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?
it has to be 1/3 chance of winning, since you do not play any direct role in the game except for volunteering your money. it would not matter whether you can see half the card or not. if you put your money out up front before he draws a card, only one of the three cards in that hat has a red AND black face and the odds of that card being of 2 colors is therefore 1 in 3. but on the other hand, if you put your money out after he draws one, then you can exempt one of the cards automatically, and your odds would be 50/50. i seem to have contradicted myself, but i can't help it cause this question confuses me. i just thought i'd take a stab at it.
bleh
