Gambling Puzzle

[dinjo99]

This is probably an old one but I only came across it recently.

Can someone tell me the answer and explain why please.

You are offered the choice of two sealed envelopes.
Both contain cash but you don’t know how much.
The only information you have is that one envelope contains double the amount of cash as the other one but obviously you don’t know which envelope contains the larger amount.
You open envelope A and it contains €100.
You are then given a choice, keep the €100 or open envelope B instead.

Should you swap and why?

[Mellor]

My first reaction was another monty hall problem. but being only two envelope makes it different.

I think the answer is that you should swap. The other envelop either has 50 or 200 in it. So you either lose 50 or gain 100, assuming that its 50% for each, swaping is worth an average if +25 EV

[dinjo99]

Does that mean Noel that I should swap.
No matter what sum is in the envelope i open it will be +EV to swap so why not just open the other one in the first place!!

Is this a puzzle that doesn't add up mathematically?

[Hitchhiker's Guide To...]

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[Bubbleking]

Depends on your level of risk aversion obv. People are approx twice as adverse to loss compared to how much they enjoy gains. Thus the ev of £25 of opening the new box wouldn't necessarily be enough to some people and they'll stick with what they have.

(aware that's not the main point of the question, though)

no but its a very important point. swapping envelopes will always be +EV to the tune of 25% however as the sum of money gets bigger so does the potential loss so its very person dependent if you take the swap or not.

to put it in poker terms and Individual Chip Value. would winning an extra x amount mean the same as losing x amount when faced with a decision.

to put it in practical terms if i open an envelope for a million - winning an extra million wouldn't effect me as much as losing 500k.

[Mellor]

Peple may do tht, but doesn't make it right.
I'm pretty much not averse to risk at all. Its like on WWTBAM and got to the 64k question, if I had a 50:50 left I'd have no problem guessing even if I had got a clue

[dinjo99]

I think the puzzle is interesting because mathematically from a +EV point of view you should always swap.(Ignoring risk aversion)

In other words if you did this 100 times and found 100 different sums you should always reject this sum and choose the other envelope because over the long term you will gain.

This again begs the question, if you are always going to swap, [BWhy not just open the other envelope in the first place?[/B

[dinjo99]

and this is where stupidity takes hold of some people in discussions. It is an irrational question.

The full and final answer and the one that should end all discussion on the puzzle is that we have different information sets - and base our decision in each case on the information set at hand.

OK so!!

[whyno]

I'D put one envelope in each hand pretending to way them and then do a legger with them

[Guest]

I got an 'A' in my GCSE maths. Was my best subject lol.

Totally clueless about this tho! Havent read the replies but i would prob add up all the %'s and devide by 17.

Or possibly take the top 3 likely ones and devide them by the sum of the others.

Am probably completly wrong tho.

EDIT this should be in gimmeabreaks thread!

[Mellor]

In other words if you did this 100 times and found 100 different sums you should always reject this sum and choose the other envelope because over the long term you will gain.

This is where your thinking is wrong. You are assuming the wrong point of reference for gain. The reason that you should swap is because it increases our EV over the point when we have opened the first envelope only. This is because before we've open any, we have no reference for the money we may win.

If two people were to do it 100 times, one always swapping, the other never swapping. The EV of each set of 100 is exactly the same. Albeit unknown. In that sense it's a bit of a mathematical paradox, artificial EV

[dinjo99]

This is where your thinking is wrong. You are assuming the wrong point of reference for gain. The reason that you should swap is because it increases our EV over the point when we have opened the first envelope only. This is because before we've open any, we have no reference for the money we may win.
If two people were to do it 100 times, one always swapping, the other never swapping. The EV of each set of 100 is exactly the same. Albeit unknown. In that sense it's a bit of a mathematical paradox, artificial EV

Tx Mellor, I must say this makes sense to me.

Now there is this one about a game show, 3 doors, 2 cars and a goat.........