I think that one could make this question a bit more objective, while I think keeping the same spirit of the question.
- Gather a bunch of N-by-N game records played by professionals and/or top amateurs (high dan levels).
- Show only the first X moves of each game to some strong (like a professional or top amateur) observers (assuming that they are not already familiar with those specific games).
- Ask the observer to guess which color won each game, and record their success rate.
With data from enough games and observers, while varying the parameters X and N, one could put together a table of statistics that would contain information like “very stronger observers on average have a Y% success rate of guessing the winner after observing X moves of an N-by-N game by similarly strong players”.