Hi there
I love this topic. Thanks for posting. You've asked some interesting questions. Most people are pretty dismissive of the perfect play outcome being anything other than a draw. It's nice to see someone having a more open mind about it, so let me address your two questions.
On the first you are absolutely correct. The point can be illustrated with the far simpler game of tic-tac-toe, at most nine moves long in which there are only a few thousand different games, as opposed to Shannon's number for chess. You probably know that if both players play tic-tac-toe perfectly the game is bound to be a draw: neither can force a win without the opponent erring. But there are many different ways this can be done. For example, the first move doesn't have to be in the centre. Even if you could force a win fron the start, as you can from many tic-tac-toe or chess game positions there might be several ways to do this. They are all equally good, although computers tend to be programmed to choose the fewest moves to victory against best play.
On the second point, it is pretty clear that having the first move is an advantage in both tic-tac-toe and chess. So on that basis I think it is highly unlikely that the perfect chess game is a win for black. It would imply that the opening position is a 'zugzwang' situation and that somehow every one of the 20 possible opening moves puts white in a worse position than he starts in; that the best move, if it were legal, would be to do nothing. Put to one side the amusing fact that, since the position is symmetrical, black would then wish to do the same, resulting in stalemate. Suppose we make a special dispensation, only for white, to effectively swap pieces at the start of the game. We can consider, with the simplest of probability calculations, how likely that is to be optimal, without bringing our (perhaps ultimately flawed) human knowledge of chess into it. If we have no reason to believe that any one of the now 21 possible board positions after the opening opening move is the best one then each one must have an equal chance of being the best. If it's better to play as black then doing nothing on your first move as white has to be better than every alternative. But there is only a 1 in 21 chance that this is the case. This translates naturally enough into the probability that, given that one or the other player can force a win it is black that can do it, just under 5%.
At around 25:00 https://www.youtube.com/watch?v=6L4yA-mGtAI International Master Vitaly Neimer discusses opening moves in the context of the latest computer chess engines, giving g4 as an example of an opening move that creates weaknesses for white. Every indication is that not all opening moves are like this, so our knowledge somewhat strengthens the likelihood that, if anything, it's advantage white. The main question is whether or not this advantage is enough to force a win.
I have heard it said that in checkers it is better not to have to make the first move. In fact, like tic-tac-toe this game has been 'solved' and it turns out that that perfect lines of play result in a draw. Nonetheless it is interesting to apply the above argument to checkers. There are seven possible opening moves in checkers giving the a priori probability of doing nothing being better than all of them as 1/128. But there may be reasons to suppose that, not withstanding the game's stale solution, the opening position has advantageous properties. None of your pieces can be captured, for example. Whatever the case really is or has been in checkers (the computer-aided solution of the game renders such arguments moot) the prevailing view in chess is strongly to the contrary, suggesting that the 1 in a million a priori estimate would be an overestimate of the chances of black having the advantage, whether it is a critical one or not in the final analysis.
Hi guys, recently I've become very interested in the topic of the perfect chess game- a hypothetical chess game in which the best moves are played by both sides. Obviously, the result of this game is very speculative- many people argue that it would end in a draw, while others believe white would win.
I have 2 questions about this topic:
As I understand it, in the perfect game the only way to come up with the best move is through brute force till the end result of the game; both sides must evaluate each move in this manner: if after this move is played, if both sides play the best possible moves (evaluated in the same manner) until the end of the game, will the end result be the best possible result I could attain. Therefore, my question is:
1. Because chances are many different moves from both sides lead to the best end result (not sure how I came to this conclusion), wouldn't chance favor that there are a multitude of "perfect games", rather than just one?
2. Could anyone suggest a possible argument that black can/ can't win a perfect game(s) of chess?
A lot of what I just wrote may or may not be complete gibberish, but one thing's for sure: this is no simple topic. I'd appreciate all possible discussion.