Interesting Mathematical Paradox?

[Magic_Man]

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make that number 100,000 times bigger.

Would you still switch?

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Would totally depend on the amount of money in the box that I have opened.
If it was 1000 dollars I would take the money and not switch, because no way I could ever believe that there would be 100 million dollars for me waiting in that other box; I'd be sure there would be this ugly one cent coin!

But this does not solve the paradox.
Tomorrow, I'll ask my shrink for some stronger medication; I wish I never read the OP.

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Your change to the OP is easily accounted for by considering a non-linear utility function. If we exagerate your scenario a little bit and say:

There are 2 boxes. One contains X, the other contains 100,000*X. You open A, and it contains $100. Do you switch?

I'm sure almost everyone here would switch. It's perfectly reasonable to not mind paying $100 to try to win 10 million, and most economists could easily describe this choice. On the other hand, if the box you opened contained $100,000, switching boxes becomes a little more silly. It's all about risk tolerance.