A question about the "solving" of chess

@Vetinari_Computer actually the number 10^120 is really a small one compared to the all possible games that are possible in chess. For example the longest possible game in chess consist in more than 5000 moves! (and not 40)

This actually do not tell us something, because as u pointed out before there might be the "Strategy of God" for white that could be relatively short compered to that number.

But the growth of the possible game is exponential. In fact if we assume that a game on average last 80 moves (something that is not absurd because game played by corrispondence and games between engine reach easily that number of moves) the number of possibility is (30^2)^80 which is huge. Is nearly 10^236.

The point is that if there is this so called "Strategy of God" I really do not think that is possible to find it because for testing that line (something you have to do to say that is the best way of playing) with all the possible responces for black u had to "write" them down.

In a paper, in an Hard disk, or even in the entire universe, I do not think that there is enought "space" for that incredible research, because I don't think that this line can be so short to fit with it (if it really exist, that is not obvious).

If this line is 100 moves long probabily (unless most of the moves are an endgame with few pieces) we and nobody else in the universe can't find it. It is even possible that we have already the initial part of this God Line in the Opening Theory and we are not aware of it beacuse we "gave up too early".

It is possible, at least in theory, to find this line by using an incredible powerful engine instead of using the brute force method.
An engine, like an human being cannot stand against this enormous number so it (and us) are forced to "cut" some move that we do not consider good. We select the moves a priori, before calculating.

In this research, even the best engine or the best AI can make some inaccuracies that will compromise the whole work.

I let here an example that even the best tactical player in the world, Stockfish (that is really a tactical-monster) miss a really short tactical combination because of his "cut".

It is not a matter of improving the engine (or AI) there will be always a chance of mistake with such an incalculable possibilities.

In this position White has a force win but Stockfish, because of his a priori "cut", cannot realize it untile it is too late.

This is just an example that every a priori method to find moves is not perfect because of the fact that is what it is, a priori.

Even if the probability to make inaccuracies is nearly 0, multiply by the enormous amount of moves it become compromising for the research.

@SharpMind1 You once again miss the point.
To prove a game like chess you would never ever build the entire game tree. The point is you build a big, maybe even 32 men TB instead. Here's why:
The number of 32 men positions is less than 64! / 32!. (you choose in what "order" all the pieces / empty squares are, however the empty squares are indistinguishable so you can divide by 32!) In fact it is much less than that but let's keep this number as an upper bound.
Now quite clearly that number is bigger than 64^32 = 2^192 < 10^60. So there's less than 10^60 legal positions.

Now to solve that you "only" need to backtrack there. Assuming you have a 31 men TB before starting (you can get that by doing the same I describe now, except with one piece less) you then look at all the positions with 32 pieces that are mate on board. You then look at all possible "unmoves" in those and in lost 31 men positions to find all positions where a player has mate or conversion in 1. Then you search for all positions where all moves of a player lead to them losing in 1 to have all the losses in 1. Then you find wins in 2 by unmoving in those again etc.

That way you find and label all winning/losing positions. Per construction all the remaining positions are drawn so you just need to check the starting position and if it's not in the set of winning positions it is a draw.

All these calculations would only need memory and calculation power in the order of magnitude of 10^60. (and as said before, that bound can be decreased much further)

Looking at every possible game of chess is definitely unnecessary as if we see a position, in which the player to move has a mate in 1 we don't need to look beyond the mate to know that the position is a win. The ways to show that a position is a draw are to
1. Show that there are no legal moves that can result in checkmate for either player.
2. Show that whoever makes the first move that deviates from the line that results in the draw loses by force.
3. Show that all legal sequences of moves that result in a checkmate for either player must include a type of move A from one player and a type of response B from the other player, in which neither move A nor response B can be forced.

For instance this position is an example of a position that can be solved as a forced draw by #3 as all legal sequences of moves, in which either player gets checkmated must include black sacrificing a rook, and white capturing the rook, but black cannot be forced to sacrifice the rook, and white cannot be forced to capture the rook.

lichess.org/editor/r3kb1r/8/3p1p2/2pPpPp1/1pP1P1Pp/pP5P/P7/3K4_w_-_-

Also any position that has either perfect rotational symmetry, or perfect mirror symmetry to another position that is already solved must also solved. For instance if the position after 1. e4 e5 2. Nf3 Nc6 3. Bc4 was solved then the position after 1. e3 e5 2. e4 Nf6 3. Nc3 Bc5 would also be automatically solved as it is the exact mirror image of the first position with black playing the role in the second position that white plays in the first position.