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.
How do you know if one of your miners was the one to find a block?
Several ways:
For 1, my monitoring software tells me as soon as it happens
2, check your miner GUI - most will tell you if you found one
3, KanoPool lets every registered user know who found it and keeps full records of everything from day-1 of the pool.