The question isn't how rare are they, the question is do they exist. In order to answer that question you have to exhaustively examine the tree anyway so you haven't actually saved any work.
PERFECT GAME

These type of simplifications, in order to be valid as a part of a proof, need to be based on absolute equivalence, not approximate equivalence. It was one of the strategies used to simplify the solution of checkers (or draughts) to a manageable problem, but at no point was an assumption made. Equivalence was proven first and then the trees collapsed.
A simple example can be found in the solution to tic-tac-toe which can be reduced eight-fold by considering each of the four rotations plus their respective mirrors to be equivalent. Again, though, they are precisely equivalent -- there is no room for approximation or assumption otherwise you've invalidated your proof.
As I said, you can reach a high degree of likelihood, but not certainty through these means and solving chess means certainty.

In a perfect game it can easily be a win for white just because of one reason, white has an extra tempo by having the first move. Black is always reacting to what white is doing. That alone may not sound like much but in GM level chess it is worth as much as half a pawn. Chess is so convoluted that it may not be proveable, but white should win.

My belief is that it's a draw -- I suspect that the first move advantage is just too small to translate into a certain win. Consider that positions such as K+N vs K are drawn and that's a much larger imbalance than half a tempo.
My belief is also that it won't be solved by traditional computing but may be solved if quantum computers ever become a viable reality.

Though a forced white win is certainly possible, it is likely black's 'perfect' gameplan would be considerably different then what we are used to (playing against far from perfect opponents.) more importanlty an opponent black KNOWS is perfect Maybe as soon as move 1 black prepares for a material down endgame and just plans on holding on. Instead of trying to equalize at every oppurtunity, black immeadeatly seeks to set up a K+B+P vs K draw (wrong rook pawn thing)
Perhaps black's only option is to play for a K+N+N vs K (which is a draw), who knows, but don't count on that first move being decisive

Of course you could not equivocate analyses, you would have to search to the nonexistent "bottom" and the problem is that like counting you can always search deeper. Chess is too complex with many positions bordering on chaotic to prove anything quantitatively.
Keep in mind that talking about perfect play is really talking about perfect analyses position by position. What I don't get about these kind of discussions is the need to dive off the deep end so to speak and indulge in these abstract/hypotheticals. To use a chess analogy, what is the point in trying to play on an empty board?

Though a forced white win is certainly possible, it is likely black's 'perfect' gameplan would be considerably different then what we are used to (playing against far from perfect opponents.) more importanlty an opponent black KNOWS is perfect Maybe as soon as move 1 black prepares for a material down endgame and just plans on holding on.
That's quite a good description of the current fashion at top level, actually. 1.e4 e5, then play the Marshall Attack as black, stay a pawn down but with the bishop pair, reaching an ending where white is better but he can't win, and still in opening theory.
Or play the Schliemann the way Radjabov does - if White plays the optimal moves, you reach another pawn down endgame, which can be held because of the bishops of opposite colours. Again, while hardly leaving theory. [my knowledge of these things is limited to reviews of the "Attacking the Spanish" book, which explains how to do this...]

A perfect chessgame would probably be really boring, no tactics only endless manuvers and exchanges to a dead position.
-For tactics to work you need a mistake from your opponent, tactics is just a forced win in a won position. But tactics is fun annyway :)

boungcloud guarantees the win +-. (1. e4 xx 2. Ke2!)
But seriously, its pretty impossible to say.
Bobby Fischer can be quoted as saying "I believe that with best play, chess is dead drawn". And that's a super genius who always played for the win. But it isn't a definite answer, as no human being could possibly be sure about it.
Endless discussion!

The question isn't how rare are they, the question is do they exist. In order to answer that question you have to exhaustively examine the tree anyway so you haven't actually saved any work.
I have never met any such a position, where the result of a sacrifyce is revealed in 10 or even more moves, without being noticed before that. You see this is possible only in such a case, where not only the computer program we use to elavuate the position does not calculate that far, but also nothing shows that there is a compensation (I mean, no any attack or initiative). But these positions are exactly what we are going to prune, because there no compensation and the computer evaluation of the position is clear.
Show me one and we will consider this statement refuted.

I'm afraid the onus is on you to demonstrate that the pruning approach is sound and will not compromise your proof. Show me that no such position/line exists and I will accept it -- unfortunately, for you to do so you'll need to exhaustively examine all of the candidates....

Didn't google just recently "solve chess" so I think if both sides played perfectly then it will be a draw, however, I also think White has a better chance of winning just because it starts out first.
ADK
That was an April fools joke
Really? LOL
ADK

In a perfect game it can easily be a win for white just because of one reason, white has an extra tempo by having the first move. Black is always reacting to what white is doing. That alone may not sound like much but in GM level chess it is worth as much as half a pawn. Chess is so convoluted that it may not be proveable, but white should win.
I disagree that white should always win in a perfect game. Below is a game I recently played and to date, one of the best games I ever played. The game has been analysed and shows alternative moves that should have been made instead of the ones that were actually played, Yet, these alternative moves detract from I believe to be my 'perfect game'. The pureists out there would comment that there were so many errors, blunders and inaccuracies and I whole-heartedly agree, because most of the errors and inaccuracies were done by me. However, I went with my gut feelings and led to black winning,
During the above game, my opponent stated twice that he wanted to offer a draw twice, but failed to post the offer of the draw. You will see that I had a passed pawn on the a file, and asked whether or not my opponent would accept a draw with a passed pawn. The reply I received back 'ok, let's see where this goes as this is an interesting game'. The ending, to me, was perfect.
when you get your GM status and a 2900+ ranking then tell me about your best game played.

