Chess is 'solved' and it's a draw.
As in shown/discussed in my recent article on academia.edu:
An ('ultraweak') solution for chess
In 2007 dr Schaeffer wrote the academic paper: "Checkers is solved":
https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
But with this (provocative?) title he 'only' meant that checkers was 'weakly' solved,
nevertheless this confirmed that with best play the game would end in a draw.
The situation (draw) is similar for chess, although not (rigorously/mathematically/
experimentally) 'proven' (yet). An 'ultraweak solution' (Allis et al) means that the theoretical
outcome of the game has been determined. And for chess that outcome is a draw.
Beyond all, or any ('reasonable') doubt. Last year, there were some -sometimes-
vehement reactions (and discussions) on talkchess.com that this is not rigorously
mathematically proven; but that is irrelevant (i.e. doesn't matter) relating
'ultraweak solutions' according the definition (which is 'determining' the
theoretical outcome, not rigorously mathematically proving it).
In the recent ICGA conference, Nov 2024, the talk by Prof J. vd Herik (Leiden)
the topic of his talk was "our aim is to solve chess" (keynote 4):
https://icga.org/?page_id=3907
But from his -entertaining (but imho not always up to date_ presentation it becomes
clear he means 'weakly' solving. And whereas he previously estimated around the
year 2035 for such a result, he now delayed that to approx. 2060 (whereby
dr Schaeffer is even more skeptical and predicts 'not until 2100...).
In this respect, first of all some background about solving games:
https://en.wikipedia.org/wiki/Solved_game
So my narrative is different, and i claim that the ultraweak solution for chess now
has been found; for the game of Hex, the ultraweak solution was found with
some strategic arguments, for chess i have used other methods (e.g. cumulative
evidence), but thereby i am convinced i have 'determined' the theoretical outcome
of the game (not only if both players play 'perfectly' but simply when they stay
within the drawing margin(s). Draw; beyond all ('reasonable') doubt.
In addition, because there are no foreseeable zugzwang situations in chess with 'perfect
play' (contrary to checkers and draughts, this also mean that we can predict the outcome
of a weak solution (draw). Although strictly spoken, this remains a 'conjecture';
but for me (and in my opinion also in reality) 100 pct true.
Example, the Goldbach 'conjecture' in mathematics (1) also hasn't been rigorously proven
(yet?); nevertheless it's (generally accepted to be) true (2). Also, in mathematics, there
exist (other) truths which cannot be proven (Gödel); so i don't worry about proofs.
At the end of my article (on academia) as given above, I mention as suggestion for
further research to first find 'weak' solution for international draughts (similar as for
checkers), which certainly is not impossible (but will require more computing powers).
And only then for chess (as it will require vast computer resources). But the outcome
already is known by now (although Steinitz already claimed it end of 19th century):
it's a draw.
Small side note, in the article i refer to the 'perft' search on the chess programming wiki,
with perft meaning (engine or search) performance test; here's the contemporary research:
https://grandchesstree.com/perft/0/results
Far from a weak solution, but analyzing the results will continue to show
that Black can always keep a draw; ergo, it's 'solved' and it's a draw.
Does this mean that computers have 'destroyed' chess: well far from that.
First of all, a weak solution wouldn't mean that the program knows the
best move for *every* (imaginable) position, this would be a 'strong'
solution; and that has not even be achieved for Checkers.
Note the term 'weak solution' in game theory seems to come from
a(nother sort of) mathematical definition:
https://en.wikipedia.org/wiki/Weak_solution
In game theory it's a completely different thing, of course. But anyway it's important
to know that such a 'weak' solution (eg. draw) is not so 'weak' in principle, because it
means that the outcome of the game (with best play) is exactly known.
So checkers is a draw, (experimentally) 'proven' indeed (by Schaefer in 2007).
For chess we can argue, whether there is a (rigorous) proof (3), but this doesn't matter
so much, as for the 'ultraweak' solution it simply means that the theoretical outcome
(with best play) has been 'determined'.
Historically, it was thought that in chess the first mover (White) has a slight advantage (4),
and most opening during the last century was also based on this (elusive, imaginary) idea.
Because with cumulative recent (eg. the last decade) evidence, it now has been been determined
that the outcome of a game of chess with 'best play' (or simply staying within the draw margin)
from the start position with free choice of opening/defense choice (White/Black) will be a draw.
Beyond any ('reasonable') doubt; just like the Goldbach conjecture is generally
accepted to be true.
Generally, it was thought that a solution for chess would 'destroy' the game, this is
not true of course (except for correspondence chess, and possibly, slow Fide chess.
On the contrary, the 'drawish' nature of the game opens up complete new avenues
in opening theory, with (new) gambits, and so on (6). As for a 'strong solution' for
chess, it will be almost impossible to achieve, so there' s still (some) hope for
problem-chess (eg mate in x puzzles) aficionado's (and programmers, as well) :)
Note this draw 'problem' is already known for some times by top-engine tournament
organizers, like TCEC, where the games nowadays start with a set of unbalanced openings
(with free choice in opening play from the start); in ICCF correspondence chess it's a paradigm
change which is still ongoing, as here the organizers seem to be reluctant to adapt the
(eg possibly endgame) rules.
