn't believe Marcus, and rather than get all uppity, Marcus was just like "okay, let's see." A great demonstration of the power of rational logic -- unlike homeopathy, Hinduism and haunted houses, it works even if you don't believe in it. Although Alan was still pretty unlucky to win 2/20...

[Kieran Child]

The Monty Hall problem is good, so long it's worded correctly.
Unfortunately, the way it was worded on the show, in an abstract situation, the better option would be to stick.

In order for the better option to be change, and all the analysis to be valid, the quizmaster has to declare, before any of the three is picked by the contestant, that he will reveal a goat afterwards.

The animators also got pi and the Navier-Stokes equations wrong, but that's just me nitpicking.

The show itself was very good I thought.

If you liked it, I highly recommend "how long is a piece of string?" and "why do busses come in threes?" which is in the same vein of interesting mathematics with very few numbers.

[Phil Reynolds]

In order for the better option to be change, and all the analysis to be valid, the quizmaster has to declare, before any of the three is picked by the contestant [my italics], that he will reveal a goat afterwards.

Surely that's not the case? All he has to do is let the contestant choose a door, then say, "Now, before we see what you've won, I can tell you that I happen to know that behind this door is a goat," and open one of the other two doors. The analysis hinges only on the host revealing a goat that he knows to be there (as opposed to opening one of the other two doors at random) and then offering the switch, not on the contestant being informed of this in advance of the game.

[Jon Corby]

In order for the better option to be change, and all the analysis to be valid, the quizmaster has to declare, before any of the three is picked by the contestant [my italics], that he will reveal a goat afterwards.

Surely that's not the case? All he has to do is let the contestant choose a door, then say, "Now, before we see what you've won, I can tell you that I happen to know that behind this door is a goat," and open one of the other two doors. The analysis hinges only on the host revealing a goat that he knows to be there (as opposed to opening one of the other two doors at random) and then offering the switch, not on the contestant being informed of this in advance of the game.

I didn't see the show, but Kieran's right in what he's saying if the rules weren't clearly laid out beforehand. If the host decides to show a goat on a whim, you can't draw the same conclusions. For all you know, he may have just happened to see backstage that that particular box held a goat, and thought he'd spice things up a bit by showing you. Had you picked that box, he wouldn't have done so etc etc. The rules need to be in place at the start of the game. I guess you could say that it doesn't matter if they aren't revealed to the contestant until after he has chosen his box, but you're getting into silly detail then, as the contestant does need to be assured of this for the analysis to be correct.

(I don't agree that sticking is ever "better" though actually - it might not be worse.)

[Paul Hammond]

I don't think time would have allowed them to set out the necessary conditions beforehand, but I think most people would assume that Monty Hall knows what's behind all the doors and will always reveal a goat behind a non-picked door. I think Phil's right that he doesn't need to declare this before the contestant chooses, though. He can just say, "I already knew what was behind the doors, and look, here's a goat that you didn't pick."

I was kind of hoping they'd do that nice demonstration of the counter-intuitive result, the variation where there are a million doors and Monty reveals 999,998 unpicked goats. In that scenario, it's obvious that you should swap.

[Phil Reynolds]

I didn't see the show, but Kieran's right in what he's saying if the rules weren't clearly laid out beforehand. If the host decides to show a goat on a whim, you can't draw the same conclusions.

I take your point that the contestant needs to be aware that the host was always going to do that, regardless of which door the contestant picked first (which is what I was attempting to convey with my wording of the host's patter). My point remains that the contestant doesn't have to be told the rules before picking a door; but, as I've probably just demonstrated, it's a lot clearer if she is!

And yes, even if you were unconvinced about the maths, you might as well switch since even people who get the maths wrong still think it's a 50/50 choice. The extraordinary thing is that there are some people whose intuition will tell them that seeing one of the other doors opened to reveal a goat somehow adds to the likelihood that their first choice was correct, and will stick fervently. (This basic human stupidity is, of course, exploited daily on Deal or No Deal.)

[Jon Corby]

I think Phil's right that he doesn't need to declare this before the contestant chooses, though. He can just say, "I already knew what was behind the doors, and look, here's a goat that you didn't pick."

The contestant still needs to be assured that he was always going to do that though, so the most sensible way to achieve this is to lay the rules out at the start.Otherwise, is the host just trying to steer you because you have actually picked the right box, or the wrong one? etc etc.