White has a decisive advantage at the beginning of the game because the kings are an even number of squares apart so white has the opposition.

In a perfect game it can easily be a win for white just because of one reason, white has an extra tempo by having the first move. Black is always reacting to what white is doing. That alone may not sound like much but in GM level chess it is worth as much as half a pawn. Chess is so convoluted that it may not be proveable, but white should win.
I disagree that white should always win in a perfect game. Below is a game I recently played and to date, one of the best games I ever played. The game has been analysed and shows alternative moves that should have been made instead of the ones that were actually played, Yet, these alternative moves detract from I believe to be my 'perfect game'. The pureists out there would comment that there were so many errors, blunders and inaccuracies and I whole-heartedly agree, because most of the errors and inaccuracies were done by me. However, I went with my gut feelings and led to black winning,
During the above game, my opponent stated twice that he wanted to offer a draw twice, but failed to post the offer of the draw. You will see that I had a passed pawn on the a file, and asked whether or not my opponent would accept a draw with a passed pawn. The reply I received back 'ok, let's see where this goes as this is an interesting game'. The ending, to me, was perfect.
when you get your GM status and a 2900+ ranking then tell me about your best game played.
Firstly, the game didn't post as I would like.
Secondly, MrWrangler, that was uncalled for. I am entitled to my opinions as well as you are. I was merely pointing out a fact that your assumptions that white should always win in a perfect game is wrong. And another thing, what gives you the right to state that I must be GM with +2900 before posting what I believe to be my perfect game to counter your statement that white will always win - NONE. I must point out that +2900 has never been achieved by a human, although Kasparov came close to doing so.
Reading your statement again, it sounds like you are pissed because someone has the audacity to question you on your assumption(s).
Did you know that with white opening of e4, the chances of white winning was put at 50%, whilst if white played d4 it had a 40% chance of winning? There is no need to answer the question as I am again, merely pointing out that in a perfect game, the outcome would be a draw rather than a win for both sides

In a perfect game it can easily be a win for white just because of one reason, white has an extra tempo by having the first move. Black is always reacting to what white is doing. That alone may not sound like much but in GM level chess it is worth as much as half a pawn. Chess is so convoluted that it may not be proveable, but white should win.
I disagree that white should always win in a perfect game. Below is a game I recently played and to date, one of the best games I ever played. The game has been analysed and shows alternative moves that should have been made instead of the ones that were actually played, Yet, these alternative moves detract from I believe to be my 'perfect game'. The pureists out there would comment that there were so many errors, blunders and inaccuracies and I whole-heartedly agree, because most of the errors and inaccuracies were done by me. However, I went with my gut feelings and led to black winning,
During the above game, my opponent stated twice that he wanted to offer a draw twice, but failed to post the offer of the draw. You will see that I had a passed pawn on the a file, and asked whether or not my opponent would accept a draw with a passed pawn. The reply I received back 'ok, let's see where this goes as this is an interesting game'. The ending, to me, was perfect.
when you get your GM status and a 2900+ ranking then tell me about your best game played.
Firstly, the game didn't post as I would like.
Secondly, MrWrangler, that was uncalled for. I am entitled to my opinions as well as you are. I was merely pointing out a fact that your assumptions that white should always win in a perfect game is wrong. And another thing, what gives you the right to state that I must be GM with +2900 before posting what I believe to be my perfect game to counter your statement that white will always win - NONE. I must point out that +2900 has never been achieved by a human, although Kasparov came close to doing so.
Reading your statement again, it sounds like you are pissed because someone has the audacity to question you on your assumption(s).
Did you know that with white opening of e4, the chances of white winning was put at 50%, whilst if white played d4 it had a 40% chance of winning? There is no need to answer the question as I am again, merely pointing out that in a perfect game, the outcome would be a draw rather than a win for both sides
I had no malice in my statement i was just saying that we are talking about a perfect game. You chose to take offense. I could have been more politic in my wording, but that isn't in my nature. Until you or I or Anad or someone comes up with enough skill to play without mistakes we will never know, but the first move is and will be powerfull.
I'd offer this as an example of why the assumption doesn't work:
Suppose that the result in the "perfect game" (assuming a single best move from either side for every position) is that White does in fact win, but during the game White's best move at one point is in fact to sacrifice his Queen in order to secure that win.
Your methodology would discount this line as lost and may consequently arrive at the wrong result.
Primie Facie, it would appear that my methodology would give us the wrong result; however,it would only give us the wrong result in situations where the justification of the sacrifice occurs many, many moves later. (since we would obvoiusally use the best chess playing computer we have to judge the position as "without comp" in the first place)
The question is, how likely (rare) are these Occurances? (supposing they even exist!)
your sort of reasoning seems to me absurd[forgive the following strawman :)]:
"I think that the below position might be a draw, since I cant see all of the possible logical continueations, Black might have compensation somewhere!"
also in addittion to my original post: if there is a forced mate, then we can ignore all other possible continueations....so once again, it is false to say the the enormous amount of possible positions prevents chess from being solved.