A dealer offers to you to play a game. He shows you three two-sided cards: one with both sides red, one red and black and the other black and black. He puts them in a hat, and randomly (no tricks here) takes out a card and puts it on the table.

You both see only one side of the card. At this point he says that if the bottom side is the same as the top, he will take your money. If the other side is different, you double it. He explains that by now one of the cards is ruled out - if you're seeing red, the card cannot be a double black card, and vise versa - so you have a 50/50 chance of winning.

Is this a fair game? Why or why not?

Let's look at it this way. When he shows you a side of the card (say red), it's either the front of the double red card, the back of the double red card, or the red side of the red/black card. You have a 1/3 chance.

Posted by Ryan on 2003-05-07 07:22:41