i agree that you need to be a better player than your opponent to win the game he he he cause with in a game there are blunders along the way between two players which they will know sometimes after the game or several moves later because every player have their own focus or game plan . as normally seen in weaker players once your a kibitzer and you are of a higher class than with those two antagonist then you can comment if you are allow to their mistakes right away . so along the way  who ever comes firts to analize the mistakes of his opponent and materialize it up to the end is the winner that is why we have the master level and grandmaster level who spend most of their time to achieve less error with their games as a fact a rated player can bet masters and grandmasters also if during the game they play BETTER than the masters they are fighting with he he he .

   Comparing chess to math, mathematician GM John Nunn once said that in math one had to be completely accurate, while in chess one needed to only be more accurate than one's opponent.
    I always figure a mistake isn't a mistake unless my opponent proves it to be. In order to play perfect chess, one needs to be a computer, and who wants to be that?

You sure could have cut your work short several times, but you got the job got done nonetheless.