Okay, I have an engineering degree (UNL) and have taken several statistics courses. Everything I've read and studied tells me there is no such thing as "luck". That is, you can't get on a hot streak (or cold streak) so that the dice, cards etc. favor you (or disfavor you). But, damn, from experience it sure seems like a guy can have hot and cold streaks.
Hm...randomness doesn't mean a different result on every coin flip -- that would be highly regular. Random outcomes will invariably have streaks - you could flip a coin 10 times and get 8 heads in a row. Globally the trends will tend to 50/50.
The distinction here is that those are the results of randomness, and being on a streak doesn't influence the next outcome. Getting 5 dice rolls in your favor in a row doesn't make the next one any more or less likely to favor you; it's an IID random variable.
I would consider "luck" and "streaks" to be different things. Chance events that fall in one's favor, that's lucky. On the other hand, let's say a basketball player makes five shots in a row, does that mean he's on a streak? I'm not sure what the numbers say, but it's possible that the added confidence -- and the lack of confidence from the defending team -- could contribute him to be sharper on his next throw. Or maybe the pressure will get too big for him and he'll fold.