Chess will never be solved, here's why

We're all guilty of choosing the wrong way occasionally. Even you. We should be conscious of that and of not needing to force our beliefs on others. We can give an argument that the Bentley is a better car than the Rolls because we like its colour better and that's a valid argument. It may not be taken seriously by some but it's still valid.

I prefer Bentleys.

10^17 is based on using the (1) wrong (2) approximation on (3) the wrong subset of (4) the wrong set.

1. It's based on a quantification of the subset of the number of possible GAMES that need to be evaluated
2. the square root formula is based on assumptions of constant branching factor, games of equal length and no transpositions. The last is probably the most catastrophically wrong. Transpositions are ubiquitous in chess analysis.
3. @tygxc ignores all positions with promotions or multiple promotions. He missed the further simplication of ignoring all games with knight moves.
4. It was not a formula for the number of states anyhow, since states can be reached in an ENORMOUS number of ways. Not going to 34 specific positions on this move does not imply none of those positions will be visited later. For example, they may be on the route to a repetition of position.

All a care about is he switched to blitz chess lol

First page has the most amount of downvotes i've ever seen...

Nearly 100 thumbs down!

Janko is getting close

He's almost halfway there

You know, I don't believe that.

Anyway, I wasn't specifically linking 10^17 to arguing from authority. However, where did he get it from? I can't see him coming up with it.

I just googled and there's a lot of rubbish being written, However:

Does it really matter if Chess is solved? Chess.comhttps://www.chess.com › forum › view › general › does...    20 Dec 2022 — To weakly solve chess requires 10^17 relevant positions, that is about 10^15 games. ... "To weakly solve chess requires 10^17 relevant positions.

It's clear that 10^17 refers to positions, not games and also clear that the maths is very wrong.

he actually came up with it himself.

1. He takes a starting number of chess positions (which he draws from an authority),

2. and reduces that number to the amount without what are deemed 'unnecessary' positions, taking a number from another authority. (although tygxc doesnt sufficiently demonstrate that the type of positions removed by his authority is the same type of positions 'unnecessary' to factor into calculations as he claims)

3. tygxc takes the square root of that number as an heuristic to simulate considering only one side's variations. (IE, the game tree splits into every possible black response, but continues through only ONE white response, or vice versa)

the approach as a whole is sound, however the individual steps and interpretation of the resulting number are very flawed

a) insufficient justification/misinterpretation of the authority for the first reduction. The current upper bound for the number of chess positions without promotion is 10^37. (i cite an authority here that you can look up, however the number itself in the article is locked behind a paywall that I got through with a college account). tygxc's number at this stage is 10^34. it is very likely possible to reach this number (or even lower) through calculations of simplification to the 7 man table base, although I would like to reiterate that the level of proof for this would be VERY loose. tygxc provides no such justification.

b) using a square root to consider only one response from white means that tygxc's heuristic calculates only an estimate of the size of the solution tree itself, NOT the computational power required to FIND that tree.

For example, the total possible checkers positions is 10^20.

the number of positions calculated in order to solve checkers was 10^14, excluding the endgame table bases.

( https://www.cs.mcgill.ca/~dprecup/courses/AI/Materials/checkers_is_solved.pdf )

per tygxc's claims, only 10^10 positions would have needed to be calculated.

this is an obvious contradiction

How is the "only one white response" to each move found?

I was aware of the reason for the sq rt and I remember him making the argument maybe two or three years ago. It made no sense to me and so I'd assumed it was Svesnikov or someone. I and possibly others mentioned to him that the white move has to be chosen with equal precision, or there's no evidence. I believe his theory was that it would be chosen by three GMs. It was at that point where I stopped reading his comments until recently, when I thought he has moved forward by focussing on the 106 or now 108 games. I thought at least that was evidence of taking a scientific approach but he has never responded, so far as I'm aware, to what I wrote about the absolute necessity to explore games of say 150 to 200 moves and also to explore strategies of slow pawn moves and slow and careful strategy in general.

Unfortunately, he cannot take on board even constructive criticism. It's a shame.

the "how is the white move found" is key. there is no room provided for finding the move in tygxc's calculation.

(from tygxc, typos corrected and equivalent numbers rewritten)

"2.07e37 legal sensible positions starting from 26 men
in analogy to the checkers proof: square root of this: 4.55e18 relevant positions 
cloud engine 10^9 nodes/s
4.55e9 s = 144 years on 1 cloud engine for the whole of chess"

tygxc assigns only 1 node to each position. the ICCF games that tygxc offers as 'perfect' chess required over a billion nodes for each position.

https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?page=5#comment-66899947

It's simply wrong that you get a 1000-fold shrinking of the number of positions by using a "small" tablebase (like 7 or even the future 8 piece), These tablebases are just a tiny subset of the positions because there are way fewer classes (like KkQ) and typically way fewer positions for each combo, compared with with bigger tablebases. The set of positions is in fact a set of 30 tablebases for 3, 4, 5, ... 32 pieces. They keep getting bigger most of the way, but at the end it is less clear, as there are fewer classes. Only one class for the 32 piece tablebase, since you can't promote without a capture. Someone has done analysis to adequately estimate the sizes.

