Mining: is there also "luck" factor ?
Yes there is a luck factor - mining is just probabilities, it is all about luck and probability. Technically every miner, no matter how big, has a chance of mining the next block. But more powerful miners have a higher chance, like they've bought more lotto tickets, than those who have only smaller mining rigs. This makes the probability of mining a block using a GPU so tiny that it's almost certainly never going to happen.

See this answer for more info: In the ASIC-age, is it worth starting mining Bitcoin at home?