Also if pieces are only legally allowed to only move 48 times, 48x32x64 would be the total amount of legal moves possible would it not? not 10 to the power of 50
'legal moves possible'
as opposed to distinct sets of moves.
FI your number very much understates the number of possible move sequences.
Perhaps your post addressed a very specific and limited context defined by other posts.
I'm replying to your post on its own.
"That is why it is a heuristic, provional evaluation, it changes as the calculation gets deeper."
unfortunately you only assign 1 node per position in your "calculations".
a whole lot of waffling you do, but it's not too hard to spot the contradictions you make.
1 'node per position'
MEGA acing tygxc's disinformation.
'nodes per position' needs a lot of qualification ...
and tygxc's posts filled with double cross signs are not going to do that job.
You are stating that so called "weak chess" is considered making a drawing strategy.
Not quite, I used a precise technical term (one which is confusing to people who have not seen the definition). A weak solution of a game is an explicit strategy for each side that achieves the optimum result. If one player has a forced win, the other player's strategy is trivial, so it's really only one strategy. A corollary of a weak solution is that it tells you what the optimum result of the game is (that is the result when both players play perfectly).
Most people would bet the optimal result of chess is a draw. If so, a weak solution of chess requires a drawing strategy for each side.
So then what does strong chess mean?
A strong solution of chess is essentially a tablebase for every possible legal chess position. See wiki article about tablebases
I suppose it means brutally attacking the other opponent for checkmate? And if you look at higher elo evaluations to find for draws, what is the point if people cannot understand them??? such as openings, I suppose based on your statement of looking at higher elo players to better understand, you can unveil such complex variations such as Sicilian defense, Najdorf, Dragon, Alapin Variation, Sicilian Defense Kan variation ,
Mark Taimanov, Four Knights variation, Rossolimo, Scheveningen, Smith-morra Gambit, Evgeny Sveshnikov,Classical variation ,
Nimzovich Sicilian ,Scheveningen ,VariationSicilian ,Sveshnikov, Classical Sicilian? And you can understand them instantly and in 1 go?
A strong solution of chess would tell you the way to play every position in every opening perfectly to the end, and what result you will get if the opponent plays perfectly.
A weak solution of chess will only include a single opening book for each side, like a player who always plays the same move in the same position. But the books go literally to the end of the game in every variation.
double cross signs
i like em. i like em alot.
double cross signs
i like em. i like em alot.
Like #?
ie checkmate?
Regarding Elroch commenting about tygxc's massive obfuscations we got
"No-one who understands how to reason (even with uncertainty) from empirical data would ever claim such things"
Correct.
Unless they were being paid a lot of money to do things like tygxc does.
And mpaetz 's post about what 'weakly solved' is ... like other mpaetz posts a voice of calm and reason.
--------------------------------------------
heu·ris·tic
/hyo͝oˈristik/
adjective
1. enabling someone to discover or learn something for themselves.
"a “hands-on” or interactive heuristic approach to learning"
2. Computing
proceeding to a solution by trial and error or by rules that are only loosely defined.
noun:
a heuristic process or method.
---------------------------------------------
And I'm adding -
in addition to chess not being solved neither 'strongly' nor 'weakly' ...
there has not been established a legitimate way to cut down the 4 x 10^44
possible legal positions to be solved.
Emphaisis on the word 'possible'.
Its not established as to how that number could be accurately cut down by finding positions that are unreachable legally.
Point: the 4 x 10 ^ 44 number is already a 'cutdown'.
But its a legitimate one.
Because some cutdowns are relatively easy and obvious and therefore can be done accurately and legitimately.
For example - only two Kings. At least 32 empty squares always - pawns can only be on 48 squares and so on.
----------------------------
What number is the primary number being cut down from ?
13^64. 13 multiplied by itself 63 times.
Why? How?
64 squares is obvious.
But each square only has a maximum of 13 possible states.
Six black piece types. Six white piece types. Or square empty.
6 + 6 +1 = 13.
The 13 ^ 64 number is gigantic.
