Chess will never be solved, here's why

You clearly meant Elroch, not Tygxc, who is on your side of the "assertions are facts" aisle.  Whose sell date were you talking about again?

I think this sums it up. 

https://youtu.be/XtgZKwK6C3U

@4175
 "lack of a supporting link in the drop from 10^44 to 10^17"
https://github.com/tromp/ChessPositionRanking 
10^44 is the number of legal positions,
i.e. the number of positions for strongly solving chess i.e. a 32-men table base.

None of the 3 random sample positions in the link is sensible: all 3 have 1 or more underpromotions to rook or bishop on both sides. The only reason to underpromote to a rook or bishop instead of a queen is to avoid stalemate i.e. to avoid a draw. It makes no sense for both sides to avoid a draw, so one side must have made a mistake underpromoting instead of queening.

A better figure is 10^37:
https://arxiv.org/pdf/2112.09386.pdf 

A random sample of 1000 positions shows these are not sensible either.
On the other hand some positions with 2 or 3 queens are sensible.
Together that gives about 10^32 sensible positions.

Weakly solving a game requires less positions than strongly solving.
Weakly solving Checkers required 10^14 = 500,995,484,682,338,672,639^0.676 positions.
https://www.cs.mcgill.ca/~dprecup/courses/AI/Materials/checkers_is_solved.pdf 
Weakly solving Losing Chess required 10^9 positions.
http://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/ICGA2016.pdf 

Each pawn move and each capture renders huge amounts of positions unreachable.

Weakly solving a game only requires to determine one strategy for the initial position to achieve the game-theoretic value against any opposition.
Once it is proven 1 e4 e5 achieves the game theoretic value i.e. a draw, it is irrelevant if 1 e4 c5 draws as well or not.

This leaves 10^17 legal, sensible, reachable, relevant positions needed to weakly solve Chess.

No, it doesn't.  It leaves 10^44 with a bunch of rationalizations and false equivalencies.

Note in fact the lack of a supporting link for the initial value of 10^44. Tromp's value (actually 4.8x10^44) represents the number of basic rules positions, but @tygxc wants to solve competition rules chess.

Traditionally chess analysis has mostly related to the basic rules and ignored the 3-fold repetition and 50 move rules even when those were part of the basic rules, so the word "position" has mostly come to mean the game state in the absence of those rules and with no regard to clocks and arbiters etc. (and specifically either at the start of the game  or at the point a move has just been made).

By game state I refer to those attributes of the situation that determine what continuations of the game are legitimate. Under basic rules with no 3-fold repetition and 50 move rules, the board layout (diagram), side to move, castling rights and possible e.p. square are sufficient to determine the game state. (Almost; the pieces touched by the player having the move should strictly be included.)

I also refer to the game states in competition rules chess as "positions". @tygxc doesn't; he still refers to the attributes of the situation that would determine the game state under basic rules with no 3/5-fold repetition and 50/75 move rules (i.e. current basic rules) as the "position" under competition rules.

That is his prerogative. But then the number of such "positions" would appear to be irrelevant to his argument; his chosen vehicle, Stockfish works with competition rules game states, not basic rules positions.

Is there much difference? Yes it's vast. You'd probably need to increase Tromps index by around 200.

Let's make this very simple.

@tgyx's thesis is based, for one thing, on the assertion that a modern chess engine always finds a best move in its top 4 choices.

This is not only unambiguously not certain,  it is almost certainly false. Very crudely, the probability that an engine misses a best move in its top four choices is (on a logarithmic scale) something like the fourth power of the probability that it misses it on its first move. There is no doubt this happens quite often. I estimate this fourth power to be around 10^-12.

Thanks. Yes, I accidentally misattributed it. It was @MARattigan, responding to a post of yours.

Per second even.

Does anyone not understand my point that when you have something that may have a quantifiable probability of 1 in (say) a trillion of being false it can be reasonable to be certain it is true, even to "know" it is true, but the epistemological situation is that certainty cannot be justified?

An example is the proposition that with an excellent source of random bits (say least significant bit of analog to digital conversion of thermal noise), the next 40 bits will all be zeros.

