This is the 15704th most frequent Polish word.
szasnę
"Szasnę" is not a standard Polish word. It seems misspelled; perhaps you meant "szansę," which means "chance" or "opportunity" in English.
Here, 'szansy' refers to an opportunity or possibility, used in the genitive singular form indicating possession or specification.
Nie mogłem przegapić takiej szansy.
I couldn't miss such an opportunity.
'Szansę' in this sentence is used in the accusative singular form as the object of the verb 'see' ('widzieć').
On zawsze widzi szansę, żeby coś poprawić.
He always sees a chance to improve something.
Here, 'szansę' is used in the accusative singular form to inquire about the possibility or likelihood of an event occurring, in this case, winning a competition.