There is a nice discussion of this problem (also called "Secretary problem") athttp://www.math.uah.edu/stat/urn/Secretary.xhtmlFor N large, 1/e is indeed the right strategy.

As I explained earlier, the general answer ism ((m-1)/m)^n.For m=10, n=18, this is indeed 1.50094635...

<t>This is in fact the hunters problem, when they are shooting geese. The answer is N ((N-1)/N)^M, where M is the number of balls (hunters), N is the boxes (geese). Formally, you introduce N random variables (the indicator function of the emptiness of a box), and the expected number of empty boxes i...