[Macgyver]

Originally Posted by Aindreas_Daoc

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.

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?