Higher or Lower card game ... from game shows.

[1800GAMBLER]

Hey. Two questions please guys.

Firstly, The higher or lower game show card game, i.e. one card gets turned, player guesses if the next card will be higher or lower than the previous card(ace low) if correct then carries on. I was wondering how you work out the probability that the player gets N amount of answers right, assuming they play perfectly.

Secondly, the probability that a player wins his first hand of blackjack. Assume the blackjack game were players have no edge. Assuming all the odds are even through blackjack (i don't think that's true, but i don't know) i thought this could be worked out backwards from the percentage the casino takes per dollar. So i just want to know those figures really. This question might be too general since there are so many different times of game, i don't know, i don't play blackjack. I'm not using this as a get rich quick idea either, hopefully i should be on the house side eventually.

Thanks to all.

[1800GAMBLER]

Bump because i'm really curious how the first is solved.