Apparently more than the number of atoms in the observable universe.
----------------------------------------------
Can be cut down.
But then there's a Stop Sign at 4 x 10^44.
Construction. Road Closed. 'Go back and take car ferry to small Tablebase Island' Warning: No electricity on T Island. No internet access.
Bring own batteries and USB drive reruns of Kill Bill Vols I and II.'
@11720
"A 9.2.3 criterion for when positions are to be considered equal for the purposes of 9.2/9.6 can't be taken as an intended definition of position in the FIDE laws." ++ It is the only reasonable definition.
Reasonable or not, it can't be taken as an intended definition of position in the FIDE laws, because various articles don't make any sense with that definition, e.g. the dead position rule as I illustrated here. When one of your positions arises in a competition rules game it doesn't necessarily determine whether either player can checkmate the opponent’s king with any series of legal moves.
But FIDE's interpretation of the term is an aside.
In practice it is a FEN without move #.
You're still trying to use two different definitions of "position". I pointed that out already here, but you haven't corrected it. FEN without move # does NOT correspond with the 9.2.3 criteria.
The FEN fields are
( diagram , side to move , castling rights , e.p. capture square, PLY COUNT , move # )
So FEN without move # would be
( diagram , side to move , castling rights , e.p. capture square, PLY COUNT )
9.2.3 doesn't state the ply count of two positions should be the same to be considered equal for the purposes of 9.2/9.6. If it did the rules would never apply.
An engine checks the 3-fold repetition rule and the 50-moves rule like an arbiter would do: from the PGN (score sheet), i.e. history.
An arbiter would need his head examining if he checks positions before the last ply count 0 position for either rule. The engine won't.
"A node is something an engine traverses in a game tree and assigns evaluations to as it goes along. They don't come ready evaluated."
++ A node is a branching point in the game tree. As the engine reaches a new branch point, it attributes a provisional heuristic evaluation to it, which changes as it calculates deeper.
So we now seem to agree on what a node is from your first sentence. It's not the same as your previous definition of node. It contains no history or evaluation by a particular engine. If "game tree" refers to the fully reduced game tree that the engine tries to traverse many different histories can lead to the same branch point. (That's the whole point of the reduction.)
And yes the engine will assign many evaluations to the node. These do not create new nodes for each evaluation.
"The fully reduced version has no repetitions of the same foliage at different points in the tree, which enormously reduces the number of nodes."
++ A full version with all possible transpositions is impossible.
You're very good at meaningless statements.
In what way impossible? The full version obviously exists and it's very easy to prove that what I've called the fully reduced version also exists.
The nodes in the latter correspond with @Elroch's game states. Game states represent the same node if and only if the possible game continuations are identical. They're also what I usually refer to as positions and that corresponds with your 9.2.3 definition in basic rules chess but not in competition rules chess.
There are between 10^29241 and 10^34082 possible chess games and only 10^44 legal chess positions, so each position can be reached in about 10^30,000 ways.
4.85 x 10^44 legal positions according to one of your definitions of position and 4.85 x 10^46 according to the other.
You don't say how you arrive at your last figure, but it's irrelevant anyway because reaching the same position according to either of your definitions doesn't necessarily result in reaching the same node in the full game tree, the fully reduced game tree or any intermediate tree that SF may follow. (Indeed in the full game tree each node can be reached in only one way, so if you really insist on the full history being a part of a node you're saying there are no transpositions of nodes.)
Even the position after 1 e4 can be reached in enormous number of ways: hop around with knights for 49 moves, play e3, hop around with knights, bishop, queen for 49 moves returning them home, play e4.
You've missed a few again.
I post five partial games.
Each of these finishes in the same position according to your 9.2.3 definition but {A,B}, {C,D} and {E} finish in three different positions according to your FEN without move # definition.
You give both definitions so you can use Tromp's figure for legal 9.2.3 positions (casually dropping a 4.85 factor) as a starting point while asserting that the FEN without move # positions represent the nodes in the tree traversed by SF and pretend you're talking about the same thing.
