A Riddle with a Gambler's Twist

A bookmaker comes to you and says, “I have a game for you which means you could get Man City at 40/1 to win the 2011/12 Premiership” . Your interest is piqued. “Go on,” you say with an air of hesitation in your voice.

He says, “I have three doors: behind one door is a card that says Man City and behind the two other doors are cards that say Arsenal and Tottenham. Whichever door you pick you have to take the odds of 40/1 and you have to place a 1000 euro bet”.

You think to yourself: that’s not too bad because Arsenal and Tottenham are about 40/1 to win the Premiership anyway and Man City are big favourites, so you decide it’s a game you would like to play.

The bookmaker asks you to pick a door each Labelled A, B and C. So you pick C. At this point the bookmaker tells you that the card with Man City on it is NOT behind door A and he offers you the choice to change your decision.

Now you can either stick with door C or change to door B. To give yourself the best chance to find the card with Man City on it should you change your pick, stay with your pick or will it make no difference either way? See if you can work it out and have fun!