Impeccable logic - part 2

[megawatt]

Jackpot wrote:

You surprise me Softus on your condesending and contradictary posts

Really

No surprise at all to me Jackpot ... It's his trademark. He just likes everyone to think that he's wading in as the voice of reason with his underpants outside his trousers.

That's why he's posting both as himself and as Observer.

This thread has all the hallmarks of the never ending story

MW

 

[Observer]

Perhaps so, but so is a bunch of other h*rseshit and colourful new scenarios that have nothing to do with the OP, which is why I was hoping you'd provide a brief statement that defines the point on which you and jackpot disagree.

After all, if you can't even agree what it is that you disagree about, what hope is there is resolving that difference and coming to any agreement? None - that's what I say, and at the moment you're just trading mildly condescending posts without any party attempting to see anyone else's point of view.

The contentious issue was restated. What's the problem?

The assertion is that the probability of the contestant's box holding the prize, which is 1 in 20 at the time it is chosen, reduces as boxes from the other group of 19 are eliminated. That is wrong.

You say it's wrong, but in one of your very recent posts you appeared to agree with it. Still, at least now we know that you think it's wrong.

That's what I've been saying consistently over the last few pages. I have not simply asserted it, I've laid out the mathematical theory and provided illustrations.

....in the MH game, switching gives a 2 in 3 probability of success.
.
.
.
The same principle applies to DOND.

IMHO, this is the whole crux of the argument. There are those who believe that same principle applies, and those who don't. And yet I haven't seen anyone who thinks it's different give a reasoned, dispassionate, non-insulting, explanation of why it's different - more often than not the attempt includes yet another scenario involving goats, coins, doors, audiences, and Uncle Tom Cobbly.

The same principle does apply and I have explained it several times. I don't think I have been insulting - possibly less patient than a saint.

]I have (several times, first here) agreed that in the narrow circumstances of the OP, if it is stipulated that the £1 box and ONLY the £1 box can be the 'other' box, then 50:50 is correct.

I wish I'd read this before typing some of the above. Now I'm completely lost as to whether or not you agree with the OP.

The OP said:

OK, in a particularly moronic moment you apply to go on Deal or no Deal, and surprisingly you are accepted. When the moment comes, you chose a box (out of 20?) and by a combination of blind chance and good fortune, whittle the lot down to two boxes, yours and one out there. The boxes have in them £250,000 and (say)£1. The banker, being possessed of malicious humour, offers you the swap. You think for a few moments, this time using impeccable logic. What should you do to maximise the chance of choosing the £250k box?

Apologies to Monty Hall.

I have added the word (say) as it appears to me that the object of the post was to invite a debate on whether there is any merit in switching or not switching where the game has come down to two boxes, one the £250k prize and (any) one other (the reference to Monty Hall tends to show that). If all the other boxes contained £1, the switch strategy works. If the 'other' box, instead of being the ONLY £1 box, was <any other box with a lesser prize>, the switch strategy works

]At the same time, in a real game scenario, where there is an equal probability that any of the other 'losing' boxes is the other box when it comes down to the final two, the probability that a switch secures the £250k prize is 0.95.

Why are you even writing about a real game scenario, when the OP is so clearly not about that?!

"Realistic" may have been better. Anyway, there is no possible practical benefit and little academic interest in knowing that what appears at first blush to be a 50:50 chance of winning a prize is, mathematically, a 50:50 chance. There is a huge potential practical benefit, and a lot of academic interest, in knowing that a particular strategy converts what appears at first blush to be a 50:50 chance of winning a prize to a 19 in 20 chance.

That is simply proved by the thought experiment I suggested, where we see that the 'always switch' strategy will always secure the £250k prize except where our first box holds the £250k prize (which will occur 1 in 20 times).

Oh well, if you've proved something then it must be right.

No-one has found (or stated) an argument to counter the thought experiment. It is a simple and imo compelling proof of the mathematical theory (you will note that it perfectly reconciles to the theoretical mathematical probabilities that I argue actually apply).

 

[megawatt]

After that little lot is anyone still in doubt that Softus and Observer are one and the same?

 

[jackpot]

Multiple personality springs to mind!!

 

[megawatt]

Attilla the Hun + Pol Pot + Delusions of Stephen Hawking I think

 

[johnny_t]

I'll say this again in case it was missed the first two or three times - in the OP, I agree the 50:50 analysis is correct IF but only IF:

(i) there is only one £1 box in the 20

(ii) you stipulate that the £1 box and no other losing box must be the 'other' box in the end game.

This is exactly the scenario we are discussing though, isn't it ? When you end up with two boxes, you have two known values.

The fact that they are £1 and £250k in this case has no real significance beyond an emotional one, and we could be talking about any two values, but it still remains 50:50

 

[Trazor]

The fact that they are £1 and £250k in this case has no real significance beyond an emotional one, and we could be talking about any two values, but it still remains 50:50

Correct, and to add we could be talking about any 2 boxes as well.
To much significance is given to the contestants box, it is but one box, among however many are left, and its odds should be worked out in exactly the same way as all the other boxes.

 

[Bahco]

Has anyone come to the correct conclusion and got the definitive answer as the suspense is killing me!

 

[oompah]

Has anyone come to the correct conclusion and got the definitive answer as the suspense is killing me!

If you read all the post every body has come up with the correct solution.I think there as only been one winner of the £250k on dond so the next winner will probaly be some one posting on here or someone reading it.

 

[megawatt]

I'd say this thread has run its course as, despite overwhelming discussion and evidential postings by many individuals, no clear outcome has surfaced which everyone will agree with.

Such is life.

MW

 

[Bahco]

Watch out for Impeccable Logic PART 3 appearing at a forum near you.

 

[blondini]

I've enjoyed this thread. It has been thought provoking and entertaining, and I'm not ready to give up on it yet. They certainly didn't call MH a paradox for nothing.

It was a right royal PITA that the original was locked so lets not give the mods any excuses.

 

[megawatt]

I too have enjoyed the discussion I was just reflecting on the fact that, despite many seemingly conclusive posts, we are no closer to an agreement now than when the first topic was started

 

[jackpot]

Agreed. Its actually given something entertaining to think about and by the size of the thread(s) has given a much debatable subject.

I wish there was more threads like this that we could discuss/debate on here as ive quite enjoyed it.

 

[tim west]

What if the boxes where on a moving conveyor belt and.....