But even if we were to miss your subterfuge it still doesn't work. The possible game continuations from C and D, for example, which are the same position according to your FEN without move # definition are not the same, so they don't represent the same node.
Try for example the continuations 13...Nc6 14.Bb5 and 13...Nc6 14.Qh5 in analysis.
The fact that two nodes have the same position under either of your definitions is not a sufficient condition for the nodes to transpose.
Only the fully reduced version makes sense.
All versions make sense to anyone who understands them.
Engines handle transpositions with a transposition table.
"Your version with full history applies to the full tree." ++ No.
++Yes. ++Obviously.
"An engine keeps the full history only for the game record"
++ It keeps the PGN and/or the string of consecutive FEN.
It receives startpos or FEN + zero or more moves whenever it's the GUI's turn if it's using UCI, but there's no reason for it to retain any information prior to the last ply count 0 position. You're playing the GUI, the engine is just a consultant, so the GUI maintains the game record.
"it's interested only in the history from the last ply count 0 position"
++ It builds up history i.e. PGN and/or string of FEN from the initial position.
Just to waste space?
"what castling rights exist" ++ Castling rights, and en passant flag, and side to move are attributes of a position: included in the FEN.
How very interesting. I'm sure not many people knew that. Is it just for information or was there some point?
"the whatsit was obviously not part of the node"
++ Adding a provional heuristic evaluation is what the engine does as it visits a node.
Otherwise it is not an engine that can play chess, but a legal move generator.
It assigns evaluations to nodes. You don't get new nodes every time it evaluates. The nodes are vertices of a graph and the graph stays exactly the same.
"[It's not anywhere near as ]full of transpositions under competition rules[ as it is under basic rules.]" ++ competition rule 9.2.3 defines transposition
9.2.3 doesn't mention transposition. Two nodes in the full game tree are transpositions if the possible continuations are identical. Just the fact that the 9.2.3 attributes match is not sufficient to determine that.
"I couldn't spot a single up/down mirror image in the whole game"
++ They played a Grünfeld Indian Defense up/down mirror game: 1 d4 Nf6 2 c4 g6 3 Nc3 d5.
And I couldn't spot a single up/down mirror image in the whole game. Can you?
"You wouldn't get a definite answer even if you specified a set time a specific version of a specific engine a hash size and the exact machine to run it on"
++ That is why it is a heuristic, provional evaluation, it changes as the calculation gets deeper.
And also why your node definition is ridiculous.
"Rare in what kind of play?[It has to be rare in the positions that will be searched by your process. Currently you have no definition of a process that will result in a solution.]" ++ Rare in reasonable play as represented by master games in a database and rare in perfect play as represented by the 114 ICCF WC Finals draws.
The answer to that is in the bit I've reinstated as you were no doubt aware before you snipped it.
"definition of a process that will result in a solution" ++ The process is the ongoing ICCF WC Finals. The human ICCF (grand)master receives a move. Calculates on his twin 90 million positions/s servers for average 5 days and after thus considering
90 positions/s/server * 2 servers * 3600 s/h * 24 h/d * 5 d = 8*10^13 positions
he advances 1 ply towards a certain draw.
Which is patently not a process that will result in a solution.
"[There are almost certainly more weak solutions for competition rules chess or ICCF chess than, for example, Tromp's figure for basic rules positions. (For basic rules the number of weak solutions is most probably infinite.) In all probability nobody has ever seen ] a game that doesn't end in an agreed draw in a relatively short number of moves that corresponds with any of them"
You've stopped even trying to make the bits you snip out actually make any sense.
++ Look at the ICCF WC Finals.
This game ends in a 3-fold repetition in 15 moves:
https://www.iccf.com/game?id=1360225
This game ends in a 7-men endgame table base draw in 38 moves:
https://www.iccf.com/game?id=1360155
Not what I really meant by relatively short.
