What should be the core functions of games which represents an excellent game? What quality goals it should achieve to become successful game?
Any concise formed answer will get me on track.
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This is an insanely difficult question to answer and unfortunately I don't have an answer for you (but this is longer than a comment, thus posting as an answer).
AFAIK, there are no metrics concerning methods to quantify the fun factor in a game during the design and implementation phase. Otherwise, you wouldn't have bombs and metacritic wouldn't be overly useful.
It's fairly easy to find out whether or not a game is fun after having played it: If you want to play it again, then you've achieved your goal. Having said that, even this metric is entirely subjective, so you'd need to focus test it against a broad audience before knowing whether or not you've achieved your goal.
Find games that you enjoy playing (preferably ones that are popular and perhaps have a high'ish metacritic rating (although that's not always the end-all-and-be-all of how fun a game is)) and "borrow" ideas from it. Play others and "borrow" ideas from them. Throw together a design for a game and talk to a few people about it. Get their opinion.
If you have the time after that, throw together a prototype. Have some of your friends try it. Get feedback and use it. Then, look at implementing the real thing.