Answer by Michael Greinecker for How is it that you can guess if one of a...
This is a problem that becomes much simpler if one makes the effort to make the problem precise. The following is somewhat inspired by [Alexander Gnedin. "Guess the larger number." arXiv:1608.01899...
View ArticleAnswer by Tyler for How is it that you can guess if one of a pair of random...
The numbers are supposedly chosen from an infinite distribution...There is no valid way to "sample" an infinite distribution of integers to get x and y, nor is there a way to get r from an infinite...
View ArticleAnswer by Steven Landsburg for How is it that you can guess if one of a pair...
It might be useful to the intuition to consider the following simpler strategy: If the revealed number is positive, guess that it is the larger of the two. If the revealed number is negative, guess...
View ArticleAnswer by Daniel Mehkeri for How is it that you can guess if one of a pair of...
I'm finding most of the above either wrong or unnecessarily obtuse. My take is that the paradox arises in two parts. The first is a simple trick. The game looks like it reduces to:(Incorrect:) The game...
View ArticleAnswer by sigoldberg1 for How is it that you can guess if one of a pair of...
As previously explained above, the success of the proposed contestant strategy is entirely dependent upon the assumption made by the contestant about the host's method of choosing x and y. An example...
View ArticleAnswer by BlueRaja for How is it that you can guess if one of a pair of...
The problem is that there's no way to define a random sample over all the real numbers, where every real number has equal probability of being chosen.See this related problem and solution by Randall...
View ArticleAnswer by dorkusmonkey for How is it that you can guess if one of a pair of...
Consider the following simplified problem: I will pick two numbers from the non-zero integers with probability proportional to $ \frac{1}{|k|} $. So:$$ p(|k|) \propto \frac{1}{|k|} $$And we play the...
View ArticleAnswer by Darsh Ranjan for How is it that you can guess if one of a pair of...
After Bill's latest clarifications in the commentary on Critch's answer, I think the question is interesting again. My take:One thing that always seemed to fall through the cracks when I learned about...
View ArticleAnswer by Tyler for How is it that you can guess if one of a pair of random...
I don't think there is any need to reason about your opponent's probability distribution (and therefore the above explanations of the paradox seem spurious). For concreteness, say that you draw your...
View ArticleAnswer by Steve Flammia for How is it that you can guess if one of a pair of...
There is a related "paradox" known as the two envelopes problem which has a nice article on wikipedia.
View ArticleAnswer by Andrew Critch for How is it that you can guess if one of a pair of...
Thanks for writing out the proof in detail, so that answers can easily refer back to it! The math is fairly straightforward, but as a paradox I find this very interesting.Spoiler alert: Paradoxes are...
View ArticleHow is it that you can guess if one of a pair of random numbers is larger...
My apologies if this is too elementary, but it's been years since I heard of this paradox and I've never heard a satisfactory explanation. I've already tried it on my fair share of math Ph.D.'s, and...
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