Agreeing on a draw instead of waiting for a 3-fold repetition is just like resigning instead of waiting for checkmate. Here is an agreed draw in 32 moves. Would you force them to play on?
https://www.iccf.com/game?id=1360123
No. It may be a win, but it's probably beyond Stockfish, it can't even manage mates in difficult positions with only five men on the board, so there wouldn't be much point.
"It is likely that some solutions include a significant percentage of positions with many promoted pieces on the board."
++ If you mean promotions to pieces not previously captured then no, that is nonsense.
Yes, I mean promotions to pieces both previously and not previously captured.
We have but one solution to any of competition rules chess which is the Syzygy tablebases. They give multiple solutions to each of the covered positions but a miniscule fraction of the total number of solutions for those positions which are in turn a miniscule set compared to the total number of solutions of chess.
I showed you in the post you're responding to a Syzygy solution with five white knights, and obviously you'd have six or seven with 8 or 9 man Syzygy tablebases.
All you can do is say, "big red telephone says no".
Here's Syzygy solving a KPPvKPP draw. About 75% of the positions have four queens on the board. Again obviously that would be six when we get the 8 man tablebases.
If you had any definite plan for solving chess you might be able to come up with some argument that neither your solution nor the nodes encountered in producing it would contain a significant fraction of such positions that was more convincing than ++No.
But of course you don't.
As I said before, This argument only started because some people think chess is a competitive sport while others think it is a meaningless sequential game.
Less controversial would be that chess is a competitive game. "Meaningless sequential game" is (ironically) a meaningless phrase. But as well as being a competitive game, chess (with a specified ruleset) is what is called a finite, deterministic game of perfect information, a class of game studied in the branch of mathematics (broad definition) called combinatorial game theory.
If every move is chess is solved, and each of the opponents know all moves, such as patterns, tactics, etc, then it would be a draw. But if the opponents didn't know at least 1 move. It could lead to a win to the other opponent.
These things need to be dealt with more precisely, and are.
And if the question is "Can chess be solved?" Well, it technically is solved, if not, how would we know there are a finite amount of moves or not.
That would be because proving chess has a finite number of legal positions, or that there are a finite number of legal games, are entirely different questions to "what is the result of a game of chess with perfect play by both sides?".
You are confusing entirely different questions.
Or it could be really actually incorrect, and all chess moves we so found are only a part of the story. It all really depends on the users opinion.
In a mathematical field (like combinatorial game theory), questions are either answered or not, and when they are answered, people agree on the answer. There are good reasons for this.
For example, @TheChessIntellectReturns thinks chess can never be solved if it is considered meaningless, and merely sequential, other then if chess is competitive, it is solvable. Some moves are called openings because they have been found and named. Technically, you can create a infinite number of openings merely because it is possible. If an opening so call end if you develop pieces, there are no openings since you already developed the pawn to control center. But there are book moves which count as openings which are considered about 10 moves. So 10x 10 to the 50th power would equal 10 to the 500th power of openings which means if chess is solved. Then basic match principles say there should be at least 10 to the 500th power of openings in chess, but there are a merely 3000 chess opening and variants (You can also search it up if you wanna) so technically, chess wouldn't be solved right now cause you would need at least 100 to the 50th power (or 10 to the 500th power) of openings for chess to be at least complete.
Actually one thing that is known is that a strong solution of basic rules chess "only" has to deal with 4.6 x 10^44 positions. In a clear sense, that's all the absolute knowledge that can exist about the game.
Yes. There it is again. The 'Tromp' number.
But frankly - I don't like that name 'Tromp'.
It sounds far too much like ...
So just 4 x 10 ^ 44. Much better. Or maybe '44th power number'
Positions. Not moves.
Moves and sequences of moves generate much larger numbers than the 44th power number - making the task needlessly even more difficult.
'Game tree' analysis is especially hopeless in projects like this.
Instead - there are tablebase projects proceeding backwards from just two kings on the board.
But again when 8 pieces are on board its
'Road Closed'. Construction.
'Get car ferry back to mainland to view beginning of game.'
@12141
"I couldn't spot a single up/down mirror image in the whole game."
