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Originally Posted by Macgyver
This was in response to the "how can we be sure it's 50/50?" question, and I'd like to ask something about it. Bear with me/humor me/laugh at me, but it's something that I've been thinking about.
When you double, you have the dealer's card face up and four cards to pick from, correct? If the card you pick is higher than the dealer's, than you double your winnings (hence the name).
Doesn't that mean, though, that you have a 1 in 4 chance of picking a higher card (which isn't 50/50)? I know that's over-simplifying things a lot, but it's a start to this nagging question. Not to mention that you have to factor in the possibility that if the dealer has a King, you only have a 4 in 51 chance (deck is missing a King and only one of the four Aces can give you a win).
Does that make sense?
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It doesn't matter whether there are 4 cards to pick from, or all remaining 51: an unseen card is an unseen card, assuming that those 4 are picked out on random.
Pretend you're playing the game with a real deck of cards: Pick one card out and look at it. You need to find a card that is bigger than what you looked at first. Does it matter if you pick one out right away, or if you pick 4 first (face down), then pick one out of those 4? Of course not.
Only the upcard matters. Yes, when you pick out an ace first, then you don't have a chance of winning. However, this is balance when picking a deuce first where you can't lose.