Lucky numbers or lucky days are indeed just a coincidence of something happening on same occasions.
It's not necessary for something to happen again and again over that so called lucky number/day.
I believe in luck and that it favors us some times but I don't believe in lucky number or day.
It is not bad to believe on such thing and believing in your lucky day could give you a good positive and good mood during gambling session and for me it is nothing wrong to believe in lucky day or number but if it is too much then that is bad, for example wasting so much money for the day you believe that is your lucky day even though you are losing.
This is what happens to me on my birthday I said to myself that I can pull off a big win but I kept on losing and didn't give up until the losses grow bigger. I feel somewhat disappointed at the end but few days later I hit my target multiplier but the wins was not huge enough as I am only a small gambler.
I still believe on luck until now. This was some kind of a tradition already on my place. As long as it doesn't harm us physically I think it's alright and like you said it can motivate us which was good for our overall health. To the op's question, my answer is both of course, that way, there is no need to jump from one site to another because the site you are playing have it all.