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Red Queen Puzzle

There are only two red queens. For flip number x to show the second queen, the first queen has to show up somewhere before x. The later x is, the more earlier spots there are for that first queen. No flip has more earlier cards than the last one, so its chances are highest. It’s still a long shot, but it’s the best long shot you’ve got!

If this doesn't quite make sense, you can imagine the game with three cards: two queens and one king. The possible permutations of a shuffled "deck" are:

  1. QQK

  2. QKQ

  3. KQQ

You will not pick spot 1, as that's a guaranteed loss. But there is a clear advantage of picking spot 3 over spot 2. If you pick spot 2, there is a 1/3 chance of winning, whereas if you pick spot 3, there is a 2/3 chance. The same general idea applies to the full deck, just at a larger scale.

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