This is the 16986th most frequent Russian word.
сотую
"Сотую" means "hundredth" (ordinal form).
Numbering: 'сотую' indicates the ordinal number (hundredth) relating to the feminine noun 'страницу'.
Я отметил сотую страницу книги.
I marked the hundredth page of the book.
Ordinal enumeration: Again 'сотую' links to 'попытка' (attempt), stating ordinal feminine numbering.
Это была его сотую попытка решить задачу.
It was his hundredth attempt to solve the problem.
Achievement count: 'сотую' describes the sequence of games (ordinal) related to 'игру', showing ordinal association.