Hacker News Reader

Comment by the_sleaze9 | Hacker News Reader

I have to admit I remain unconvinced. Has anyone ever run a real world experiment to verify the math?

For whatever reason I can't get past my intuitive feeling that this problem is just a simple 50/50 and these proofs are just fancy window dressing.

View on HN

You remain unconvinced that switching is pointless? Unlike most paradoxes, this is one where the intuitive answer is the correct one. It's a paradox because of the flawed, but convincing, reasoning that is given in favor of switching.

Is it?

"No proposed solution is widely accepted as definitive."

I mean for me this is totally a "cannot see the forest because of all the trees" situation and the intuitive solution is the right one.

But I thought the same of the monty hall problem (back in school) and only was convinved, after I wrote a small program to simulate it, which confirmed it.

But unlike in the monty hall problem, there is no new information here, when you are given the opportunity to switch. So the discussion seems weird to me.

That means that no solution to the paradox is definitive, but also there is no argument.

Switching back and forth obviously doesn’t have any positive. What they mean by “is not definitive” is what explanation is the definitive one.

It's much like the Monte Hall problem, in that people often forget to include the portion about the revealed door ALWAYS being a loser. If it were a randomly opened door then the option to switch would actually just be 50/50. This can be shown by just running the simulation over thousands of iterations. The same is true here. It's not actually going to yield better outcomes to switch. Sometimes logicians just need to own up to the fact that empiricism and applied mathematics is where the rubber meets the road.

I’m not sure how literally applying Bayes’ theorem and reducing the sample space accordingly is owning logicians but you do you.

The difference between this and the Monte Hall problem is there's no new information revealed or pool reduction here.

I wrote a pretty detailed analysis about this problem here in case you're interested:

https://mindbowling.wordpress.com/2020/09/14/two-envelope-pa...

It all depends on how the envelopes are prepared.

Reply on news.ycombinator.com