as long as a device has enough energy to submit a single share, how fast other pools operate is irrelevant.
an s3 statistically has a 1:16245 chance of solving a block per day at the current difficulty.
1PH = 1:7
2.2G = 1:2,865,671
powerball ticket = 1:292,201,338
If this is true-and-accurate, then you sir have delivered the best news I heard this year .. cheers. Would 3.5 PHs give you a 50/50 chance, to hit within a 24 hour period?
if waiting 2 million days for a decent chance to solve a block cheers you up with 2.2G, i'm glad to have helped.
most sane people avoid the lottery

edit: re: 3.5PHs maybe. Will 7PH give you 100%, no. Over a period of time it will be 1 a day. some days sooner some days not.
Welp.. here's hoping that the difficulty plummets after halving, because the cloud mining operations and massive pools all croak, and no more hardware is made .. so we old bastids can dust off our Butterfly Labs chit and make some coins when BTC is at $700 per