> This game tree only makes sense if you change the definition of A.

Switching away from using A to avoid ambiguity.

> This is a fuzzy explanation that gives a feeling "something about this explains the issue", but it's not a complete explanation that precisely pinpoints what is wrong.

Yes it does, actually. Well, to me. I'll go more in depth so it less fuzzy for you.

The issue is that when you handle imperfect information correctly you have counterfactuals implied by your state-oriented reasoning, because you can't actually escape into perfect information world - you're not in it. When you combine the state-derived probabilities the - I don't know the word for this, so forgive me, but the - superposition of the two counterfactuals implied by those state-derived probabilities end up occupying the same space. They exist, because they are implied by the imperfect information game. They just aren't writing them out in the equations on wikipedia.

Edit: My 'spatial' probabilistic reasoning in my head is explained here, but I show you the identity rule that proves this in the next section.

> I never claimed that A = 2A

You aren't, but the counterfactual terms that get realized into the same position, but which weren't written out, claim that Z = 2Z and that Z = Z/2. The two cases were under two different games. So their implied counterfactual components don't agree with each other and we should never have been allowed to combine them.

We agree on this!

You're just more focused on the they come from different games part and not noticing the other part of what I'm telling you: you can equate the counterfactual components that they don't show between the two games, because there is an identity implied by being under imperfect information. Look at the set relationship closely across the two subgames and you'll realize that the set is defined to be equal to itself across all subgames where the set is used.

That is quite literally one of the logical contradictions. This is where they claim that 2=1. The sets aren't equal to each other after their operations. So by the identity implied by the set, they've claimed 2=1.

And yet when I try to claim this is a core aspect you throw out this...

> This is false. We can easily construct imperfect information games similar to this one, but tweak a few things in such a way that a "naively constructed EV calculation" yields the correct results.

This is a really dumb nitpick with very poor support. If you're going to be this fallacious, you might as well go all out. Why not say I'm wrong because first graders learning to add numbers aren't learning how to handle imperfect information subgames? After all, your argument for me being wrong is that the pedagogical value of problems is independent of the subproblems they contain.

> Nope! I was very clear about which very specific claims I was refuting.

You have a more subtle point than I thought you were making. I'll check out your other post.

> I didn't say "I spotted error X in Wikipedia which explains Two Envelope problem", I said "I spotted error X in this other poster's Hacker News comment". Please read the very specific comments I made about very specific claims made by the person.

Well, he does have another error; EV isn't defined over all policy choices. It is a problem on many of the wikipedia solutions too. He does see it - its why he mentioned other people talking about infinite series - but his correction attempt was more like "halt here because of type error" which is something that I as a programmer can respect.