Chess will never be solved, here's why

Promotions to bishops may be the rarest, but they empirically occur in 1 in 33,000 games i.e. well over 1 in 10,000,000 moves, which is likely not too different to the frequency of positions where such a move is optimal. That is plenty to use the intuitive argument I provided why a substantial fraction (something like 0.1%) of all legal positions with multiple underpromotions are reachable via optimal play.

The argument that promotion to a bishop can only be strictly superior to queening in a winning position sounds correct.  However, I believe eliminating lines where an opponent can win by promotion to bishop could be crucial to analysis of a drawing position (in order to avoid getting into them -  assuming the opponent can only queen could be fatally deceptive). That makes such positions potentially important. The same for positions with 5 underpromotions to bishop to achieve a win.

Yeah, if the idea is that the weak-oracle can't play optimally in every legal position, but it's impossible for it to lose when playing a game from the starting position, then I don't know how you can ignore underpromotion.

If the idea is that the weak oracle will almost never lose, but it would be impossible to meaningful improve its play short of fully solving chess, then I don't know how you can ignore underpromotion.

If the idea is that the weak-oracle will almost never lose, and future improvement is possible... well ok, but that's just a strong chess engine. We're already cataloguing analysis. Analyze a well known position on lichess and the depth is instantly at 40. Load up live book on chessbase and some positions have analysis saved to depth 60+.

"The fact that it happens over and over should clue you in, but as we know from other examples, some people are not that good at picking up on clues that they might be off the beam"

He's already asserted - twice now that he's 'pretty sure he knows more than anybody here' ...
its more than 'not that good'.
Its 'serving notice'.   And it explains his reactions and policies.
You don't tell him something.  He tells you something.
Tell him anything - and we'll get another column of unfounded assertions instead of acknowledgement. 
He'll even try to claim the speed of the computers doesn't matter.
Has.  Vehemently.

Is this all to 'vindicate Sveshnikov' ?
I don't think so.
This is not about 'weak solving' either.
Its about 'heuristics'.   

Claimed by whom?

Calculating 10^44.5 positions is currently in the millions of years out.  Ergo, there's plenty of room for allowing for vast reductions in time and effort that still leaves us thousands of years away...there's no "just about as much" involved, nor was anything beyond "significant processing time" implied.  The thing about predicting humanity's concerted efforts is that a thousand years is effectively the same as million, or a trillion.  It's pointless to predict such in such timeframes. 

Predicting 5 years at the present time, well...that's just too absurd to discuss, really.  It merely calls for refutation, early and often.

I suggest - 'heuristics' could be key now.  Or already is.  
Throughout the 2300 posts.
There's synynoms for 'heuristics' too.  Or phrases.
Most people would not use that word - even though its meaning refers very well as to the general nature of many posts here. 

Well, "type classifying" not only is possible; actually any evaluation function, either hand crafted or produced by a neural network, is based on these "classes", whithout defining them strictly. These are the "frames" we all, humans and neural networks, use to represent the big world in our little "minds": we categorize things. Inevitably, though, these representations are biased. It's the bias-variance dilemma @Elroch mentioned. To have less bias and reduce the risk to miss some "outliers", some "monsters", the evaluation function has to be more complex, but one can never know if it really encompasses all the relevant cases for a weak solution (which is a precise thing, not a so-so solution), until the game is weakly solved. Thinking the opposite is a fallacy. Therefore, the closer the evaluation to the real value of the node, the less nodes will be searched, but:

a) a more complex evaluation function usually requires more time to make the evaluation

b) we don't know a priori the value of the node, so the search has to be performed from the beginning of the game (or both backwards and forwards as in checkers) to the end without prejudice, without skipping openings or moves that must be explored (to meet the criteria of a weak solution) because they are "surely inferior". I don't think the scientific community would accept anything else as a "solution".

It would be possible to start it, but...

That

It could be conjectured - as to what computers might have accomplished regarding 'solving' chess say by 2040.  
We could speculate they'll have 'solved' for 8 pieces - maybe even 9 -
and maybe 'tidied up' and provided for castling for 7- piece or less.
Those three projects might be Gigantic.
But they'd hardly make a small dent in 'solving' chess.

Possibly - computers might hit a 4000 Elo or FIDE strength (if they haven't already).  And if you input any legal  position at all into a dedicated supercomputer - and ask it to solve it ...
well there again ...  See the Pitfall ??

