## [0863] The Two Envelopes Problem

└ posted on Thursday, 23 February 2017, by Novil

**Cloud:** Yuna?
**Yuna:** Yes?
**Book cover:** THE BIG BOOK OF PROBABILITY CALCULUS

**Cloud:** I have two envelopes and…
**Yuna:** !

**Yuna:** I’ll take both and make you eat them!!
**Cloud:** AHHH!! WHAT THE–

**Ye Thuza:** Did Yuna like your little magic trick?
**Cloud:** Mmpppfff.
**Ye Thuza:** Told you so.

I love Yuna’s face in the third panel.

Cloud let his guard down. Bad habit for a ninja.

Reading a book of probability calculation will not help Yuna. It’s like the Monty Hall problem here, the problem isn’t calculating probability, it’s to think the right way.

Come on… two envelopes doesn’t even have to be a probability problem… Though I think Yuna isn’t in the mood for any kind of problems right now… Though if it was a magic trick then maybe… Ah whatever happened happened.

@ Crystalgate:I have to retract my statement a bit. There’s no right way to think since the problem is ambiguous. However, it is true that Yuna can read every book about probability in the universe and be no closer to the answer.

The sad thing is that the rest of the sentence was probably going to be either “… I can’t decide which one to use for something.” or “…I can’t decide which one to open and which one to give to Sandra.” or “…I can’t decide which one to give to Sandra and which one to give to you.”

Pretty sure that all of the Sleeping Beauty problem, the Two Envelopes problem, and the Monty Hall problem, have answers that change drastically based on subtle things in how the problem is stated, or sometimes what you assume about the problem.

For example, one thing that’s key to Monty Hall is that the gameshow host knows which door has the car, and will deliberately open a door that shows a goat. If you think seeing a goat was an accident, you may not get the same result.

I think good resources can help Yuna frame her problems better. If you’ve got anything of ‘the gift’ for maths (and we know Yuna does) then you can learn from the right source, and there are some very effective writers and illustrators out there; some of them will have covered analysing assumptions, and the question is whether you can find one that builds from something you do already understand.

Wait, didn’t Ye Thuza say, about 300 comic strips ago, that Yuna has never hit anyone in her life? …Well, I guess there’s a first for everything. Much like philosophical probability problems. And me needing to do something about my obsession with alliteration.

The probability that Yuna will become a mad scientist continues to increase.

Isn’t the Two Envelope problem just easy to solve? If you pick a random envelope, you either get an amount equal to x or 2x. So the other envelope can contain 2x or x, respectively, and switching will net a gain of either x or -x, respectively. Therefore:

1/2(x) + 1/2(-x) = 0

and it doesn’t matter if you switch or not.

For those who don’t know what the Two Envelope problem is: https://en.wikipedia.org/wiki/Two_envelopes_problem

Oh, come on. The Riemann-Steiltjes integral doesn’t even require measure theory, Yuna can’t possibly be frustrated by something that simple. Now, whether the cumulative distribution function is regarded as left-continuous or right-continuous might be an issue, but conditional probabilities?

Girl is now broken. Wait warmly until it ready.

@ Hobbes:That not a probability, that is certainty.

I would say she already is.

Yuna can create blackholes in the living room floor, radioactive transmitters and make it two opposite climates in her room. And she’s struggling with probabilities? I just find that odd.

Atsukiwrote:Look up “sleeping beauty problem”. It’s a problem about the ambiguity of wording, Yuna cannot solve it with studying probability, no matter how good she is. She will keep struggling as long as she tackle the problem like a probability problem.

@ DanialArin:The rest of the sentence was almost certainly going to be “and a deck of cards” seeing as how he is holding cards that we can see flying around in panel three and he was apparently doing a magic trick.

@ IYN:Depends on how you frame it. It’s usually framed as “the other envelope either has twice this amount or half this amount, with equal probability (giving you +x or -x/2, keeping the amount in your current envelope constant). This implies that the expected value of switching is 5/4 whatever I have in my own envelope. I’m not saying it shouldn’t be an easy fix (I haven’t looked into the problem TOO extensively myself), just that you have to be a little careful of how you frame the problem if you try to fix it in an “easy” way – careful in how you use the probability calculus…

Ye Thuza looks really nice in the fourth panel. Excellent depiction, Powree, very pleased. =)

@ noname:She didn’t hit him, the book hit him. =)

Now THAT was funny!

