Impeccable logic

[Kes]

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 £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.

 

[JohnD]

choose the other box.

the first one you chose was 20 to 1 against for the big prize.

If you choose again it's now even money on the other one.

 

[ColJack]

oh this stuff hurts my head..

at the time of the swap offer, it's even movey you have the right box, but even money the other one is the right box..

 

[joe-90]

There is no difference. Random chance says there will be the big prize in one box but not the other, so the odds are 50-50.
It makes no difference what has gone before as chance has no memory.
As an illustration, you can toss a coin 100 times and get heads every time - yet the odds of tossing the coin for the one hundred and first time and getting heads is still 50-50.

 

[tim west]

unless you have a rigged coin, not suggesting for one minute that deal or no deal is rigged of course

 

[Softus]

Originally I thought this wasn't analogous to the Monty Hall scenario, because the host has no knowledge of the boxes' contents.

However, the odds of the desired prize being in the set of 19 (when they're whittled down to 1) is always greater, therefore swapping increases the odds of winning that prize.

 

[Thermo]

this is going to do my head in! i see what you are saying softus, but surely once its down to the two boxes its 50-50 isnt it, regardless of what went on before? (my head hurts already!)

 

[Trazor]

this is going to do my head in! i see what you are saying softus, but surely once its down to the two boxes its 50-50 isnt it, regardless of what went on before? (my head hurts already!)

Exactly right...........If a stranger was brought into the studio, with no previous knowledge of what had occurred before, then their chance of selecting the box is 50-50.
Previous knowledge is irrelevant.

 

[Hysteresis]

I am sure Joe 90 can squeeze Schrodinger's Cat into this argument some where, albeit irrelevant.

 

[tim west]

I am sure Joe 90 can squeeze Schrodinger's Cat into this argument some where, albeit irrelevant.

They don't allow posts about cruelty to animals on here im afraid.

 

[ColJack]

that the quantum physics cat?

stuck in sealed room with a can of poison released buy the decay of a sub-atomic particle?

at any given time the cat is both dead and alive until observed by an outside source..

 

[tim west]

that the quantum physics cat?

stuck in sealed room with a can of poison released buy the decay of a sub-atomic particle?

at any given time the cat is both dead and alive until observed by an outside source..

You cruel heartless barsteward, I hope you get your cumuppence how could you treat a poor defenceless cat like that!

 

[Hysteresis]

that the quantum physics cat?

stuck in sealed room with a can of poison released buy the decay of a sub-atomic particle?

at any given time the cat is both dead and alive until observed by an outside source..

That is the very Fella.
Similar to the original Argument really, there is both £1 and £250,000 in the box, until it is opened and observed. A bit preverse I know.

Joe 90 must be asleep to day or maybe a bad night last night!!!!!!

 

[tim west]

But how can you know that the 1 or 250k are actually in the boxes without seeing them?
You really are putting your trust in the producers hands

 

[Hysteresis]

But how can you know that the 1 or 250k are actually in the boxes without seeing them?
You really are putting your trust in the producers hands

A bit irrelevant really Tim. You will know when the boxes are opened!
But Schrodinger didn't really put a Cat in the box with a Phile of poison.