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I can't imagine it differently. The advantage of the first move is in my opinion an advantage for white, yet too small to force a win. The GM's are very good at chess. If chess would imply a win for white, then would imho the rate of won games at the GM level be much higher then currently is.
Hasn't there been research indicating that the higher the rating of both players is, the bigger the chance that the game ends in a draw?
No not for me, for all the games I played in USCF, 60% of them ended in draws
Yes, the higher rating for both players--the bigger chance the game ends in a draw.
This is obvious from watching grandmaster games.
The operative word is theoretical. The trend in chess history for Super GMs playing different openings is an eventual refutation of certain lines and the process repeats itself suggesting a theoretical draw with perfect play.