Chess will never be solved, here's why

Oh, I thought you meant your daughter in law. Didn't think of Liz Truss.

Back on topic after the spamming spree of the trolls.

The game-theoretic value of a game is the outcome when all participants play optimally.

Ultra-weakly solved means that the game-theoretic value of the initial position has been determined. There is massive evidence that Chess is a draw.

1. Expert opinions of all World Champions.
2. AlphaZero self play 97.7% draws at 1 min / move, more with more time,
   even if stalemate is declared a win.
3. TCEC with imposed 50 slightly unbalanced openings to prevent all draws.
4. Human World Championships and top tournaments.
5. ICCF World Championship Finals: 136 games = 127 draws + 6 white wins + 3 black wins.
   table base win claims of > 50 moves without capture or pawn move allowed but do not occur
6. A tempo in the initial position is worth 1/3 pawn. You cannot queen a tempo.

Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.

Strongly solved is being used for a game for which such a strategy has been determined for all legal positions. For Chess this means a 32-men table base with 10^44 positions.

Weakly solving Chess needs 10^17 relevant positions.

1. Samples of the 10^44 legal positions or the 10^37 positions without promotion to pieces not previously captured cannot be reached by optimal play from both sides.
2. Checkers needed 10^14 positions to weakly solve and Losing Chess 10^9.
3. Connect Four has been solved with 9 knowledge rules.
4. A strategy can be brute force, can be a set of rules, or a combination of both.
5. An engine of 10^9 positions / s running for 17 s (or a desktop for 4.7 h) includes the table base exact move in its top w = 4 moves with 1 error in 10^20 positions.
6. The average length of ICCF WC games is d = 39 moves.
7. 1104 ICCF WC draws are perfect games with optimal play from both sides.
8. An upper bound U assuming no transpositions is U = ( w^(d + 1) - 1) / (w - 1).
9. A lower bound L assuming full transpositions is L = e^w, regardless of d.
10. An estimate E is the geometric mean of the upper and lower bounds: E = sqrt (L * U).

Cloud engines can calculate a billion positions / s.
A year counts 365.25 d / a * 24 h / d * 3600 s / h = 31,557,600 s / a.
Thus 3 cloud engines can weakly solve Chess in 5 years.
Humans are necessary to restrict the calculation to relevant positions only.

GM Sveshnikov said:
'Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess.'

The 'give me' implies 3 million $
to hire 3 (ICCF) (grand)masters 40 h / week and rent 3 cloud engines 24 / 7 for 5 years.

1.  Inconclusive.  Imperfect play.

2.  Inconclusive.  Imperfect play.

3.  Not to prevent all draws, because that was not happening, but to make games more exciting and add more decisive outcomes, yes.

4.  Inconclusive.  Imperfect play.

5. Lol, do your math again.

6. Tempo and piece valuations are derived from imperfect play.

Notice a theme?

- 10^17 has no support save for one crackpot theoretician.

- Sveshnikov made an offhand claim in an interview to impress lay people.

@5749

2. AlphaZero approaches perfect play with more time / move.
3. On TCEC:
"Statistics of the previous two superfinals show that a Leela book exit of +0.30 or lower is an almost 100% certain draw."
https://www.chessdom.com/jeroen-noomen-and-gm-matthew-sadler-announce-tcec-s21-superfinal-book-cooperation/

Of the 50 imposed openings, 19 worked as intended: a win and a draw,
22 led to two draws, 9 are busted and led to a win and a loss.

5. The math again:
136 games = 127 draws + 6 white wins + 3 black wins
https://www.iccf.com/event?id=66745 
First assume Chess a white, or black win.
Try to fit a Poisson distribution of errors / game with 127 / 136 probability of an odd number of errors. It is impossible. Thus Chess is no white or black win.
Then assume Chess is a draw.
Fit a Poisson distribution of errors / game with 9 / 136 probability of an odd number of errors.
It is possible with average of 1 error per 14 games. It leads to 99.7% certainty that the 127 draws are perfect games with optimal play from both sides.

@5751
"You don't have to wait for my KRPPvKRP runs."
++ I wait for your runs. My calculation works for 32 to 8 men. 7 men is a good verification point.
7 men or less are strongly solved in the 7-men endgame table base.

As for your 7-men position: white is lost, so this cannot result from optimal play by both sides.
Engine: Ba5.
1 Table base: Qc1+, Engine: Qc1+ Ka2
2 Table base: Bc4+, Engine: Bc4+ Nb3
3 Table base: Qg5, Engine: Qg5 Rh1+
4 Table base: Ke2, Engine: Ke2 Re1+
5 Table base: Kf3, Engine: Kf3 Bb4
6 Table base: Qd5, Engine: Qd5 Rb1
7 Table base: Kg4, Engine: Kg4 Ka3
8 Table base: Qf3, Engine: Qf3 Rb2
9 Table base: Be6 / Kh5, Engine: Qd3 Ka4, but 50-moves rule does not apply, still OK
10 Table base: Qf3, Engine Qf3 Nd4
11 Table base: Qd1+, Engine: Qd1+ Nb3
12 Table base: Be6, Engine: Be6 Bc5
13 Table base: Qd3, Engine: Qd3 Bb4
 The top 1 engine move agrees with the table base even for this not relevant position.

