For GMs, white's first move offers a very small advantage. So usually black hopes to equalize first before trying to play for a win.
If white offers black equality in stale position though, it can be very hard for either player to win. When the files that have pawns are the same for both players (like an exchange french or exchange slav) there tend to be fewer imbalances. With a similar structure and very skilled players it's difficult to win.
There are also some black defenses that are very solid and merely aim to draw. Some are technically very difficult and aren't good ways to draw for players like you and me, but they're very effective for strong GMs. For example if the only thing you do is "defend vulnerabilities" then the pressure is actually increased because you will be passive, but strong players can deal with that pressure.
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Chess is not like outdoor sports The player who makes the best moves or fewer mistakes doesn't always win. You can make 50 perfect moves and lose the game on move 51. It's more like a difficult puzzle than a game of tennis.
I have been observing grandmaster games recently (for few days). I seem to notice that many chess grandmaster games show tactical victory over their opponent, only when both strive for a win. Take a look at this :http://www.chessgames.com/chessstats.html . The number of draws are 34%, which is unimaginably high. The reason I feel this way is, when a player wants to play for a draw rather than for a win, then he would play in such a way that each move he makes defends vulnerabilities and makes sure the pressure is reduced. Doing so will make it difficult for his opponent to win, who actually fights for a win. Is my analysis correct? Or what's your opinion on this? Look I don't see too many tie matches in tennis or any other outdoor sport... Again, is it possible for a grandmaster to win another grandmaster who actually plays for a draw rather than for a win (regardless of who has the white pieces)?