If you want a good, counter-intuitive but concrete puzzle, allow me to direct you towards Monty Hall problem.
Personally, I find this "spooky math" problem little more than a guileful parlor trick. It is vague and ambiguous. We don't really know the full setup. Possible choices lead to effectively different puzzles.
In reality, both Contestant and Entertainer would have individual bias, and a very constrained range for their rand(). Assuming the Entertainer gets to choose his numbers, is he spiteful or sympathetic? Now it's a behavioral game with external factors.
The abstract problem on an infinite number set is different. In this case,
there is no strategy to take advantage of.
The third scenario, two persons and/or programs acting it out—that's just a curiosity, a sleight of mind, a voluntary(?) deception.
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