You can work harder at tossing coins and toss them more often but previous outcomes do not affect current or future outcomes in any way. No matter how many times in a row a coin lands tails up, there is still only a 50% chance that it will land heads up on the next flip.
Working harder/smarter than someone else at something for which each try increases your capability to influence the next try should give you an edge in a competition but now it's not about luck.
> I wonder if those who believe they are lucky work harder and take more chances than those who don’t.
Now, if anything, you can also postulate that people who believe they are lucky don't work harder and take less chances (hey, they are lucky, they don't need to try as much as others).
So the question would be: why do some people who think they are lucky try their luck more than some who don't think they are lucky and why do some people who think they are lucky try their luck less than some who don't think they are lucky ? It's two opposite behaviour but they have the same belief. Why ?