PERFECT GAME

It is likely that white would win. But it could also possibly a draw.

I have to disagree with that statement. White does have a slight advantage with the first move. However, if white plays agressively and black is brilliant defensively, white loses the advantage by playing a defensive move such as 0-0 or 0-0-0 as it will need one or both rooks in play to press home its slight advantage from the opening move. When white plays 0-0 or 0-0-0, black can counter-attack and put pressure on white. Kasparov did this many times against Karpov.

It is flawed logic to suppose that just because there are billions [massive understatement] of chess positions, chess cannot be solved.

If we use a few Heuristics, we can get the number of positions down dramatically.

for example:

1) Assume that if one side loses a Queen (without comp), the game is simply lost. Assuming this assumption is true, it means we can reliably solve chess without having to look at every possible logical continueation.

Any error whatsoever means that you haven't solved chess.  You simply can't make those generalizations and still have a valid proof.

The trick is in your little "(without comp)". To prove that the queen was lost without compensation, you'd still have to go down all the lines.

Also, it doesn't help much, there'd still be way too many positions.

I dont think you do.   I think we can reliably assume dropping a Queen loses. I very much doubt that in the above game on move 3027 white equalises. Dont forget that, while we cannot play the game of chess perfectly, we can play it to a reasonably high standard. Therefore, it seems unlikely that perfect play will prove the vast bulk of conventional wisdom is wrong. (i.e it seems unlikely that perfect play will demonstrate that, contary to what we thing today, rooks on open files are a bad idea, bad bishops are actually good, or that a knight is more valueable than a queen)...

put it this way, if perfection was to have an elo, what would it be? --- maybe perfection is something as low as 3000. If so, then surely that would prove that our most sophisticated players and engines are "on to something"  (i.e that conventional chess wisdom is broadly correct) since they would be able to draw/win some of the time against perfect play.

And if we can proof that chess wisdom is broadly correct, we can reliably assume dropping a queen is simply lost, without looking at any and all variations.

Good. Half the world already believes chess is a draw, but it's not proven yet.

But now it can be proven, because Blackadder thinks some things and very much doubts some others.

Prove it. That's the entire point.

You can't "reasonably assume" anything and still have a rock solid proof.  There is no place for assumption in this exercise, it has to be exhaustive.

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.

I agree. Because of white zugzwang.

Actually Blackadder is right. We can stop searching the tree of moves when one side has a big advantage (material or positional). See the "Pruning" . For that a good-playing computer is ok. If white has +3 (or -3 for black) then it is obvious that it is going to win.

Plus there will be a number of "mirrored" positions, if white loses a tempo. For example: 1. e3 e5 2. e4 ... and we get a position where black is in white's place of having a tempo and they can play Rui Lopez or King's Gambit on their choice.

There are much more such pruning conditions. The only problem is to discribe them all. :)

I'll let Mr. Morphy know that the pruning theorists have declared several of his most famous wins to be losses because of the queen loss.

Pruning is demonstrably not perfect because of the horizon effect.  Understand that a proof needs to be exhaustive.  If you discount a line because it is probabilistically not best there is still a probability, albeit very small, that you have eliminated a line that is in fact best but just looks wrong initially.  This means that you don't have a proof but instead you have a high-degree of likelihood and they are not the same thing.

Yes, but they invariably include illegal moves, for those can be found in any arrangement of pieces. A math book once said that if you ignore all the illegal moves and only consider the possible ones too, it is 1 to the power of...and the answer would indicate more moves than there are atoms in the earth. Or something like that. I found it interesting that they said the actual number is impossible to come up with, given all the off-shoot possibilities from any position.

This is one reason chess hasn't lost its appeal. If we were to eventually come up "the number" I wonder, would someone then try to figure out how long it would take to play them all?

In order to use pruning, you would first have to prove something along the lines of "the board complexity is small enough that static compensation can always be realized dynamically in under N ply" where N is small enough to be searched exhaustively. I don't have high hopes that a proof of this is possible, even though the statement might be true.

Calculating the number of moves or positions in chess is incredibly tricky.

The best estimate we have now is something like 10^50 

The number of possible games is larger than the number of atoms in the known universe. That's why it is quite possible that no computer could ever scientifically "solve" chess. (But they will certainly get good enough that they could never be challenged by a human player).

N is currently 6 I believe -- it's the size of the largest exhaustive tablebase.

[Edit -- I misread your post Loomis.  N ply, not N remaining pieces.... nonetheless as a measure of complexity it is one where we have an established answer to the question of under what value can we currently identify what perfect play is.]

Ladies and Gentleman of the Jury, and the Jury is still out on this one, because we can give or opinions, disect these opinion and give another in its place, but when all said and done, "Perfect Chess" between two humans will never ever be achieved. In life, everyone will make their own decisions that suit their own individual needs and once that decision has been made it cannot be taken back and we will have to live with the consequences.

The same can be said for chess where we make that move that in principal looks good, but the repost from our opponent has us in trouble with checkmate as the ultimate prize.

Um, Reb, those aren't computers! I think it's safe to say that it is not "the perfect game" either.

The argument about the number of possible chessgames being an extraordinarily huge number and thus chess is unsolveable fails to consider that the solution tree of the solved game would be much much smaller than the number of all possible games. That said, as I recall from a previous debate regarding this topic, it was argued to me (convincingly) that even the solution tree beginning from a single opening move, say 1.d4 (not 1.e4? which IMO is losing ;) would be theoretically uncomputably huge.

Interesting discussion.

I tend to agree that the game would end in a draw. Not because black can completely equalize white, but because he can go into a "fallback position" a dead drawn endgame where he is down in material.

So while I think white can maintain his advantage, (he may be able to force the win of a pawn or so), but he can never force the win of the game.

The black wins by zwungzwang is an interesting idea, but I suspect it is an oversimplification of the 0.5 tempo difference between white and black. (i.e white can triangulate...etc to avoid the coming zz)