Baseball Probability Question

[irchans]

A friend of mine asked me the follwing question:

"Suppose you have n "bins" and r white balls and s black balls. Further, suppose the balls are distributed randomly in the bins such that no bin contains an equal number of white and black balls. What is the expected value of the number of bins that contain more white balls than black balls? (A bin can be thought of as a (baseball) game, all the bins a (baseball)season, and the balls points (runs).)"

Any comments?

Cheers,
Irchans
(Cross posted to sci.stat.math)