You are approached by a gambler who shows you three cards, one that is black on each side, one that is white on each side, and one that is black on one side and white on the other. You are allowed to shuffle the cards yourself, without looking at them, and place one card on the table. Let’s say the face showing is black. The gambler then says, “We know this is not the card that is white on both sides, so there are only two possibilities: this is either the card that is black on the other side, or it’s the card that is white on the other side. I will bet you that the other side is black. You have a 50-50 chance.”
Is the gambler correct about your chances?