Two envelopes problem
en.wikipedia.org
Two envelopes problem
1–10 of 318 posts
Re: Two envelopes problem
#2Notably different from the Monty Haul problem where additional information is given to the player of the game prior to making the decision to switch.
Re: Two envelopes problem
#3I love this problem because it is so simple, and the false line of reasoning is so compelling that it would hardly raise an eyebrow if you saw it in an academic paper and yet the conclusion is so obviously wrong. Decision problems are tricky and in non intuitive ways.
Re: Two envelopes problem
#4Notably different from the Monty Haul problem where additional information is given to the player of the game prior to making the decision to switch. See https://en.wikipedia.org/wiki/Monty_Hall_problem
The “Monty Haul” problem is where a dungeon master in D&D awards too much treasure to the party :-)
Re: Two envelopes problem
#5I love this problem because it is so simple, and the false line of reasoning is so compelling that it would hardly raise an eyebrow if you saw it in an academic paper and yet the conclusion is so obviously wrong. Decision problems are tricky and in non intuitive ways.
Step 3 (and thus also 1 and 2 on reflection) stands out to me immediately as describing two different situations for the entire game.
The case where switching gives you 2A and the case where switching gives you A/2 describe 2 completely different universes, not two different actions in one.
Re: Two envelopes problem
#6change your mind as many times as you like, there will only ever be one actual choice
Re: Two envelopes problem
#7I love this problem because it is so simple, and the false line of reasoning is so compelling that it would hardly raise an eyebrow if you saw it in an academic paper and yet the conclusion is so obviously wrong. Decision problems are tricky and in non intuitive ways.
Step 3 (and thus also 1 and 2 on reflection) stands out to me immediately as describing two different situations for the entire game. The case where switching gives you 2A and the case where switching gives you A/2 describe 2 completely different universes, not two different actions in one.
Agreed. Step 6 is where it breaks down, because it's redefined A as being one of the two envelopes to being the halfway point between those two envelopes. Until step 6, it's describing two parallel views of the universe (depending on which envelope you first get - hence steps 4 and 5), and then mashes them together in a way that doesn't work.
Take the practical example of $100 and $200: A is either $100 or $200 depending on which envelope you receive first, so the equation is either 0.5*A + 0.5*2A, or it is 0.5*A + 0.5*(A/2). It can never be 0.5*2A + 0.5*(A/2)
Re: Two envelopes problem
#8I love this problem because it is so simple, and the false line of reasoning is so compelling that it would hardly raise an eyebrow if you saw it in an academic paper and yet the conclusion is so obviously wrong. Decision problems are tricky and in non intuitive ways.
Well, the simple way to put is that "A" isn't fixed. The "expected value" argument in steps 6-7 is acting like "A" is a single value when "A" will be larger or smaller depending on what envelope you picked.
Re: Two envelopes problem
#9Notably different from the Monty Haul problem where additional information is given to the player of the game prior to making the decision to switch. See https://en.wikipedia.org/wiki/Monty_Hall_problem
Personally I don't think you are given any new information in the Monty Hall problem that's worth anything. You always knew there was a 100% chance that one of the doors in that set has a goat behind it, which door that is is pretty much irrelevant.
Or to put it another way how many people would stick with their chosen door if instead of opening a door and showing a goat they were simply asked "would you like to stick with your current choice of door, or switch and take the best result from the other doors?"
Re: Two envelopes problem
#10> you are given two identical envelopes [...] containing money. One contains twice as much as the other
> having chosen an envelope at will, but before inspecting it, you are given the chance to switch envelopes. Should you switch?
> because the person stands to gain twice as much money if they switch, while the only risk is halving what they currently have, a case can be made for switching the envelope
I dig this, but it seems like an unavoidable nonsense pattern that congeals in pools of otherwise practically useful logic / language systems.
Like Neo in the Matrix. Remember the Architect? That guy was cool.