Maybe - but I'm thinking that tygxc is going by his indoctrination as a chess player.
Quite a strong player as players go.
He's made himself a good player. Over a period of years and years.
But like so many things - there can be flip sides.
Or are flip sides.
--------------------------
He wants to 'dismiss' e4 e5 Ba6.
For rigorous solving - such dismissal isn't legitimate.
But for 'approximations to solving' such dismissal looks quite legitimate.
The computer wouldn't have to 'Dismiss' immediately - it can take a few more billionths of seconds or whatever to make sure there's no tactical retaliations for the side that's making the blundering move and only then 'Dismiss'. Or label as 'approximately solved.'
-----------------------------------
'Material sacrifices 'to get position' are much harder than more purely tactical ones.
Although the sacrifice itself is tactical.
Its much rarer that they're sound.
Sac a knight for an f7 pawn. Say Kxf7 reply.
No immediate tactical recovery of the material.
No immediate mate.
Maybe not even immediate followup checks.
No immediate followup mate threats.
'positional' compensation.
Difficult. With its own spreading tree of game possibilities.
Might be 'sound' or 'unsound'.

@12343

"linking 10^17 to arguing from authority. However, where did he get it from?"
++ I have explained many times.
(1) There are 10^44 legal positions, but the vast majority of those makes no sense with multiple underpromotions to pieces not previously captured. https://github.com/tromp/ChessPositionRanking 
The 3 positions shown are legal, but cannot result from optimal play by both sides because of multiple underpromotions by both sides. Underpromotion to rook or bishop only makes sense to avoid a draw by stalemate, and that makes sense for 1 side only, not for both sides.

(2) A better number is 10^37 positions without promotions to pieces not previously captured.
https://arxiv.org/pdf/2112.09386 
However, that is too restrictive, as positions with 3 or 4 queens do occur in perfect games with optimal play from both sides. So multiply by 10 to include such positions.
That gives 10^38 positions without underpromotions to pieces not previously captured.

(3) Now note that even these positions cannot result from optimal play by both sides.
I inspected a random sample of 10,000 positions. None can result from optimal play by both sides. Convince yourself: take one and try to contruct a reasonable game that leads to it. E.g.

That leads to 10^38 / 10,000 = 10^34 positions.
This is a conservative estimate: Tromp conjectured only 1 in 10^6 to be sensible.
That would lead to 10^32 positions.

(4) Now assume perfect alpha-beta pruning. For N white moves we only need to look at 1 black move, hence not N * N = N², but N * 1 = N = Sqrt (N²) positions.
Hence Sqrt (10^34) = 10^17 positions relevant to weakly solving Chess.

That is also what Schaeffer wrote: perfect alpha-beta pruning halves the exponent.
Schaeffer needed 10^14 positions of his 5*10^20 legal positions, i.e. exponent 0.67.
However, chess programs have evolved more then Chinook for checkers and Chess is easier to prune than Checkers. Checkers is more like a pawn endgame in chess.

In the most optimistic case, we would end up with Sqrt(10^32) = 10^16 positions.
In the most pessimistic case, we would end up with (10^34)^0.67 = 6*10^22 positions.
10^17 relevant positions is a fair estimate of the effort needed to weakly solve Chess.

@12297

"For N = {1, 2, 3, 4, 5 ...} define the sequence of questions Q(N) like this:
Q(N) = If N games were played between two world class centaurs (engine assisted human) using current engines and it was a draw, would that be a proof that chess is a draw?
which is the least N such that the answer to Q(N) is Yes?"

++ If asked this way, then the answer is N = 0. Proof that Chess is a draw already is the deductive argument that the initiative is a white advantage of +1 tempo = +0.33 pawn = not enough to win, especially since each further move dilutes the advantage. The consecutive 110 draws out of 110 ICCF World Championship Finals games only confirm that in a convincing way. Even the results of previous ICCF World Championship Finals, which had sparse decisive games, confirmed that. To me for all practical purpose Chess is ultra-weakly solved and the game-theoretic value of the initial position is a draw.

Ultra-weakly solved to a draw does not indicate how to draw against all opposition.
That is weakly solving Chess.
The present 110 ICCF WC Finals draws are at least part of the weak solution of Chess.
The fact that they are redundant makes it fail safe.
You could object that they are not yet complete.
I would consider 272 ICCF WC Finals draws as a weak solution of Chess: both complete and redundant.

@12347

"necessity to explore games of say 150 to 200 moves "
++ The ICCF World Championship Finals games end in draws in average 39 moves.
Games of 150 to 200 moves are a myth, they only occur between two weak players that hop aroud aimlessly.
Besides 10^38 = 2^126 = 2^(63*2)
Thus after 63 moves with 2 non transposing choices per ply you have the whole of Chess.
Any game over 63 moves must contain strings of forced moves.
There are no more chess positions than there are chess positions.
That is the pigeonhole principle

@12349

"Someone has done analysis to adequately estimate the sizes."
++ Yes: Table 3