The Three Card Puzzle

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?

Three Card Puzzle

See Answer
You should not take the bet. While it may seem that there are only two possibilities, thus giving you a 50-50 chance of winning, there are actually three possibilities. The card may be showing the black side of the black-white card, it may be showing one of the faces of the black-black card, or it may be showing the other face of the black-black card. Thus, with the gambler taking black, you have only a one-in-three chance of winning. If you don’t believe it, make some cards and try it out!

 

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