So in other words, if the sequence of probabilities favours a person, we can say he is lucky?
I ask because, these sequence of probabilities you talk about is completely out of our control. You and I do not get to decide when and how it occurs. Sometimes, it's in our favour, other times, it's not.
LUCK can be defined as "something that happens to someone by chance, a chance occurrence, especially a favourable one"
So you may call it distribution of probabilities, another person may call it luck, but in the end, you are all talking about the same thing.