I'm not sure the analogy is apt, because the whole point of the Monty Hall problem is that no new information is supplied by Monty's opening the door with the goat. To understand, it's important to state the problem correctly. You wrote:

Then, the game show host, Monty, who knows what’s behind each door, opens another, revealing one of the goats.

The correct formulation, i.e. the one that makes switching the right strategy, is this:

Then, the game show host, Monty, who knows what’s behind each door, opens another that hides a goat, a move that you know he will make.

Unless the player knows that Monty knows what's behind the doors and always reveals a goat, the player cannot be sure that switching is the right strategy. As far as the player is concerned, Monty may have opened the door at random and randomly revealed a goat. In that case, switching would make no sense. (I'll leave the math to others.) But if the game is fully spelled out, the player learns nothing from Monty's move, because the player already knows that at least one of the two doors has a goat, and finding out which one doesn't help at all.

If the rules are understood, the player is simply being offered the chance to switch from the door he chose to both of the other two doors, a choice he should always make. That he knows that one of the other two doors hides a goat is not "new" information; he already knew that. That's very different from George Soros learning that the Bank of England was about to act.

I don't mean to disparage acting on new information. I'm just saying that the Monty Hall problem is not an example of doing so.