Impeccable logic - part 2

[megawatt]

Softus wrote:

(*delete as applicable.)

Great, can we delete all of your last post then please as its nonsense.

Thanks

MW

 

[Softus]

You are ignoring this user. Click here to bypass your ignore and view this post.
Click here to view your entire Ignore list.

I completely agree with that.

 

[megawatt]

 

[tim west]

Thats his way of trying to tell you he has you on ignore.

 

[megawatt]

I already know, he's been ignoring my posts long before the ignore button

Once you take Softy Boy to task a couple of times he ignores you ... It's easier than admitting he's wrong

Nice of him to re-iterate though ... Just in case I'd forgotten.

MW

 

[Trazor]

There's certainly no paradox.

There certainly is. Here it is, within one single post:

( if you think carefully about the above sentence, its all you need to know )

Its a must switch, thanks to Monty removing the goat

If Monty offers the swap, then him having exposed a goat made no difference, other than to confuse people.

Regarding the debate about whether or not Kes' first post on the other topic represented a valid MH scenario, my offer still stands, despite the action of a bored/officious/fascist* moderator.
_____

(*delete as applicable.)

Your response worries me, as it makes no sense what so ever....

It was a gross misrepresentation of my post, any one of average intelligence would follow the logic.

Softus I have to believe that you are pretending to be stupid over this simple problem, other than that you have serious problems.

 

[Softus]

Your response worries me, as it makes no sense what so ever.

OK - just tell me which parts confused you and I'll put it differently. I have no problem with a simple understanding.

It was a gross misrepresentation of my post, any one of average intelligence would follow the logic.

Let's not jump the gun then - if you didn't understand what I wrote then you can't judge whether or not it misrepresented what you wrote.

Softus I have to believe that you are pretending to be stupid over this simple problem, other than that you have serious problems.

And what might those be?

 

[Trazor]

Your response worries me, as it makes no sense what so ever.

OK - just tell me which parts confused you and I'll put it differently. I have no problem with a simple understanding.

It was a gross misrepresentation of my post, any one of average intelligence would follow the logic.

Let's not jump the gun then - if you didn't understand what I wrote then you can't judge whether or not it misrepresented what you wrote.

Softus I have to believe that you are pretending to be stupid over this simple problem, other than that you have serious problems.

And what might those be?

I,m not the one confused, your reply to my post makes no logical sense.

OK Softus, so I can help you out here, tell me which of the following 2 statements do you not agree with....

1) If you STICK with your original choice, a 1 in 3 chance, you will only win the car 33 times out of 99 attempts.

2) If you agree the above statement is correct, then ALWAYS swapping will win you the car 66 times out of 99 attempts.

 

[Softus]

I,m not the one confused, your reply to my post makes no logical sense.

As I've said, if it's a misunderstanding, then let's just clear it up.

OK Softus, so I can help you out here, tell me which of the following 2 statements do you not agree with....

1) If you STICK with your original choice, a 1 in 3 chance, you will only win the car 33 times out of 99 attempts.

I completely agree with that, and always have done.

2) If you agree the above statement is correct, then ALWAYS swapping will win you the car 66 times out of 99 attempts.

I completely agree with that, and always have done.

Do you want me to explain where I think you've misinterpreted what I wrote?

 

[blondini]

Trazor, Softus was 'replying' to Joe-90 who was agreeing with one of your posts. Joe said there was no paradox but your post actually contained one.

 

[Trazor]

Trazor, Softus was 'replying' to Joe-90 who was agreeing with one of your posts. Joe said there was no paradox but your post actually contained one.

I slightly see what you mean, but I consider the 2 statements I made, as complimentary not contradictory.

But again we are side stepping the original issue, which was whether any analogy could be made between the Monty Hall scenario, and DornoD. And obviously no comparison can be made as in Montys game the Host has prior knowledge and uses it.

For any one who believes DornoD is anything other than 50-50 in the swap scenario....Give me the maths please....Not intuition.

 

[Softus]

I consider the 2 statements I made, as complimentary not contradictory.

Yes, but you didn't make only those two statements, you made eight discrete points, and I agree with all except one of of them, viz:

The Monty Hall scenario is quite simple, and the odds can easily be followed......

