> Forget about things being counter-intuitive; that only means that you haven't considered all of the components of the problem.

It also means that the correct solution is inconsistent with everyday experience. Its counter-intuitiveness is the chief reason that the problem generates so much controversy. That makes it of interest.

For decision-makers, the psychology is just as important as the math. So the analogy to the lottery situation is entirely relevant. It partly explains why the Hall problem *is* so counter-intuitive that a vast number of people (according to Wikipedia) angrily refuse to believe the correct solution even after it's been explained to them.

That's a very unusual response, even when something as bizarre as advanced physics is being explained, Quantum mechanics makes most people shake their head and wonder how it can be: but they don't shout that the numbers are wrong and that the physicists are obviously idiots. I find that difference fascinating and possibly very important.

One reason for it is that Joe Blow has never peered into an atom but he certainly has had to make choices between two or three options.

> You seem to be trying to reinvent the wheel instead of trying to understand the Game under the rules followed in the Hall Problem.

I'm trying to grasp fully the implications of the wheel and of the rules themselves.

Jim Dixon's chart/grid/summary shows that the 2 in 3 outcome is correct. I've pointed this out several times.

But that doesn't make it any less counter-intuitive, for reasons I've already explained.

Those reasons are of interest.