[Jon Corby]

The extraordinary thing is that there are some people whose intuition will tell them that seeing one of the other doors opened to reveal a goat somehow adds to the likelihood that their first choice was correct, and will stick fervently. (This basic human stupidity is, of course, exploited daily on Deal or No Deal.)

Oh hell yeah, I've had some epic internet arguments around this game. I did try to start one here, but everyone was too damned sensible for it to get going.

[Paul Hammond]

I think Phil's right that he doesn't need to declare this before the contestant chooses, though. He can just say, "I already knew what was behind the doors, and look, here's a goat that you didn't pick."

The contestant still needs to be assured that he was always going to do that though, so the most sensible way to achieve this is to lay the rules out at the start.Otherwise, is the host just trying to steer you because you have actually picked the right box, or the wrong one? etc etc.

You're right. So stating the rules beforehand is more of a practicality than a necessity, for the analysis to be valid.

[Jon Corby]

You're right. So stating the rules beforehand is more of a practicality than a necessity, for the analysis to be valid.

Well the rule needs to be in place beforehand, so it needs to be stated in some way. So it seems overkill to present the puzzle by stating the rule first (but not to the contestant), and then repeat the rule so the contestant can hear once they've picked their box (also somehow giving them 100% assurance about the rule existing at the start of the game before they picked their box)

But, whatever, I think we all understand each other.

[Julie T]

Very interesting programme. They missed a trick, though.
They should have had the top Maths bod from the University of Hertfordshire as the expert.
He was but a humble lecturer when I was doing my Maths degree there, but now he is Professor Alan Davies.

[Phil Reynolds]

Very interesting programme. They missed a trick, though.
They should have had the top Maths bod from the University of Hertfordshire as the expert.
He was but a humble lecturer when I was doing my Maths degree there, but now he is Professor Alan Davies.

Ha. Might have been a bit confusing I suppose. Several of my maths courses at uni were taught by Ian Stewart, who is with doubt the most brilliant populariser of maths I've ever encountered. His lectures were always hugely entertaining - I used to look forward to them all week.

The programme sounds good, wish I'd watched it now. I'll try and catch it on iPlayer some time.

[Kieran Child]

About the necessity of the rules being layed out beforehand:

You're on a gameshow. You pick a door.

You don't know the rules of this gameshow. They could be flexible.

Is it a fair assumption that the host doesn't want you to get the car?

If it is, then any sane host would let you open that door if it had a goat. There's no point in complicating the game, because it just gives you more chance of getting the car.

If you picked a goat, he would let you keep the goat.

But instead, he's given you the option to change. If he doesn't want you to get the car, he would only do this in the situation where you have chosen the car. So you should almost definitely stick.

This is the answer to the monty hall problem as it was given on the show. If the rules are layed out beforehand, then it does become twice as good to switch than stick.

Another assumption that needs to be stated in the correct stating of the problem (which was correctly stated in the show) is that the gameshow host KNOWS where the prizes are. If he doesn't, and you pick a door, then he shows a goat behind another, very annoyingly, it is now 50/50 I'll explain the maths behind that if people don't agree, because once you've seen the mathematical logic behind the proper problem, this scenario then seems counter-intuitive.

[Gavin Chipper]

About the necessity of the rules being layed out beforehand:

You're on a gameshow. You pick a door.

You don't know the rules of this gameshow. They could be flexible.

Is it a fair assumption that the host doesn't want you to get the car?

If it is, then any sane host would let you open that door if it had a goat. There's no point in complicating the game, because it just gives you more chance of getting the car.

If you picked a goat, he would let you keep the goat.

But instead, he's given you the option to change. If he doesn't want you to get the car, he would only do this in the situation where you have chosen the car. So you should almost definitely stick.

Exactly. There are cases where it would not be worse or even equal to stick, but better.

[Jon Corby]

Exactly. There are cases where it would not be worse or even equal to stick, but better.

Hmmm, sure I suppose, but only if you're correctly second-guessing the host's motives. He might want you to win for all you know, it's not like the star prize comes out of his pocket. (I stress again that I didn't see the show to see exactly how it was presented)

[Jason Larsen]

I thought Carol Vorderman was going to be the star of that show!

[JackHurst]

I liked that show.

I went to see a lecture by Marcus De Sautoy last week in which he said the same stuff about the fourth dimension as he did on the show. He was quite entertaining, and even tho i only have a GCSE in maths, he still made the lecture accessible enough for me and others at my level of maths.

Although he did get Muse and Elbow mixed up, what a fool.