I do believe that people can be in situations where they are lucky, unlucky, or neither. I'd say luckiness is where something favorable occurs for you while being statistically improbable and mostly out of your control, while unluckiness would be the converse. The 'neither' case occurs when something good or bad happens to you that is statistically probable. As a whole, I think individual situations can be considered a zero-sum game when considering luck. But, in the context of your entire life, it's unlikely that anyone is especially lucky or unlucky.
SO anyway, do you guys believe in luck?
And if you do, then what is the opposite of luck? Merely the absence of it ? Or is it "bad luck"?
Both people are lucky, considering that either scenario involves the person getting a winning ticket despite horribly unfavorable chances. I think the former person does have a marginally higher chance of winning the lottery by the logic you used (where the ticket purchase improves his mathematical chance of getting the winning ticket). If the situation involved more personal choice in the outcome (since winning a lottery is generally mostly outside one's control), then there can be more of a claim to personal responsibility for the success rather than luck, but this scenario makes both possibilities a result mostly of luck since there were few defined personal choices made.
Let's say we have on one hand a person who wins a prize in a lottery.
On the other hand, a person who, by chance, finds a lottery ticket that turns out to be the winning one.
Are both persons lucky? To what degree? One could say the first person PUTS herself in the way of the wnning prize, thus enlarging the candidacy for good fortune and and leting all the rest as a matter of mathematical probabilities.