I think you are fooling yourself. Your statement means that if there were a googleplex of such examples, you would be certain about all of them. You would be wrong about some of them (quite a lot actually, with a googleplex to start with).

Small positive numbers are not zero. Even when they are very small.

@4183
"the probability that an engine misses a best move in its top four choices is (on a logarithmic scale) something like the fourth power of the probability that it misses it on its first move. There is no doubt this happens quite often. I estimate this fourth power to be around 10^-12"
++ You estimate so without any evidence at all.
I calculated that probability from extrapolation from the AlphaZero autoplay paper.
Figure 2. https://arxiv.org/pdf/2009.04374.pdf 
At 1 s / move: 11.8% error per game
At 1 min / move: 2.1% error per game
Hence
At 1 h / move: 0.37% error per game
at 60 h / move: 0.066% error per game
Assuming 50 moves / game i.e. 100 positions per game give 1 error per 10^5 positions
The cloud engine running for 15 s corresponds to the engine in the paper for 60 h.
The probability that a 10^9 nodes per second cloud engine running for 15 s misses a best move on its 1st move is thus 1 in 10^5 positions.
The 4th power of that is 1 error in 10^20 positions.

@4182

"Tromp's value (actually 4.8x10^44)"
++ For each position with white to move there is an up/down mirror position with black to move and with the same game-theoretic value. 
For each position with lost castling rights there is a left/right mirror position with the same game-theoretic value.
That leaves 1.2 * 10^44 legal positions.
As proven, the vast majority of those is not sensible and plays no role in weakly solving Chess.

Likewise for the Gourion upper bound 3.8521 . . . × 10^37 becomes 1.926 × 10^37 because of left/right symmetry after loss of castling rights
and his estimate of 3 × 10^37 becomes 1.5 × 10^37.
https://arxiv.org/pdf/2112.09386.pdf  

"ignored the 3-fold repetition and 50 move rules"
++ The 50-moves rule 9.3 can safely be ignored as it is almost never invoked before the 7-men endgame table base is reached in GM or ICCF games.
Most of these games are over before move 50.

The 3-fold repetition rule 9.2.1 cannot be ignored, as it represents a major drawing mechanism, often invoked in GM and ICCF games.

"position has mostly come to mean the game state in the absence of those rules"
++ No, not at all. From the competition rules:
'9.2.2
Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:
9.2.2.1
at the start of the sequence a pawn could have been captured en passant
9.2.2.2
a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.'
https://handbook.fide.com/chapter/E012018 

@4179
"It leaves 10^44 with a bunch of rationalizations"
++ You still do not understand:
10^44 is the number of legal positions needed to strongly solve Chess.
Losing Chess with the same 64 squares and the same 32 men
needed only 10^9 positions to weakly solve it.

Losing chess is a completely different game with forced captures...stop being disingenuous.  That's why it only requires 10^9.

It's far from ludicrous, being the current reality we all live in.  You don't know if Ba6 guarantees a black win...you cannot demonstrate it conclusively, nor can any chess player alive or dead, with or without engine assistance.  

P.S. You lumped myself and Mar with Tygxc when Elroch is the person you meant...did you even bother to review your post?

@4195
"Losing chess is a completely different game with forced captures"
++ Yes, Losing Chess is a simpler game, that is why Chess needs more than 10^9 positions.
However, it shows that the number of legal positions 10^44 is not related to the number of positions needed to weakly solve a game.

You're not even talking about the same incident, which is par for your course.  If you know that Ba6 is won for black, then you can beat Stockfish from that position, on command.  Go ahead and demonstrate, without using an engine.  You can do it on live chess.

I know that K+R vs. K is won, vs. any engine, and I will happily demonstrate it.  If you are claiming to know, 100%, then you are claiming the same level of confidence.  You would think after a decade of watching Ponz get pounded for his 99.9999% that you might have learned something about making hyperbolic assertions...but alas, no.

10^17 will never be the number for any solution of chess.  You will be cold in your grave still dreaming about that number.

@4200
I hope you are still alive when Chess is solved with around 10^17 positions.

Even if chess was solved and we knew a certain position is winning, more often than not we still wouldnt be able to beat stockfish from there. I'm not sure what this conversation is supposed to prove