I couldn't find any data about the percentage of moves that a typical human grandmaster would be able to predict in games of other human grandmasters. To clarify my definition of accuracy: The predicting player would predict the next half-move for a position from a game he or she has never seen before, only being able to see past positions from the same game (preferably without even seeing the names of the players or when the game was played). To limit the influence of blunders, only games with classical time control should be used and the predicting player would have a limited time per move to make the prediction (let's say 1 minute per move). A correctly predicted move counts as 100%, an incorrectly predicted move as 0% and these numbers would be averaged over a large number of positions.
Since I couldn't find anything, I tried it myself and achieved 42 out of 119 (35.3%) in a randomly chosen grandmaster game (Alekhine vs. Erik Lundin, 1941, Round 7), but I'm quite amateurish, not a grandmaster. Randomly guessing legal moves would have achieved less than 5% in that specific game. My conditions do not have to be followed strictly, but I'm not really interested in accuracy results for blitz games, games of weaker players or "immediate", intuition-based predictions (i.e. without giving the predicting player time to think).
I'm interested in this because I want to know how accuracy varies with playing strength of the predicting player.