How about its the opening position?   Its not going to have the answers.
How many pieces have to come off the board before the computer has a ghost of a chance of 'thorough solving' of a single position - in say an hour ?

Maybe some of the researchers know about that.
Maybe 8-piece has already reached that point -
but where it might be forgotten that an hour to solve just one position thoroughly still means millions or trillions of years for all 8-piece positions (even though the computer would have to have also solved all positions arising from that first 8-piece to pronounce thorough solving of just that one 8-piece.) ...
An 8 piece solved in an hour - and all its 'descendants' ? 
Maybe that would take many thousands of hours.  By itself.
Or more.  Much more.

You tell them, @Optimissed

To be serious, you never clearly state in a scientific manner what you disagree with. If you are incapable of doing so, you are not even expressing a scientific view, just some sort of emotional state.

Regarding the Big Bang - there seems to be overwhelming evidence that it happened.
And that most if not all of what we see in the cosmos can be ascribed to the Big Bang.
But the part where it 'creaks' is where so many infer or assert or insist that the Big Bang has to be the 'Universe'. 
With many 'coattails' coming from that.
Like T=0 or 'the  universe is expanding' - finite universe in age and size and mass ...  a whole dinner menu of items that whoever is asked to eat. 

It would be much better if the Big Bangers simply qualified at the outset that indicators of other Big Bangs elsewhere and elsewhen - would not be visible from our galaxy - or maybe from anywhere within our local big bang. 
But that isn't seen.  Pun intended.   Its not 'getting with the program'.
We're not going to 'see' that.  But sometimes - you can dig it out of them.

Getting somebody to acknowledge something they don't want to acknowledge.
Even for a dentist to obtain that ...

@Elroch - as usual - is correct. 
Its a mismatch between him and 'the other guy'.  
Also relates to @Elroch rightly asserting that a term is meaningless if its not defined.  Especially in math.  But that can apply to some other things too.  Like in science.
In art - you might get away with anything ...  

Is chess 'artistic' ? 
I would say great chess often has an artistic or creative element.
What about Tal?  Could his masterpiece tactics be considered 'art' ?
I would be inclined to 'No'.  Because they did a concrete job.
Winning the game !  
But it could be argued 'Yes'. 
Tal's creativity just too much for his opponents.

IQ - ratings - claims of superiority while actually getting many things wrong.  And over and over again.  And feeling omniscient while projecting his own negative feelings intensely.  It does have its own pathos to it.
Its a sideline in the forum though.
Usually best just to post around it.

Not exactly, because, as stated in other posts, for a weak solution some nodes (with their descendants) can be skipped, when the analysis of their siblings has already led to an optimal strategy. But you got the point.

No it's not 10^44.5, in the game that @tygxc is now proposing to solve, if you don't have a procedure for solving that eliminates the problem of repetitions. (His game includes the 3-fold repetition rule.)

Each way of reaching a position gives you a different set of positions with the same material that, if you're to mate,  you must thread a way through to avoid a draw by repetition. Different mates for different ways of reaching the position. Some ways eliminate the mate altogether.

The correct description of a position is a PGN, not a FEN. Even the PGN is slightly deficient, but, apart from the slight deficiency, a PGN from the last ply count 0 position is sufficient.

With @tygxc's currently defined game and procedure the number is HUGELY greater than 10^44.5.  

That's one of the reasons the Syzygy tablebases provide only a weak solution of chess under competition rules. You can't start playing an endgame and expect Syzygy to bail you out if you get into difficulties and haven't followed his advice from ply count 0.

If it weren't for the fact that @tygxc has dropped the idea of including the 50 move rule, the number would be a hundred times HUGELY greater than 10^44.5. Winning positions with a ply count of 99 under the 50 move rule are actually very rare (but get less rare for positions with the same diagrams but smaller ply counts).

Tromp's figures apply to the basic rules game ONLY.

@Elroch

The same would seem to apply to the "competition rules" version of checkers, which is another reason that makes me uncomfortable about the reported solution, in the absence of further info, given that Chinook seems designed to play the "competition rules" version. 

The numbers describing the state space don't seem to be correct for a forward search - but I still have to work out whether the Kishimoto - Müller algorithm in Chinook completely solves the problem. A description of that, at least, is available.

Can you stop quoting that please?

It's Shannon's approximation of the number of 40 move games with an average of 30 moves per ply, Nothing at all to do with the number of legal games.

