If computer engine ever solve Chess, it will still be interesting!

[Chessqueen]

Since there are more chess games positions (10^120) than the number of atoms in the observable universe (10^80), it is highly unlikely that chess engines will ever completely solve the game of chess with all 32 pieces on the board in our lifetime, but even if a computer would solve chess, which I doubt, I think that the branching nature of chess after every move would make it humanly impossible to memorize all the move sequences that this computer would provide us. I mean if we could do it, wouldn't we have already used stockfish for this considering it's stronger than any human anyway? We could however, maybe deduce possible themes and strategies in every perfect game the engine provides, which I think could actually be beneficial to human chess

[jefk]

No there are not are Not so much game positions,
Of course when you think of a tree you can derive such an insane large nr from
a calculation, but that doesn't take into account the -many- transpositions.

Second, avoiding simple tactical mistakes eg. ply <10 will
significantly reduce the tree.

Mind you, checkers (not sure about draughts) has been
solved, result a draw, but that doesn't mean all possible positions
have been 'solved'.

PS actually chess is almost weakly solved imo, and the
result is -as we (or a least some of us) knew- a draw.

[chesskobra]

The number of atoms in the universe and the number of possible positions in a game have no relation to the solvability of the game. We can easily construct games with much larger trees than chess, that are completely solved, as well as we know how to play them.

Another point which jefk has made: that avoiding < 10 move tactical mistakes will significantly reduce the tree size. I will go further and say that it may even happen that avoiding obvious tactical mistakes may leave at most one playable move in any position, so an engine may be able to play a theoretically perfect game by simply not playing wrong moves.

[Leo]

I dont see a need to include bad moves in a solved chess tree.

[j.t.]

Since there are more chess games positions (10^120) than the number of atoms in the observable universe (10^80)

John Tromp found that the number of sensible chess positions is likely roughly 10^44.

[jefk]

while having difficulties getting this posting through
the cloudflare wall, here's nevertheless an attempt":
Regarding mr Tromp's finding about 10^44 positions:
Ofcoursethe theoretical amount of legal positions in chess
is by far much much larger than the number of positions
which you get in a Normal game of chess....
And that is an important distinction when talking about 'solving'
the game, a game theorist as Tromp should know that,
For solving the game we Only have to look at positions which
can occur in a 'Normal' game, not at all theoretical positions.

Now there is a relatively big (imo) drawing margin
in (the endgame of) chess (eg when having unequal bishops),
but once one side is behind with eg. five points or so
in a (relatively) 'quiet' position then the game is lost for
that side (ofcourse there are combinations where sometimes
one side can appear to be behind for eg. five points and
then nevertheless win the game, but that are not 'quiet'positions.
Which is why i wrote "in a (relatively) 'quiet' position".

So, as already was pointed out, as there

1) is no need to include all kinds of big tactical mistakes in
a tree, you get a tree for chess as eg. in the Chinese database,
and from that, and Zermelo's theorem in game theory we can
infer that chess is a draw and is -almost- weakly solved.

2) for other positions then from normal games, the top engines
as SF also are close to finding the solution (not necessarily
'best'move) ie keeping a draw when possible, finding the
win when possible, and seeing it's a loss when that's the case;
on a fast comp with a few hours calc time, such positions
can be adequately 'solved' (with exceptions maybe which
would be articifically constructed and have no real value
when looking at chess from the game theoretical view.

3) there's no need to solve all possible positions in advance,
for weakly solving chess imo it's sufficient to solve the tree
as mentioned under 1) and being able -in theory- to solve
arbitrary positions as mentioned under 2). Ergo chess is
almost weakly solved. Disclaimer i'm not a math purist
not game theorist and i don't care about nomenclature,
officially with a project as the Chinese database and
Zermelo's theorem we can consider chess to be solved
in an 'ultraweak' sense, but for me that means almost 'weakly
solved'(just like checkers, for example (draw), or four
in a row (win for first side); for the last two examples
it's easier to solve arbitrary positions, but even then i dont'
think Schaeffer 'solve' all possible positions in checkers,
only those that matter (and to which he got a given result
via endgame databases). Not all positions in the Chinese
database are yet connected to endgame databases, but that
doesn't matter, it's obvious from SF's strength and the
known large drawing margin in chess, that from a score as
0.0, and remaining 0.0 you never can get in a winning
endgame position. So besides mathematical academic nitty
gritty about nomenclature like ultraweakly solved etc.
from a normal scientific perspective we can say chess
is practically solved and it's a draw.

[elpapa]

Regarding mr Tromp's finding about 10^44 positions:
Ofcoursethe theoretical amount of legal positions in chess
is by far much much larger than the number of positions
which you get in a Normal game of chess....
And that is an important distinction when talking about 'solving'
the game, a game theorist as Tromp should know that,

But that's what he said, 10^44 sensible positions.

[j.t.]

Regarding mr Tromp's finding about 10^44 positions:
Ofcoursethe theoretical amount of legal positions in chess
is by far much much larger than the number of positions
which you get in a Normal game of chess....
And that is an important distinction when talking about 'solving'
the game, a game theorist as Tromp should know that,

But that's what he said, 10^44 sensible positions.

Oh, by that I meant, positions that are legally reachable from the start position. Many of them will still be ruled out easily to be ever encountered in a game of chess where each player tries to win. If you look at that link, there are some of the weird positions displayed that are counted.

[elpapa]

Oh, by that I meant, positions that are legally reachable from the start position. Many of them will still be ruled out easily to be ever encountered in a game of chess where each player tries to win. If you look at that link, there are some of the weird positions displayed that are counted.

Ok, I didn't look at the positions.

Still, I would have thought that out of 10^120 possible positions (I assume those are legal positions, albeit not necessarily reachable) more than 10^44 would be legally reachable.

If I put a random number of pieces plus both kings on random squares, there's only 1 chance in 10^76 that position could be reached in a game? That's like picking a specific atom in a hundred billion galaxies.

Something must be wrong, possibly my train of thought.

[jefk]

ok 10^44 is smaller than 10^120, so indeed i
guess he (Tromp) meant the nr of positions legally
possible from a chess game, but again if we remove
the moves with eg. score higher or lower than SF value + or -5
(with say one hour calculation time) the nr of positions is
much lower; in the Chinese database it's a matter of billions,
but as i wrote they don't go into the endgame tablebases,
not that this matters, if the (best) score is zero and remains
zero within this tree, for all practical purposes it will remain
zero (this is not a proof, i acknowledge, but then this is
why i wrote about 'weakly solving' chess, as in checkers;
which also was not theoretically proven to be a draw,
but simply shown to be a draw from a lot of computer time
i.e. lots of positions indeed.)
PS talking about proofs and practical purposes,
here's another thought experiment: as some GM's
as Akopian and Rowson wrote, Black has just as good
chances for a draw as White; in fact, i could argue
Black has better chances, because the first move
White gives away information, on which Black can
base it's strategy. So Black has the better chances,
and indeed, if White plays a move as 1.g4(??) then
Black -most likely- can force a win (for Black).
So all White has to do is play 'sensible' moves (indeed)
like 1.e4 or 1.d4, aiming for the center, and then the
White side won't lose. But if White can ensure it won't
lose, then it's draw. Ergo, proven from logical reasoning:
chess is a draw
PS although the above was not meant entirely as a joke, I have to
admit, you need some (computer chess) experience with the game
for such claims ofcourse and i wouldn't use such reasoning
for other games -than chess- with which i'm not familiar.