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.