As someone who has studied several statistics courses for my major, I have grappled many times with the concept of randomness. At first look it seems easy enough to define: an event is said to have a random outcome if each possible outcome is equally likely to take place. Throw a die, and if it's a fair one, then each of its six faces should have equal chances of showing up. If the die's outcome is truly random, then over many tries the different possible results should show up with relatively the same frequency; throw a die six thousand times and the face with the four dots should come out around a thousand times. The same goes for all the other faces.
But people have more complicated thinking, and this clarity of definition is difficult to attain for some. If at the very start of your attempt to throw a die six thousand times, you come up with six dots for four times in a row, you would doubt the die's randomness, wouldn't you? The basic definition of randomness, however, does not actually imply that the same results cannot be achieved consecutively. Even if all the other faces possess equal likeliness of appearance, it does not guarantee them actual occurrence, especially in a small number of tries.
In the early days of systems simulation using computers, one of the first problems was that of building a random-number generator program necessary to feed the simulation models with a stream of random numbers. (You can think of the simulation models as engines running on the fuel of random numbers.) Some keen persons inspected the stream coming out of these programs and noticed that certain numbers are repeated in adjacent positions; taking this as a sign of predictability and therefore non-randomness, the programmers modified their algorithms such that the generator would not output numbers consecutively. The irony is that in doing so, they actually distorted the entire system's randomness—in trying to make the program appear perfectly random, they made it less random.
This once led me to realize that, maybe, people's attitude in life can be measured by their concept of randomness. Also, the lesson we should take away from the random-number generator story is that the mathematical definition of randomness cannot possibly be the only valid definition of this profound concept. Cold logic is sometimes too harsh to always be the main principle we abide to in our lives.
I think that the people who believe in good and bad luck have a concept of randomness, but theirs is a randomness that is not impartial, a randomness that has an agenda of dealing out good and bad fortune to persons contingent on things such as the alignment of stars and other phenomena. Then there are people who believe in a universe of utter and rigid randomness, where both mundane and life-changing events are driven by a perfectly random mechanism.
I'm tempted to say that the latter attitude is 'better', but that would be an unnecessary judgment. Instead I would say that the latter attitude can be associated with modernity, while the former, with pre-modernity. It would seem that persons who subscribe to the fair-universe view should be more satisfied with their lives, and psychology seems to agree: there is the concept of locus of control in the study of personality, which refers to the amount of control individuals think they have over the course of their lives. The more internal a person's locus of control is, the more that person thinks that her or his life is under her or his control rather than that of uncontrollable external factors. That is, I would say, a person with an internal locus of control believes in a universe driven by randomness, but one that can be manipulated in such a way as to make the odds work to that person's benefit. Psychological research has shown that individuals with a more internal locus of control have greater satisfaction with their occupation—unsurprisingly, because empowerment has always been associated with satisfaction.
I would like to play the postmodernist's part here, however, and point out that satisfaction, or by extension also happiness, cannot possibly be the only factors that determine a better attitude to life. Or if there is such a thing as a better attitude to life at all. For all its rigor and sense, psychology is still a product of modernity, and products of modernity have been shown to be biased in the past. Remember, for instance, how homosexuality used to be classified as a mental disorder until a few decades ago.
The good-and-bad-luck view of the world seems a delusion by modern standards, but think of it, wasn't it romantic? Heroic fates and beating impossible odds continue to enamor those of us who live in this day; the idea of randomness rallying behind a noble cause is still the substance of literature and films these days. We have Greek gods and Marvel superheroes and Disney princesses capturing the imagination of millions everyday. The ludicrous dreams that people from pre-modernity conceived of and believed in have become the very dreams that we, in modernity, long for.