Luck is merely chance.
The definition is:
http://www.answers.com/luck
Einstein made the comment that 'God does not play dice'. Although Albert was an atheist he meant that every event is the direct result of a cause not chance. Cause and effect. Chance is the odds of 'cause and effect' taking place in a certain sequence. Chance needs to be relative to something.
Definitions (edit: sorry that should be Examples not definitions) of 'fortunate' and 'unfortunate' are relative to the observer.
Now if 'fate' is what you are talking about, or 'karma' as they say in India, that is a different story. Buffy has an interesting idea on mental suggestion.
Proof of fate does not exist. It is metaphysical. As such we cannot say.
'Jinxes' are based on superstition yet are interelated with fate.
Positive thinking does not change cause and effect. It merely changes how you react. Same with pessimism.
One in a million is relative to what. You have one in a billion; one in five; one in 3000. In regards to casinos, I learnt whilst studying statistics, is more in the order of 1:200million odds of a casion going broke.
If you have 100 reds in roulette the odds of the next colour being red is 16:37. With a 1:37 chance is of it being green or 'zero'. The odds of the next 100 spins being red is a very high number.
The answer to this question is based on poker. Is there a meaning behind nine shuffles that helps you win? This is either mathematical, mental (thanks Buffy) or metaphysical. I'd go for mathematical first. Try mental next. If not I'd suggest it maybe the latter.
Thanks
Josephine