I agree.

1) Their are 3 doors, your chance of picking the correct door with your first choice is...1 in 3 Therefore you will only win the car 33 times out of 99 attempts, if you stick with your original choice

I agree.

( if you think carefully about the above sentence, its all you need to know )

I agree.

2) So what is the advantage in switching, well we already know that in 2 out of 3 Attempts, the car will be behind the other 2 doors, that you did not choose.

I agree.

Monty now removes the goat for you.

This is true, but irrelevant.

Thus the remaining door contains the car 66 times out of 99.

This is true, but not because a goat was revealed.

Its a must switch...

Yes.

...thanks to Monty removing the goat

No!
________

But again we are side stepping the original issue, which was whether any analogy could be made between the Monty Hall scenario, and DornoD.

I agree. Yours is a succinct summary of the unresolved issue.

And obviously no comparison can be made as in Montys game the Host has prior knowledge and uses it.

This statement is odd. You yourself stated "if you think carefully about the above sentence, its all you need to know" in reference to the 1/3 odds of the first choice being the door with the prize behind it. This means that Monty's prior knowledge has no bearing on the outcome, regardless of whether or not he uses that knowledge.

In the Monty Hall game, the only way Monty can influence the odds is by not offering the swap. He is known to always show a goat instead of a car, therefore showing the goat does not provide extra information. If Monty offers the swap, then the contestant should always take it.

For any one who believes DornoD is anything other than 50-50 in the swap scenario....Give me the maths please....Not intuition.

To me it's very simple:

Let the first box chosen be Box A.
Let the last of the other n-1 boxes be Box B.

At the time of choosing Box A, there is a 1/n chance that it contains the top prize. If n-2 boxes are then opened, all showing the monetary equivalent of a goat, then the probability of the top prize being in Box B is n-1/n.

This is the same probability calculation (not value) as the three doors in Monty Hall : n-1/n == 2/3.

For you to believe that it isn't a Monty Hall scenario, you would have to believe that Monty's knowledge, in the Monty Hall game, has an influence. And your post, trazor, contains the implicit statement that his knowledge has no influence.

QED.

No intuition involved whatsoever. No bluff. No bluster. No insults. No coins. No trick statements. No insisting that the odds are 50:50 and then inventing new scenario variants to attempt to prove a point.

________

The anomaly that people are struggling with, I believe, is that the DoND scenario of £1 and £250K being the only two prizes left with only two boxes unopened is itself an artificial one. This confuses people into comparing Monty Hall with the 'real life' DoND scenario. This comparison is a fallacy.

If you wanted to compute the probability of that artificial scenario arising, then it would be possible, but it's irrelevant because that isn't the question that Kes first posed.

 

[Chud]

On a side note there is a section in Derren Brown's book 'Tricks of the Mind' which outlines this scenario (cups and coins rather than goats and cars though).

According to him after one cup is revealed and you are asked if you want to change your mind then you should always stick - not change...can't remember his exact reasoning behind it but it's sound once you read it.

Anyone interested in this sort of stuff the book is an excellent read and is surprisingly funny.

 

[jackpot]

The Monty Hall scenario is quite simple, and the odds can easily be followed......

I agree.

Quote a softus post in the other thread

'jackpot wrote:
...the actual question is quite basic so there is no need to get technical...

I disagree.

The question, and the Monty Hall paradox that you've cited as proof of your claim that you're right, is far from basic. It has baffled many people over many years, and is an excellent example of a problem where the answer is not the one that most people intuitively believe to be correct.


So Softus first you say the Monty scenario is far from basic but now your saying its quite simple.
Hmmm your contradicting yourself !!!

 

[megawatt]

Softus's last post is total mathematical nonsense because he has committed a schoolboy error and failed to recognise the reduction in odds as every box is opened.

At the time of choosing box A from n boxes
Odds of holding the prize = 1 in n
After the first box is opened, odds of holding the prize = 1 in (n-1)
.
.
After (n-2) boxes have been opened, odds of holding the prize = 1 in (n-(n-2))

= 50:50

Don't ever play poker Softy Boy cos you'd lose your shirt.

MW