Friday Puzzler -- another three curtains

Alex Y
Or boxes for this game. At each turn, $100 is placed at random in one of three boxes. Contestants try to guess the box with the $100 in it, and get to keep the money if they find it. When one of the contestants has won $400, that contestant goes on to try for the grand prize of an auto. Both get to keep any money they have found.

Here is how it is played:

In each of rounds 1-3, Player A tries one box. If he fails, B tries one of the remaining two boxes. If he fails, A opens the last box and gets the $100. Then $100 is loaded randomly in a box for the next round.

Rounds 4, and 5-7 if necessary, are played the same, but with B going first each round.

Who is most likely to win the car?

Who is likely to win the most money?

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