I have three cups and a £50 note!

Ok everyone. I have a bit of a teaser for you. Try not to cheat, we can argue about the correct answer in a couple of days but for now give me your answers and tell me why.

Here goes...

Ok I have three cups and a £50 note. The money is under one of the cups. The game is simple. You have to guess which cup it is under. Cup 1, cup 2 or cup 3. Make your choice. After you choose a cup I then turn over one of the other 2 cups, showing it to be empty.

Now there are 2 cups left, the one you picked and one you didn't. Under one of the cups is £50.Now you can either stick with the one you chose or change your mind.

This is the test. Should you stick or swap to give yourself the best chance of winning?

Swap. I'll say why after more people have responded.

Interesting. Yeah. Good idea. Everyone give a stick or swap answer before thay say their own reason why. Then we can compare notes afterwards.

Swap.

(the theory is based on that American Quiz show)

This was discussed in some detail on BA recently, and is also the subject of a chapter in the contemporary classic novel The Curious Incident of the Dog in the Night Time by Mark Haddon. It was also covered on the TV show Mythbusters.

Intuitively it appears to be a 50/50 choice, and because people are stubborn, they tend to stick with their original choice.

Accounting for variable change, if you stick, you have the original 1/3 chance that you chose the correct cup in the first place. However, if you swap, you actually have a 2/3 chance that the cup you have swapped to has the £50 note in all along, because the host of the game knows where the £50 note is and has lifted up one of the two cups he knows the £50 is not under.

This falls under a branch of mathematics known as game theory, popularised in the late twentieth century by John Forbes Nash, and this specific puzzle is called The Monty Hall Problem, named after a similar scenario on a US game show involving a series of three doors, two of which concealed a goat and one of which concealed the grand prize, a new car.

On BA? Did I start it on there too? I sometimes (no actually, often) do that. Memory like a... what is it?

No it came up in a discussion of the game show Deal or No Deal I started a few months back.

Someone was wondering if there was any merit in the idea that if you got down to 3 boxes in Deal or No Deal and were offered the chance to swap, then swap again on 2 boxes, did the notion that you should swap in 'Monty Hall' apply to that scenario.

The answer is the benefit of swapping does not apply to Deal or No Deal, it is a true 50/50 chance, because nobody knows where the money is.

So well done. You all seem to know the answer.
So just to clarify.

At the beginning when you pick a cup at random you have a 1 in 3 chance of getting it right. Which means that 2 out of three times you will pick the wrong cup first time. So the majority of the time you will pick an empty cup.
Which means that there is only one cup left that the game master can show to be empty. So the note must be under the cup neither of you has touched 2 out of three times.

I imagine largehat and azreal would either hit it off right away or come to fisticuffs.