An interesting probability game

[strategy]

http://mindyourdecisions.com/blog/2010/11/16/an-interesting-probability-game/#more-2981

[Jabbles]

"some" means "any":

Bob tells Alice to draw repeatedly from the uniform distribution on [0,1] until her current draw is less than any previous draw, and he will pay her $n, where n is the number of draws. What is the average value of this game for Alice?