USCIS announced today that it conducted the two phased Random Selection process to pick H1B petitions. If you have filed for premium processing, you should hear a decision in 2 weeks from today. If not, you should hear no later than 2nd June.
As previously mentioned, USCIS mentioned that it will short list little more than mandated cap of 65000 + 20000. Read more about the waiting list in USCIS original update.
USCIS conducted two random selections, first on petitions qualifying for the 20,000 “master’s or higher degree” (advanced degree) exemption, and second on the remaining advance degree petitions together with the general H-1B pool of petitions, for the 65,000 cap.
USCIS Update (26KB PDF)