Can you answer this veridical paradox?

mervyn · May 11, 2020

I want you to imagine 3 green doors. Behind two of the doors is a donkey. Behind a third door is a Ferrari. You don’t know which is which. You are invited to choose a door. If you are lucky you win the Ferrari, if not, a donkey. Please make your selection.

Before we open your door, I open one of the other doors to reveal a donkey. There are now two doors left, your choice and one other. Before I open your door I give you the opportunity to change your mind. You can either stick with your original choice, or change to the other door. Which should you do?

(I'm)Stranded · May 11, 2020

My head hurts....

GreenThing · May 11, 2020

It depends on whether my original choice was also your original choice. If it was, I’d be daft not to change my mind.

Pogleswoody · May 11, 2020

Unless you have opened the middle door to reveal the donkey, I would open the door at the opposite end.
If the donkey were behind the middle door I'd know whether I saw it's head or it's rear so would take the door 'beyond' it's head. There is, after all, only 'a' single donkey behind two doors? :think:

mervyn · May 11, 2020

Pogleswoody":3k8c2kb0 said:
Unless you have opened the middle door to reveal the donkey, I would open the door at the opposite end.
If the donkey were behind the middle door I'd know whether I saw it's head or it's rear so would take the door 'beyond' it's head. There is, after all, only 'a' single donkey behind two doors? :think:

Sorry, I should have worded it better. There are definitely two donkeys, each behind their own door.

Neilio · May 11, 2020

You always take the opportunity to switch in that scenario!

mervyn · May 11, 2020

Neilio":46viu0bb said:
You always take the opportunity to switch in that scenario!

But why bother, if common sense/logic tells you whatever the choice it’s 50:50?

xmastree · May 11, 2020

mervyn":14t9pwxj said:
Neilio":14t9pwxj said:

You always take the opportunity to switch in that scenario!

Click to expand...

But why bother, if common sense/logic tells you whatever the choice it’s 50:50?

I would switch. Before my first choice it's a straight one in three. You then had a one in two, but by ignoring the door that neither of us has chosen you have strengthened the case for the Ferrari being behind that ignored door. Does that make any sense ?I'm not convinced it does!

xmastree · May 11, 2020

mervyn":6rspurpb said:
Neilio":6rspurpb said:

You always take the opportunity to switch in that scenario!

Click to expand...

But why bother, if common sense/logic tells you whatever the choice it’s 50:50?

I would switch. Before my first choice it's a straight one in three. You then had a one in two, but by ignoring the door that neither of us has chosen you have strengthened the case for the Ferrari being behind that ignored door. Does that make any sense ?I'm not convinced it does!

Lousy Pint · May 11, 2020

When you first choose one of the three doors, you have a 33.3% chance of getting the Ferrari.
When one donkey is revealed, the other door has then a 50% chance of being the Ferrari, while your chosen door is still in effect 33%.
So I guess you should change.

... or something like that.

roblem:

mervyn · May 11, 2020

Lousy_Pint":45i265hz said:
When you first choose one of the three doors, you have a 33.3% chance of getting the Ferrari.
When one donkey is revealed, the other door has then a 50% chance of being the Ferrari, while your chosen door is still in effect 33%.
So I guess you should change.

... or something like that. roblem:

You and Xmas tree are spot on. By switching you double your chances of success from one in three to one in two. Large scale computer programmes have been run to prove this. I’ve known this conundrum for years, but only today learned that it’s called a veridical paradox. Basically the name for an answer to a puzzle that seems to defy common sense or logic.

German Shepherd · May 11, 2020

Surely it's 50-50 so wouldn't make a difference if you swapped or not. But that's too obvious I suppose.

davie nine · May 11, 2020

I’d keep to my original selection as you wouldn’t have offered me a swap if my first choice was wrong.

Emeraldinho · May 12, 2020

You’d better pray you can afford the insurance and road tax too. :silent:

davegreenarmy · May 12, 2020

Change your mind. At the start the odds of picking the correct door are 33%, and 66% chance of you picking the wrong one.

Those odds don't change just because it's now been reduced down to 2 doors - there's still a 66% chance you were wrong with your original choice so you should always swap.

Derren Brown did a similar thing and explained it well

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Can you answer this veridical paradox?

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