You have a deck of 32 playing cards. Somebody draws one card after another and shows them to you. At any point of time you may bet that the next card is black. If it is indeed black you earn $10, otherwise nothing. If you don't do anything you earn nothing as well. Find the optimal strategy.
In other words you should find the point of time where the quota of remaining red cards in the deck is maximal.
Any hints how to to this?