Quiz time

[duckman]

Silent c, this isn't an argument about maths and the real world and about different peoples opinions. I'm really, really, really suggesting that you and your partner try it as it is impossible to convince anybody on this using logic or argument or probability etc. It's just that when you try it, it starts to become clear that switching is obviously the right answer.

Pleasetry it

Whoa there! Please don't mistake the enthusiasm of the particpants in this quiz as an argument. I for one find this problem quite enthralling. And after reading SilentC's lastest post, I think I am now beginning to see where I was going wrong.

The first choice, as Silent has pointed out, IS relevant and I should have been looking at the chances of selecting a goat door and the effect that would have on the odds of selecting the car door on the second guess.

Phew... this is a good one. Please continue..

[simon c]

Duckman - I think silent & I were having an argument, but a good one. It's probably not possible to have this much enthusiasm without it becoming an argument.

This is one of the best puzzles I've ever seen as even though i know the right answer and can explain it mathematically and can see it happen in real life, it still doesn't feel right.

[Tristan Croll]

Here's a really good way to think about this one.

What if, rather than 3 doors, there were 100, 99 of which had goats. You make your choice, and then the host removes 98 of the remaining doors, leaving two. So, in your first choice you had a 99/100 chance of choosing a goat, and only a 1/100 chance of choosing the car. Therefore, you have a 99/100 chance of winning if you switch.

[duckman]

Duckman - I think silent & I were having an argument, but a good one. It's probably not possible to have this much enthusiasm without it becoming an argument.

You're probably right. Of course we could argue about that.

This is one of the best puzzles I've ever seen as even though i know the right answer and can explain it mathematically and can see it happen in real life, it still doesn't feel right.

I think it becomes clear when one looks at from the perspective of the odds of selecting a goat door rather than the car door.

Damn good puzzle in any case.

[silentC]

Was reading some history on this puzzle. It was first 'solved' by Marilyn vos Savant (smartest person in the World apparently, highest IQ anyway).

When she published the answer (2 of 3) she was shouted down by a few mathematicians who said that the answer should be 50/50. The reason is because she never stated the assumption that the host knew which door had the car and that he always gave the contestant the option to choose another door. She later clarified these assumptions.

There's a simulator here: http://planettom.home.mindspring.com/vossavant.htm

[silentC]

I just did 12 trials and got a 50/50 result, which just goes to show that probability is a load of rubbish

[Bob Willson]

I also did a run of 12 trials. Got a 75% success rate when I switched every time.

[silentC]

I should point out that this simulator is using the Javascript math.random function, which is only a simulated random number generator. Computers are incapable of selecting a truly random number. But then game show creators are probably no better at it.

[Tristan Croll]

Well, I did 12 trials and got an exact 2/3 success rate. Just goes to show that I am entirely predictable...

[simon c]

Silent c, if you tried it 12 times and got 50/50 then that shows that statistics is a load of rubbish - which I agree with.

I remember reading something about how many times you have to repeat an event statistically before you can prove/disprove it. In theory, you can't disprove something using statistics because as silent c said in an earlier post, it's possible to throw 100 heads in a row. However, I read somewhere that if you throw a certain number of heads in a row (it may have been as low as 12) then it is more likely that the coin is double headed than it is a random event.

[simon c]

Marilyn vos Savant (smartest person in the World apparently, highest IQ anyway).

I like the way you put a question around the correlation between smartness and IQ. I'm lucky(?) enough to have a very high IQ. Does this make me really smart? No it just means I'm really, really good at those stupid puzzles they put in IQ tests.

[simon c]

Computers are incapable of selecting a truly random number.

Here's a philosophical question. Is it possible to ever pick a truly random number?

PS silent, I'm not picking on you - I'm just enjoying the discussion

[hexbaz]

Wow - what a hornet's nest we've stirred up! Neat simulator! I achieved 65% with 50 tries (switching and sticking alternately; not too scientific). I liked the explanation given by Tristan Croll (100 doors), which really shows how the host's knowledge is skewing the probabilities.

The key to me getting it right was that the host will always show a goat. He will never show that you have won without 'allowing' you to switch. It is this simple fact which screws the mind. Nice to see that it was originally solved by the smartest person in the world.

I got way more clues probably - but then again I a member of Mensa!

As Simon C says, I do not believe that my IQ equates to smartness, and the Mensa entry test in no way tests knowledge - just the ability to work out puzzles. Maybe you should join, Simon! ... But then, like me, you might be accused of being a nerd (as I have been in this very board).

Nice puzzle Simon.

[outback]

I'll take a stab atit, seems no-oune else is game to make a goose of themselves.

As the contestant, with three choices, the chances of picking the car are 1 in three.
The compere will always be able to pick a goat, but this has no bearing on your chances, they are still 1 in three.

Stick, swap, doesn't matter, the chances that you pick a car are one in three.

[hexbaz]

I'll take a stab atit, seems no-oune else is game to make a goose of themselves.

As the contestant, with three choices, the chances of picking the car are 1 in three.
The compere will always be able to pick a goat, but this has no bearing on your chances, they are still 1 in three.

Stick, swap, doesn't matter, the chances that you pick a car are one in three.

Seems you missed the answer amongst the 'debate'. The answer was given way back - read down the last 10 or so posts.

It does matter - and you should switch!