[jonath_laurent]

This comment explains the fundamental reason why the reasoning is incorrect. I offer the same perspective in a different comment (https://news.ycombinator.com/item?id=31569991).

In my opinion, the Wikipedia article is making a disservice to readers by mentioning unnecessarily complex mathematical arguments involving bayesian reasoning and infinite distributions. I believe all of these are distractions from the more fundamental typing error that invalidates the switching argument.

[mike_hock]

They also fail the article's own premise

> in particular, the puzzle is not solved by the very simple task of finding another way to calculate the probabilities that does not lead to a contradiction

[JoshCole]

Honestly, the more I've thought about this problem the more that statement bothers me. It is just such a nonsense goal.

The reason the calculations are wrong are fundamentally related to why correcting the calculations leads to the correct probabilities. If you understand why the problem gives you the wrong result, you proceed to correcting it, and you get the right result - that doesn't mean you didn't understand. It means you did. You can tell you did, because you have the correct answer.

But if I show the calculations produce the correct answers, well, that is a step too far. We can now dismiss the understanding on the basis that it got the correct answer, apparently?

It's no wonder the author of the wiki writes such a bullshit claim - that no one can agree on a definitive conclusion. Their terms of engagement are self-defeating. Correctness is error, because correctness means you didn't /really/ understand. Its a no true scottsman fallacy - get the right answer, and you aren't engaging with the 'real' problem.

But its a flawed no true scottsman, because it defines something measurable: it tells us the goal, that it is to avoid this type of mistake in our thinking. And generalized algorithms for solving decisions problems that include this as a case which is successfully solved are many - and they just so happen to be in the imperfect information setting. And that setting has studied the problem of infinite recursion and has solutions for them. Which I can apply. To get the right answer. And, in general, avoid the problems they claim we aim to avoid.

More importantly and to the point of this thread - this isn't an intractable debate, because its been solved and used in production settings for literally decades. So what if some people are going to pretend it isn't? This isn't an unsolved problem. The actual game theory math is /well/ beyond this level of complexity. Its contending with things like environments where you have so much complexity you have to reduce to a blueprint abstraction, not stumbling at a decision problem that is quite literally simpler than rock paper scissors.