a puzzle

ok, here's one for you.

a psychologist sits you down and tells you that you're going to play a guessing game for some money. he pulls out a deck of (playing) cards and allows you to take a cursory look at them; only long enough to ascertain that there are indeed red and black cards in the deck. he shuffles the cards. the game is this: he turns the cards up one by one. before he turns each card up, you guess whether the card is red or black. if you're right, you win $x. if you're wrong, you lose $x. the object of the game is to win as much money as you can.

once you finish playing that game, the psychologist pulls out another deck, explaining that for this second game, the rules are exactly the same, but this time the card faces only show either a solid red, or a solid black rectangle (they have normal playing-card backings). you play the game again.

so:
1) what's your strategy for the first game, and why? if at some point you notice a duplication of cards (e.g. you see the 9 of diamonds appear twice in a row), does this change how you play?
2) what's your strategy for the second game, and why?