reinout-g: And here is the new puzzle!
If you have trouble solving it, feel free to give the easier one a try.
Easier one:
There are 31,542 people attending a concert. One person is picked from the audience and if his birthday is a monday he will win $1.000.000
What are the odds that that persons birthday is a monday?
Hard one (I'm curious to see whether anyone can find a different strategy than I found.) :
Steve again wants to play a game with you but you need $2 for each time you want to play.
Now, each time you play the game, Steve has the computer print 100 blank cards with 100 random different integers.
After that you can flip the cards for as long as you like until you choose to stop flipping. If your last card flipped is the highest card in the deck you will win $10.
Think of a strategy where you expect to win money in this game.
Hint: The cards you previously flipped can give you some kind of information.
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