Positive Expectancy with Random Chance A conversation came up at work about positive expectancy. I am having difficulty getting the same answer as the guys so I am throwing the question out to you folks...  Any help is appreciated.
A game costs €50 to play. If you win you get €100. You get 52 chances to pick the Ace of hearts from a deck of cards. Every time you pick a card it is then returned to the deck and the deck is shuffled again. You pay the €50 once and you then have up to and including 52 tries to get the Ace of Hearts. Is there a positive expectancy on this game?
I worked it that you have a 1/52 chance of winning every time you pick a card. While you do get to pick 52 times your chance of winning is still 1/52 each time you play. 
( 1/52 * 100 ) - ( 51/52 * 50) = (200 - 4750) {I used rounded 2% for 1/52 and rounded 98% for 51/52}
What do you folks think?

You fail each time with probability $51/52$. Since you return the card to the deck, the draws are independent so you fail all and lose the game with probability $(51/52)^{52} \approx 0.36$. Since you win with probability greater than one half, the odds are good for you.