Conclusion: Chess now (2025) has been solved, at least in the 'ultraweak' sense .
And the outcome (with 'best' play) is certain (draw).
PS as for 'number crunching' projects aiming for a weak 'solution for chess with
similar methods as done for Checkers, as mentioned in my (academia) article, I
suggest to start first with international draughts, as e.g. discussed on talkchess.com:
Draughts has not been solved
But then anyway, for chess i don't think such a number crunching method is the right
approach. Instead, I advocate more theoretical research in game theory, exploring the
concept of 'balanced games' (with an equilibrium) and possibly proving (or at least
demonstrating beyond any reasonable doubt) that chess is such a 'balanced game'.
Achieving a 'weak' solution for chess would only have some small practical
results such as knowing if some wrong opening moves such e.g. as 1.g4 for
White would be fundamentally lost; but then in practice, except in blitz, most
players already avoid such -known- worse moves.
References:
(1) https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
and it's generally assumed to be true.
https://www.lesswrong.com/posts/iNFZG4d9W848zsgch/the-goldbach-conjecture-is-probably-correct-so-was-fermat-s
(2) While apparently there still is no official proof (like also for eg. the Riemann
conjecture) there exist already a lot of tentative proofs on youtube, probably
using one of these methods (but now i'm digressing from the original topic/chess...):
https://journalspress.com/LJRS_Volume21/Two-Ways-to-Prove-Goldbach-Conjecture.pdf
(3) solution methods for (and progress with solving)complex problems in complex math (and thus game theory) are not as simple as eg. as puzzle -or question- in a math Olympiad. According to Lakatos, the famous expert in the philosophy of mathematics, for more complicated it's a gradual, complex process, almost like in physics (whereby in the latter situation a 'proof' of a theory would not be applicable and thus only falsification methods can apply (Popper):
https://hps.elte.hu/~kutrovatz/LakatosEng.pdf
In chess the only -or at least best- falsification method to show that the (now in 2025 determined)
'weak solution' would be incorrect, is to find a forced, winning line for White, starting from the
opening position. But from modern opening theory we know this is impossible; a point of criticism
may be that not all opening lines have been explored, thus that there still may exist some
unknown opening lines, leading to an advantage. Because of such reasoning, I developed
decades ago a 'book correction' module in my program Bookbuilder (7). Thus later being able
to examine systematically the complete tree of opening move (although not brute force, at
least within reasonable alfa/beta bounds); and thus came to the conclusion there is not
fundamental opening advantage possible (to achieve) for White. A finding which later was
corroborated with the billions of opening positions analyzed in the Chinese opening base,
by many different chess analysts. Thus there is no 'winning strategy' (Zermelo (5))
thus the game must end in a draw. Simple as that.
(4) First move advantage in chess
(5) To be precise, the theorem by Zermelo states that if there is a (forced) win for one side,
then there must be a winning strategy. And imo for the game of chess, such a (imaginary)
'winning strategy' would already start in the opening phase. But that's simply impossible,
such a strategy as the -by now exhaustive- analysis of modern opening has shown, simply does
not exist; it is not possible for White to gain an advantage in the opening phase.
Also easy to understand for anyone having sufficient experience with (correspondence)
chess and or (preferably) computer chess; if there is a balanced position, (evaluation
0.00 at sufficient depth) we know with the modern Nnue (neural network)
engines that there is no way that this one side can force a win (with sufficiently strong
defense by the other side), because of the relatively large branching factor in chess,
especially in the middle game. Thus, whereas in the past in some special situations
some 'Boa-constrictor' (Karpov) style of positional chess could be applied to squeeze
out a win in such situations, this nowadays simply is not possible anymore.
(6) https://sourceforge.net/projects/chess-gambiteer/
(7) https://sourceforge.net/projects/Bookbuilder
PS in the above academia article I mention a Nash equilibrium, with this, strictly speaking,
usually in game theory something else is meant (for multiple person 'players' with statistical
uncertainties) but the idea must be clear: there are balanced games, and if the players stay within
the drawing margin, there is -and remains- a static equilibrium and the result must be a draw.
Question/thought experiment: what if with much deeper search in certain (rare)positions
it appears that it wasn't in equilibrium ? Answer, then one player has not played 'perfectly'
i.e. not good enough, i.e. not stayed within the drawing margin, and in a subsequent,
better game this can be avoided. Which again means that later games with
such knowledge (avoiding mistakes) will be drawn.
Discussion, the concept of a 'balanced' (two person) game appears to be rather new
in game theory. Instead of a complete, exhaustive search within the tree, with this
concept it would be sufficient to 'prove' that chess is such a 'balanced game' (*).
So far this of course has not (yet) been 'proved' , but at least it has been shown in
practice that this is the situation; which again corroborates the 'ultraweak solution'.
(*) this is highly plausible, because in chess, all pieces except pawns can move backwards,
contrary to checkers (and draughts) thus, in combination with the 3 pos repetition-draw
rule giving a high 'degree of freedom' for both players and a relatively high draw margin.
