[DrVanNostrin]

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Three cards; one ace, two blank cards. You pick one keeping it face down. After that I pick a blank card (randomly or not) and place it face up, and the other I place face down. You can now take the first or the second face down card. You win if you get the ace.

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I'm concerned about the "randomly or not" part. If I don't choose the ace, what is the probability that you'll turn the ace face up? 0?

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You should pick the second face down card as the odds of it being an ace are 1/2 as it was dealt after the blank card. The odds of the first face down card being an ace are 1/3 as it was dealt before the face up card.

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If you turn a blank face up one of the two remaining cards must be an ace. So the probabilty of the first being an ace plus the probability of the last card being an ace must equal exactly one. You have it at 5/6. It's 2/3 and 1/3 for Monte Hall, not 1/2 and 1/3.

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If this would be a poker game and the same question would be answered, it would be answered incorrectly. The only difference is that both down cards would have been dealt before the blank up card. That's why that "blank" up card has no effect to the preflop probabilities - it would only effect it if it would be an ace as there are no aces left.

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The flop does alter your opponent's range.