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Solution

Posted By: Timothy Chow
Date: Tuesday, 7 November 2023, at 2:29 a.m.

In Response To: A similar puzzle (Bob Koca)

The answer is that it doesn't matter what strategy you use; your probability of success will be 1/2 regardless.

Peter Winkler has called the following argument the "predestination card" argument. Suppose that when you finally decide to commit, the dealer, just before dealing you the next card, reverses the order of the remaining (unseen) cards in the deck. Since the deck was perfectly shuffled to begin with, this reversal has no effect on the probability that you'll get a red card.

But the effect of this reversal is that you'll always be dealt the card that was initially at the bottom of the deck, regardless of when you decided to commit. And that card will be red with probability 1/2.

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