The Monty Hall Problem

[Verbal]

I like this. I posted about it on another board an it has created near meltdown with the conflict of opinion.

Suppose you are on a game show in which you can win a car, and you are given the choice of three doors - behind one door is a car, the others, nothing.

You pick a door, say no.1. The gameshow host, knowing what is behind the doors, then shows you one of the other doors (say no.3) which has nothing behind it.

The gameshow host then asks you if you would like to change your choice to door number 2. Is it to your advantage to switch?

[blurred]

You always change. It's mathematical fact.

3 options, let's call them ABC. For argument's sake we'll say the car is behind A.

If you choose A, he shows you B, you switch to C and you lose.
If you choose B, he has to show you C, you switch to A and you win.
If you choose C, he has to show you B, you switch to A and you win.

Only one of those 3 will be correct from the off, and two will be correct after switching.

Close the thread.

[BWFC_Insane]

You always change. It's mathematical fact.

Close the thread.

Indeed take the change everytime.

Isn't this like known and understood by everyone?

[Prufrock]

Yep change. Fact.

I hate people who write '.Fact.' at the end of things, but in this case it is justified.

It is also another minor reason why I hate people who like Deal or No Deal. Said idiots don't seem to get that in that case it is irrelevant as nobody fecking knows what's in the boxes and it is in fact a game of pure chance played by tosspots 'promising' their boxes will contain high numbers where contestants have a 'system' for going round the room. I'd love to go on, pick box thirteen as my box, then go through the others in numerical order, pausing occasionally to swear at Noel Edmunds, always sticking with my box all the way to the end. That or take the first offer, let's see them make 45 mins of telly from that!

I think I have hate 'issues'. Too many idiots, that's who I blame.

[jimbo]

Yep change. Fact.

I hate people who write '.Fact.' at the end of things, but in this case it is justified.

It is also another minor reason why I hate people who like Deal or No Deal. Said idiots don't seem to get that in that case it is irrelevant as nobody fecking knows what's in the boxes and it is in fact a game of pure chance played by tosspots 'promising' their boxes will contain high numbers where contestants have a 'system' for going round the room. I'd love to go on, pick box thirteen as my box, then go through the others in numerical order, pausing occasionally to swear at Noel Edmunds, always sticking with my box all the way to the end. That or take the first offer, let's see them make 45 mins of telly from that!

I think I have hate 'issues'. Too many idiots, that's who I blame.

I've thought exactly the same for some time. How they have made so many episodes of that crap is beyond me.

[BWFC_Insane]

Yep change. Fact.

I hate people who write '.Fact.' at the end of things, but in this case it is justified.

It is also another minor reason why I hate people who like Deal or No Deal. Said idiots don't seem to get that in that case it is irrelevant as nobody fecking knows what's in the boxes and it is in fact a game of pure chance played by tosspots 'promising' their boxes will contain high numbers where contestants have a 'system' for going round the room. I'd love to go on, pick box thirteen as my box, then go through the others in numerical order, pausing occasionally to swear at Noel Edmunds, always sticking with my box all the way to the end. That or take the first offer, let's see them make 45 mins of telly from that!

I think I have hate 'issues'. Too many idiots, that's who I blame.

I've thought exactly the same for some time. How they have made so many episodes of that crap is beyond me.

Thirded. Its total and utter bollox.

Who watches it? Can only be intellectually challenged individuals.

A while ago a friend of mine was watching it and stating "oOOOOOO he shouldn't have picked that one" at which point I had to leave before I pointed out the complete chance to the pointless game!

[General Mannerheim]

Kevin Spacey poses the same question in the flm '21'

[Montreal Wanderer]

You always change. It's mathematical fact.

Close the thread.

Indeed take the change everytime.

Isn't this like known and understood by everyone?

Blurred clearly understands the principle of restricted choice (he is after all a Liverpool supporter) and explains it clearly. However, it is apparently not generally understood by the contestants (or do they always switch?), or those on Verbal's other board.

[BWFC_Insane]

You always change. It's mathematical fact.

Close the thread.

Indeed take the change everytime.

Isn't this like known and understood by everyone?

Blurred clearly understands the principle of restricted choice (he is after all a Liverpool supporter) and explains it clearly. However, it is apparently not generally understood by the contestants (or do they always switch?), or those on the General's other board.