Ugh, that little brat…. =_=

If she isn’t tormenting her brother, she’s taking her frustrations out on him.

“It’s Tuesday, and I’m bored, what should I do? I know! I’ll go trigger my daughter with a semi-complicated math problem, make my son further trigger her by tricking him into doing a magic trick for her, and sew a shirt… Did I do this last week?”

I dunno about you guys, but I think that’s just good parenting right there.

Might I suggest that Yuna read

A Million Random Digits with 100,000 Normal Deviates? 😛Do you want to exchange your two envelopes for 400 DM and Gate 3?

I thought it was the Monty Hall paradox rather than the problem, since it was proven that changing one’s original decision was more likely to win the prize?

Funnier when you consider the academy awards are coming up soon.

His vision will be “cloud”ed for a while

HAHAHAHAHAHAHAHAHA I need friends

Nah, there is an easy answer for you, Yuna: The chance for everething is 50%!

They can either be happening, or not! You just overcomplicate it. This is what Larisa understands, and use for “distort reality”, and “bend the laws of phisycs”.

Ye Thuza, you are SO cruel. LOL.

How do Yuna behave against Schrodinger’s cat?

Tomaswrote:She either pets it . . . or doesn’t.

Aww… I wanted to see a magic trick.

Tomaswrote:She clones the cat and creates a quantum computer out of the felines.

It can crack several commonly used cryptographic protocols and run realtime simulations of protein-folding and weather prediction algorithms, but only when it wants to.

It also simultaneously wants stay inside and go outside the house at all times…

…just like a normal cat. :/

TvTropesgotmehookedwrote:It is also simultaneously both inside and outside, while still wanting to be the other.

IYNwrote:I’ve had a look at the wiki page, and as far as i can tell you’ve got the choice of two envelopes, both containing money (one containing twice the amount of the other). so you pick one and it contains $10, maybe the other one contained $5 or $20 (or maybe it also contained $10 and they’re just messing with your mind). my answer “who cares, that’s $10 more then I had before”

nonamewrote:If she “threw the book at him” then she probaly would miss

Tomaswrote:AH yes Schrödinger’s cat, the famous quantum physics example, until you open the box you won’t know if it’s dead or alive, but no one considers the third option since it’s an imaginary cat in an imaginary box, the cat just had to stop imagining and escape

shazz_smifffwrote:LOL. You win this round… 😀

@ Kindren:I’m fairly certain the last panel implies that she tried to talk Cloud out of doing that trick (thereby teaching him a valuable lesson about heeding warnings on occasion)

For a whle, I feelt like back to scool. Tanks you, Mr. Novil.

Yuna’s trouble comes from that “credence” implies “reasonable guessing” and “reasonable” is context dependent and not allways perfectly defined. However, I afirm that, Given Ru = 1, Yuna can’t contradict perfectly rational extraterrestial beings who know the same things as her.

Let’s tink as extraterrestrians, watching a scene shot at an unknow day. We notice two independent events: scene happens on Monday (M) or Tuesday (T), and the coin has landed heads (h) o tails (t). Each pair of events determines a result: Yuna sleeps (S) o Yuna is awaken (A). So we have four possibles “alternative universes”:

(M, t): A

(M, h): A

(T, t): A

(T, h): S

The scene happens in a “A universe”, so for us credence for h is 1/3. So the same is for Yuna.

The Ru value? The Ru coefficient mesaures the correlation between cause and consequence. In a universe with Ru = 1, consecuence allways follow cause. In Ru = 0 there is no causality and pure hazard rules. No, it is not from “Steins;Gate” from but Joanna Russ’ “Souls”. If Ru < 1, we are all fictional characters. Who knows?

There ends my short trip to the 80's. It was fun. Thanks again, Mr. Novil.

@ Crystalgate:I still think the main problem with actually doing the experiment is that amnesia-inducing drugs don’t work as reliably as necessary for experiment.