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If you could tell the parents "Greece is about to win this World Cup!" then you could also say "Вам повезло, что у вас такая прекрасная дочь"

Sounds like stupid joke, but nice and funny. Just very...

Мне та-а-ак повезло, что я тебя встретил!

Синонимы слова

I agree that there is no single universal word to apply in all situations described,but among endless list of "approximations", I would
suggest

1) наглый
2) нахрапистый
3)...