re: miner size and 'Luck'... As Kano said, each block is found by just 1 miner. I must add that it does NOT have to be particularly big/fast one.

2 years ago my "Lucky" r9 running 8-9THs found the third block in its lifetime by returning a diff of 151.7009T which is far beyond what is needed for any ridiculously high diff we will see in the at least near future. Hopefully many years out... Just goes to show it can easily be done with even a small miner if the miner software is working right.