Srap Tasmaner

Saw what you did there.

If we skipped all the preliminaries and just offered for sale, at the price of £10, envelopes advertised as containing "either £5 or £20" -- well, I'm...

Repetition is actually built into the game. You choose between a pair of envelopes, then you choose again between that same pair of envelopes. More re...

If you know only one value, you don't have enough information to prefer either sticking or switching. Flip a coin. That's what you did the first time ...

We're given a choice between envelopes valued unequally at a and b. We won't know which one we picked. The expected value of switching is \cfrac12(a-b...

When I was looking for a way to describe "success", I picked the average value as a cutoff; more than that is success. The curious thing is that there...

It sounds to me like you're trying to figure out what would be a good prior for what amounts to "Pick a number." I mean, you could do research, see wh...

This is the part I'm still struggling with a bit. Even if I were to convince Michael that he had mistakenly assumed the chances for each criterion of ...

Yes, I believe it is entirely consistent with criticizing the conclusion of the faulty inference. I think we would like to believe that invalid infere...

@"Pierre-Normand", @"JeffJo" I believe there is not a paradox here but a fallacy. Outside of being told by reliable authority "You were successful!" y...

Yes! This is exactly what we disagree on. -- For a change, I'm going to take a little time and think through my response. --

Yes, absolutely, and this is specifically beyond the OP. The distributions we've been talking about have almost always been (or should have been) unkn...

This makes no sense to me. Initial distribution of what? If these are pairs of envelopes from which will be chosen the pair that the player confronts,...

I have come, in broad terms, to see probability as a generalization of logic, or logic as a special case of probability, take your pick. I would credi...

I'm not sure which of @"JeffJo"'s examples you're referring to. As for my "tree" and what it predicts -- You face a choice at the beginning between tw...

If I hadn't gone inside for coffee, I would have had the 1000th post. I feel bad now, but I have coffee.

Some might unkindly note that it hasn't stopped me.

I might also have pointed out that when I first started doing this a couple days ago I said The point of the tree is to show that the last decision yo...

Once again, @"Jeremiah", @"JeffJo", @"Pierre-Normand", and @"andrewk", I'm terribly grateful for the patience you've shown me as I try to learn someth...

https://www.urbandictionary.com/define.php?term=smile%20when%20you%20say%20that ((Evidently nearly coined by Owen Wister, author of The Virginian, the...

Smile when you say that.

Sorry, I'm not following this. This sounds like you think I said your expected gain when you have the smaller envelope is zero, which is insane. Well ...

Except that you cannot, and you know that you cannot. Suppose the sample space for X is simply {5}, one sole value. All the probabilities of assignmen...

Here's my decision tree again, fleshed out in terms of @"Michael"'s £10. https://image.ibb.co/k5RGW8/envelope_tree_d.png The value of k is either 5 or...

My current, and I think "final", position is that this isn't really a probability puzzle at all. Here are my arguments for my view and against yours. ...

Here's a straightforward revision of the decision tree: https://image.ibb.co/k5RGW8/envelope_tree_d.png Opening an envelope "breaks the symmetry," as ...

What if we did say that all of the player's choices are conditional on the host's choice? That is, suppose we had X = k, where k is some unknown const...

Post something when you feel like it. I'll keep the thread bookmarked.

@"Jeremiah", @"JeffJo" This pissing contest is detracting from the thread. Both of you quit it.

The fallacious premise of the switching argument is that you could observe a given value, whichever envelope you chose and opened. If the envelopes ar...

There is a 50% chance that you observed a, because you chose and opened the X envelope; there is a 50% chance that you observed b, because you chose a...

Here's a reasonable way to fill out the rest of the decision tree. https://image.ibb.co/fZWpyo/envelope_tree_b2_1.png Either you observed value a, and...

Here's the OP: Problem A 1. You are given a choice between two envelopes, one worth twice the other. 2. Having chosen and opened your envelope, you ar...

Sure. But I'm not trying to figure out whether I should switch. I'm trying to figure out where the fallacy in the 5/4 argument is, and that's an expec...

Yes. I accept that the expectation of gain would apply whether you looked in the envelope or not, and thus there are symmetrical expectations that eac...

I know! It's why I'm still here.

You're not in my league at messing up the math! It is a nice clear argument, using @"JeffJo"'s multiple sets of envelopes, and makes the point I keep ...

You just telescoped the step of multiplying by the chance of picking that number. Could put & where you have |.

This isn't what you mean, is it? P(lower | 5) = 4/4 = 1, P(lower | 10) = 1/5, P(lower | 20) = 0/1.

Reinventing math step-by-step is interesting, and I'm gaining insight by making every possible mistake, and doing so in public, but it would be far mo...

Imagine u around .75L and v around .9L. They're just randomly selected values in . We can't say at the same time that P(u < v) = .9 and P(v < u) = .75...

It's also slightly more complicated than I wanted because of the "reference" problem. If you don't designate either u or v as the reference variable, ...

True.

Coin flips and coin flips with colored envelopes are just the wrong kind of example to look at, because (a) you have categorical instead of numeric da...

Admittedly, in strident moments I have said things like this. But look at my last post. It's not about interpretations of probability. It's about how ...

Let's leave the envelopes aside for a moment. Imagine an interval for some positive real number L. Now let u and v be unequal real numbers in that int...

All right, man.

1. For a single trial, the player cannot calculate an expected value for the other envelope, and therefore either (a) they cannot make a rational deci...

It's only the difference between describing your expectation conditionally and unconditionally. By describing your expectation conditionally, you leav...

I share your frustration, Michael. If I offer you a choice between envelopes containing $5 and $10, you have a 50% chance of picking the envelope that...