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To extend the fishing metaphor, the premise of ~100 balls is also important: If each lake could only sustain one (good) fish, you would actively avoid anywhere someone had already caught one from.

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I guess the counterpoint to this is as the number of balls goes from 100 to infinite, it becomes increasingly harder to predict, correct?

No, the higher the count goes the closer it becomes to the single removed ball not mattering at all, so the only thing that matters is the information you got about which urn you're selecting from.

According to the original poster on Twitter:

"One cool thing is that this probability doesn’t change if you replace 100 in the statement of the problem with some other number (as long as it’s at least 2), as these arguments show."

Source: https://x.com/littmath/status/1752167731682492522?s=46

That's "what's the probability you've caught the world's meanest fish".

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