21 Jul '10 20:41>
Originally posted by Mad RookYou are right about a need for a weighted average but a bigger question is whether the result of any analysis of RHP historical results can help answer the question being asked.
That's what I thought... You can't do that, Geoff. It has to be a weighted average. 🙂
(Lies, damn lies, and statistics)
While chess is a game of perfect information in information-theory terms, actual games are played by imperfect humans or human-made imperfect machines. We all have experience with blunders by ourselves and/or our opponents. We know that many of our completed chess games contain at least one suboptimal move, that is, where a better move was available, and where the suboptimal move either was, or could have been, exploited to achieve a theoretically win or to salvage a draw from a lost game. In some games, the bad move is very hard to detect, but we tend to believe one was made. At least one.
Why should any such game be counted in answering the question that was asked?
If we rely on historical results, the games that should be counted are the games in which the optimal (best available) move was made at that point in the game when the suboptimal move was made. In fact, the games that should be counted are the games in which the optimal move was made at every point in the game, by both sides.
This selection criterion is impossible to apply because it requires proving a negative: "There is no suboptimal move in this game." Also, it suggests that there may be only one completely optimal game! In that case, the outcome will prove that there is either an overwhelming advantage for W or B if one side wins, or no advantage, if it is a draw.