It's misinterpreted all over the internet (and obvious b*llocks).

Bad enough with @tygxc trying to swamp the internet with the fact that there are 10^2 legal chess positions.

Yes, good point that hadn't sprung to my mind.

The number of legal games (say until mate, statemate or some repetition rule) is absurdly large with any ruleset, most ridiculously with basic rules. In that scenario with nothing like the 50 move rule, consider where you are in one of the equivalence classes of positions defined by the existence of a legal path in either direction between them. It is legal to traverse the entire set of positions before moving on to a new equivalence class, only restricted by some sort of automatic drawing repetition rule (unlike the ones where the draw needs to be claimed, when the number of game is clearly infinite). There can be a ridiculous number of positions in an equivlance class. Eg with some pawn configuration and a set of other pieces, the pieces can reshuffle themselves into any legal configuration they can reach. A game typically consists of passing through up to a hundred or two equivalence classes (pawn moves and all captures always move between equivalence classes).

Though this is of purely abstract interest, the exact drawing repetition rule might affect whether it was possible to visit every position in an equivalence class (a bit like a multipiece version of the knight's tour problem.  An equivalence class of positions has a directed graph whose directed edges are legal moves leading between two nodes which are legal positions.  It is not necessarily possible to navigate such a directed graph without visiting the same node 2 or more times (the exact possibilities that can occur in chess would require some investigation).

For example for the equivalence class with just two kings there are somewhat less than 8000 legal positions (determined by the locations of the kings and which player is to move). The number of edges from a node is the number of legal moves, and the number of edges to a node is the number of legal moves leading to the positions (or the number of legal reverse moves).

I hypothesise there is a legal sequence visiting every legal position (with just two kings) once (like in the even simpler knight's tour problem). [Exercise for reader: prove this hypothesis ]

Anyhow, the number of legal chess games even if you use a 50 move rule is absurdly large. Way more than 10^N where N is the longest legal game.

Depends, I think , how abstract "abstract" is.

Here is the first game I played against the version of Rybka I downloaded to replace the version with an "e" on the end that, unlike current SFs, could handle 50 move deep KNNKP endings without a tablebase (on 20 year old kit).

(A bit disappointed I was - even GNU chess could do those on 20 year old kit.)

But if you look closer, it actually forces me to take its bishop on move 49, which is obviously an effect of the 50 move rule.

If you look a bit closer still it seems to be avoiding even single repetitions, so it's interesting to speculate what would have happened under current basic rules if the 50 move rule handling had been disabled in Rybka.

My guess is that after exhausting almost all its variations in the h8 corner its repetition avoidence algorithm would force it to eject me from the corner, probably towards a8 and it would then mate me about 20 moves later.

But there is also the possibility that it would paint itself into a corner (and me into the h8 corner) and draw under the triple repetition rule.

Both possibilities very similar to possible attempts at the knight tour.

I've met similar situations with SF8 in KNNKP.

It has been solved before bozo 🤡🚬

I continue to maintain that the repetition rule and the 50 move rule are sidelines compared with issues like whether forced checkmate is available in a game. 
And very analagous to whatever time controls are used in a game ...
as example:  somebody might assert (we see it periodically here) that the game is a draw with best play by both sides -
but that can be Instantly Disproven ...  somebody's flag falls on their clock and its called and even though 'mistakes' are not found in the move selection by either side - 
the game is in fact Not a draw. 
Somebody has won and somebody has lost.  Yes - insufficient material could be called too - for draw - but that exception does not invalidate the fact that best play does Not always lead to a draw.
Far from it.

When you have a position in front of you for solving or tablebase purposes - is it necessary to make it 100 positions according to how many ply of the 50 moves are left to win within that rule?
Or should it be regarded as one position ?
I've commented on that before.
But there's new ways to comment about that.

Attention does have to be given as to whose move it is - whether en passant is available - and whether castling rights are still there.
Note - isn't it kind of strange to ignore castling rights issues - or arbitrate castling as illegal while attaching importance to the 50 move rule?
Looks quite arbitrary.

But anyway - I've got better ways to resolve that 50 move stuff -
not stated yet.  

Is it necessary to consider a position as potentially two positions because of whether there has been no - or one repetition of position already?
Arguing that the theory of play must be different since a player might  then draw by looking to force another repetition?
Or should that be regarded as just one position?
Again - there's ways to put that in perspective.