"There is no specific number of cases accepted each year. The Court typically hears between 60-75 oral arguments per year, and reviews approximately another 50-60 more cases on paper. The total represents a mere 1-2% of the cases submitted on appeal, due to limitations on the amount of work a nine-Justice Court can handle."
Would love to hear from a litigaor with USSC experience. Fact that government will probably oppose lowers normal number further.