Its just done the rounds so many times on various internet boards/emails/puzzle games etc! Thought it was well established!

[Verbal]

You always change. It's mathematical fact.

Close the thread.

Indeed take the change everytime.

Isn't this like known and understood by everyone?

Blurred clearly understands the principle of restricted choice (he is after all a Liverpool supporter) and explains it clearly. However, it is apparently not generally understood by the contestants (or do they always switch?), or those on the General's other board.

At the time this problem was posed to Marilyn vos Savant, a fair chunk of PhD mathematicians didn't understand it. Just thought it was relatively interesting when I was watching a show on it last week.

[Montreal Wanderer]

You always change. It's mathematical fact.

Close the thread.

Indeed take the change everytime.

Isn't this like known and understood by everyone?

Blurred clearly understands the principle of restricted choice (he is after all a Liverpool supporter) and explains it clearly. However, it is apparently not generally understood by the contestants (or do they always switch?), or those on the General's other board.

At the time this problem was posed to Marilyn vos Savant, a fair chunk of PhD mathematicians didn't understand it. Just thought it was relatively interesting when I was watching a show on it last week.

That is rather interesting, Verbal. The point that all these PhD's appeared to miss is the fact that the host knows the answer. If the host randomly opened a non-winning door with no foreknowledge the odds would indeed change to 50-50 (of course half the time he would open the winning door and the contestant would immediately switch). Since he knows however, his choice is restricted every time the contestant (2 in three times) picks a losing door. Marilyn might have fared better if she had used blurred's explanation in the first place instead of rattling on about a million doors.

[Prufrock]

Yep change. Fact.

I hate people who write '.Fact.' at the end of things, but in this case it is justified.

It is also another minor reason why I hate people who like Deal or No Deal. Said idiots don't seem to get that in that case it is irrelevant as nobody fecking knows what's in the boxes and it is in fact a game of pure chance played by tosspots 'promising' their boxes will contain high numbers where contestants have a 'system' for going round the room. I'd love to go on, pick box thirteen as my box, then go through the others in numerical order, pausing occasionally to swear at Noel Edmunds, always sticking with my box all the way to the end. That or take the first offer, let's see them make 45 mins of telly from that!

I think I have hate 'issues'. Too many idiots, that's who I blame.

I've thought exactly the same for some time. How they have made so many episodes of that crap is beyond me.

Thirded. Its total and utter bollox.

Who watches it? Can only be intellectually challenged individuals.

A while ago a friend of mine was watching it and stating "oOOOOOO he shouldn't have picked that one" at which point I had to leave before I pointed out the complete chance to the pointless game!

It honestly makes me angry. Fools wasting their life thinking that they can get a 'good feeling' about a box. I have also had somebody, trying to be all clever quote the problem Verbal mentioned, stating that the contestants should always swap their box. A part of my soul died.

[blurred]

It honestly makes me angry. Fools wasting their life thinking that they can get a 'good feeling' about a box. I have also had somebody, trying to be all clever quote the problem Verbal mentioned, stating that the contestants should always swap their box. A part of my soul died.

Do you mean if they are offered a 'switch' on the remaining two boxes after the others have been eliminated?

[Prufrock]

It honestly makes me angry. Fools wasting their life thinking that they can get a 'good feeling' about a box. I have also had somebody, trying to be all clever quote the problem Verbal mentioned, stating that the contestants should always swap their box. A part of my soul died.

Do you mean if they are offered a 'switch' on the remaining two boxes after the others have been eliminated?

That's the one, I think that's what happens anyway. Said person didn't get the difference was that in the Monty Hall the person offering the swap KNEW which box the good thing was in.

[Jakerbeef]

I think I understand this, but are we basing it on the assumption that the presenter is trying to mislead the contestant? What if he's trying to help them?

[Prufrock]

I think I understand this, but are we basing it on the assumption that the presenter is trying to mislead the contestant? What if he's trying to help them?

He can't mislead them, he HAS to take away one of the empty doors, from which point the contestant should always swap.

[mummywhycantieatcrayons]

I think I understand this, but are we basing it on the assumption that the presenter is trying to mislead the contestant? What if he's trying to help them?

He can't mislead them, he HAS to take away one of the empty doors, from which point the contestant should always swap.

Unless, of course, the contestant has a 'feeling' about the box he already has.