Take a fifty-two-card deck. It is easy to arrange it however we please. For example, we can put the spades first (ace, king, queen… 4, 3, 2), followed by the hearts, clubs and finally diamonds. We can also shuffle the deck so that the order is unpredictable—random. Suppose we arrange the deck in a particular way and you know nothing about how it was done. You would then be hard-pressed to say or predict which card was on top! And if you assess your chances of predicting correctly, you would be wise to say: "One in fifty-two." Your chances of a "correct prediction" are therefore the same as the odds you would give yourself if the deck had been "well shuffled" rather than arranged.
Bewildering phenomena
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Now imagine a countably infinite deck of cards, numbered 0, 1, 2, 3, 4… Can you arrange the deck however you please? No! You cannot put the even-numbered cards "first" and the odd-numbered cards "afterwards," since both groups are infinite. Can you at least "shuffle" the deck so that, whatever integer you think of, the corresponding card has the same probability of being on top?
