Melody: 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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Alright then. I am assuming that I can only go through the 100 cards once.
I'll split the deck into 2deck of 50 cards each.
I'll go through the first 50 cards and note the highest integer.
Then I will stop at the 1st integer higher than this one in the second 50 cards.
If there are non higher then, I would have lost already.
The chance of success is not particularly high but it is better than no strategy at all.
Have you got a better idea reinout-g?