What a heap of b*llocks. There's nothing anywhere in your calculation that refers to the number of men and If you count the men in my example very carefully you should arrive at 7 anyway.

@5753
"There's nothing in your calculation that refers to the number of men"
++ There is: results derived from more men than the table base.

Then derive said results with same number of men as tablebase. That was the purpose of posting my games. 

" As for your 7-men position: white is lost, so this cannot result from optimal play by both sides."

Is that what your calculation says? Show the working.

@5755
My calculation is based on positions with > 7 men.
Chess is already strongly solved for 7 men or less by the endgame table base.
So weakly solving chess is from 32 to 8 men.
I agree 7 men drawn positions provide a calibration point.
So I await your KRPP vs. KRP as promised.
I have added a short verification for your irrelevant 7-men position and find good agreement even with top 1 move, not even needing 2-3-4.

Your short verification has nothing to do with your "calculations". You've just cribbed it from the engine that's playing the games (which gets it wrong in all the cases). 

Your "calculation" is not based on any number of men.

What you mean is you've already tried your "calculation" and it doesn't work.

@5757
I checked the engine against the table base.
So I have tried it on your irrelevant example and it works: top 1 engine move in line with table base.
Now give an KRPP vs. KRP.

And quite possibly your ICCF players got their first moves right.

You say the position is winning (correctly, according to Syzygy). All the games were drawn That should tell you something about whether the remaining moves were correct.

What do your so called calculations say? The exercise is to check the validity of your method.

I'll give the KRPP vs KRP games when complete, though I think it's still doubtful you'll take any notice. Fifty move games at half an hour per ply take some time.

In the meantime, there's absolutely no reason why the games I posted should be less applicable. Why don't you try those now?

@5759

"You say the position is winning (correctly according to Syzygy)." ++ Yes

"All the games were drawn That should tell you something."
++ You did something wrong. When I check the engine top 1 move against the table base I see agreement, except for move 9, where the engine top move would run into the 50-moves rule if it were applicable. Anyway, this example is not relevant.

"I'll give the KRPP vs KRP games when complete" ++ Post 1 KRPP vs. KRP, do not wait for more.

"it's still doubtful you'll take any notice" ++ I even took notice of the irrelevant position.

"Fifty move games at 34 minutes per ply take some time."
++ Just one position is enough.
It probably will not take 50 moves. Long games are typical for pawnless positions.

tygxc wrote:

'"Fifty move games at 34 minutes per ply take some time."
++ Just one position is enough.
It probably will not take 50 moves. Long games are typical for pawnless positions.'

I don't see how your calculations would say much at all with one game. It's your method we should be examining, but here's one SF15 v SF15 2048 secs per ply (adjudicated by 6 man Syzygy). I await a worked example of your "calculation".

@tygxc thinks a technique of trashy advertising - repeating the product name zillions of times - is an good way to sell his claims. No-one with any expertise is buying.

What are you saying I did wrong? I wasn't playing; it was SF15.

Why is my example irrelevant and KRPP vs KRP relevant?

@5765
"Why is my example irrelevant and KRPP vs KRP relevant?"
++ Your first example cannot be reached from the initial position by optimal play from both sides. That is why it is irrelevant for weakly solving Chess.

@5764

"I now see what he is doing." ++ No, you are not.

"He has now refined his method" ++ No, not at all.

"instead of (inadequately) claiming to consider the top four engine choices for the opponent"
++ No, still for 32 to 7 men: running a desktop for 4.7 h, the table base correct move is among the top 4 engine moves.

"reduced to three at some point" ++ When starting from a drawn ICCF WC game,
there is already one calculated move, so only needing 4 - 1 = 3.

"that inadequate approach generates way more than 10^17 positions"
++ No. The upper bound without transpositions U = (w^(d + 1) - 1) / (w - 1) can exceed 10^17, the lower bound with full transpositions L = e^w is smaller than 10^17.
The geometric mean sqrt (L * U) is smaller than 10^17. So 10^17 is good.

"he has decided it is necessary to only look at one choice - the top one."
++ No, not at all. Only for the irrelevant example given the top 1 move is enough to coincide with the table base, not even necessary to look at top 2, top 3, or top 4.

"To determine the value of an opening line, you just play two very strong engines from the position and accept the result they reach as the evaluation."
++ No, I investigate 4 moves for white: the ICCF played move and 3 alternatives per move, that until the table base or a prior 3-fold repetition.

"as the earlier version" ++ No, there are no 2 versions.