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Originally Posted by Macgyver
OK, I can understand that reasoning ... but doesn't that still mean that every time you double, you stand a 4 in 51 chance of winning rather than a 1 in 2 chance? 
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No. Before any cards are turned over you have a 1 in 2 chance (ignoring ties) because you can only turn over one card for yourself (the other down cards don't matter; they might as well still be in the deck after you pick).
Once the dealer card is shown, then the odds change since there are only 51 cards left and you have to pick one to beat that upcard.