Daniel Kahneman posted the following on the Judgment and Decision Making site: Have there been studies of the calibration of expert players in judgments of chess situations — e.g., probability that white will win?
A lot depends on the relative skill of the players. Gary Kasparov could probably beat me from a position that would be hopeless if he were playing against a typical computer chess program. The status of the board, by itself, is not enough information to decide anything about who is going to win. Heck, telling your human opponent "I'll give you a large amount of money to throw the match" is a strategy that could potentially generate a win from any situation in which the game has not yet ended, no matter how hopeless.
Furthermore, trying to define the players is a bit of a lost cause. If you assume that the players never make random decisions and that past games do not affect the outcome of future games (a reasonable assumption for computer programs, much less so for humans) then the outcome of the game is entirely determined by the starting position of the pieces. Either White will always win, Black will always win, or the game will always be a draw. I could play one memoryless, deterministic computer chess program against another memoryless, deterministic computer chess program as many times as I want, and they will always make the same moves in the same situation.