++ That whole game is an up/down mirror image. White shed a tempo with d3 and d4.
"Which is patently not a process that will result in a solution."
++ The 114 draws out of 114 games in the ongoing ICCF WC Finals are at least part of a weak solution of Chess, redundant and thus fail safe, but not yet complete.
"Not what I really meant by relatively short." ++ 38 moves is reelatively short.
"It may be a win" ++ No way. 2 ICCF (grand)masters after days of analysis with engines conclude there is no point in continuing and a very weak player doubts that. That is like a grandmaster losing a piece and resigning and a beginner questioning why not play until checkmate.
"About 75% of the positions have four queens on the board"
++ Those are included in the 10^38 positions.
@12141
"I couldn't spot a single up/down mirror image in the whole game."
++ That whole game is an up/down mirror image. White shed a tempo with d3 and d4.
There is not a single pair of positions that are up/down symmetrical images of the type you originally referred to. And your point was completely unrelated to what (after snipping out the relevant bits) it was meant to address in any case.
"Which is patently not a process that will result in a solution."
++ The 114 draws out of 114 games in the ongoing ICCF WC Finals are at least part of a weak solution of Chess, redundant and thus fail safe, but not yet complete.
Twaddle. If the blunder rates I've measured for SF in simpler positions is anything to go by there is likely an average of at least five blunders per game, and there's a large overlap between games. Even if it were true, claiming that it's part of a solution is like saying you're ready to build a cross channel bridge because you've got a nut and bolt and sod the engineering plans.
"Not what I really meant by relatively short." ++ 38 moves is reelatively short.
Enough for about four blunders.
"It may be a win" ++ No way. 2 ICCF (grand)masters after days of analysis with engines conclude there is no point in continuing and a very weak player doubts that. That is like a grandmaster losing a piece and resigning and a beginner questioning why not play until checkmate.
Days of analysis with engines that can't manage mates with five men on the board and whose blunder rates increase as you increase the think time.
No I don't think you're such a great player that you can decide these matters. We're still waiting for you to post your wins as Black against SF (a win against a 32 man tablebase would be an entirely different proposition) after 1.e4 e5 2.Bb6.
"About 75% of the positions have four queens on the board"
++ Those are included in the 10^38 positions.
Only because the tablebases are limited to 7 men. As I remarked that will most likely be six queens when the 8 man Syzygy tables appear, which won't be included.
++ The 114 draws out of 114 games in the ongoing ICCF WC Finals ...
I've already explained why at least one of those draws was an example of sub-optimal chess from White (the 15-move draw that you linked to), and therefore of dubious quality.
A 15-move draw from White suggests that White is not playing the best possible moves. The best moves from White delay the draw as long as possible, by introducing the most complications and challenges for Black to survive.
The longer the game goes before reaching a draw = stronger (more accurate) chess from White.
The quicker the draw is secured = weaker (less accurate) chess from White.
The length of a game matters. If it's mate in 22 and the winning player delivers mate in 23, then that player, by definition, has played inaccurately and therefore did not play the strongest possible chess.
Similarly, if White allows Black to draw earlier than needs to be, then White has played inaccurately and therefore did not play the strongest possible chess ...
Perhaps unsurprisingly, the player who had White in that game is the lowest rated player in the current ICCF WC field. This makes it quite evident that their tournament strategy may be to secure draws as early as possible, especially when paired up against players whom this particular competitor may feel at a disadvantage.
I see this player, as White, also allowed a draw in 22 moves, and another draw in 20 moves.
As White, there are obviously more testing lines that can be played - which suggests that the human involved may be using tournament strategy to impact his games - aiming for draws as White when he feels it minimizes his risk.
I'm not sure you understand tournament strategy, but if you do, then you'll know that players don't always aim to play the best possible chess - often players simply aim for a particular outcome, based on tournament standings.
In this case, the player in question appears to be allowing quick draws in particular situations.
This makes many of the draws in the ICCF WC suspect.
Unfortunately, this then weakens your argument about ICCF WC games being the "strongest chess on the planet" ...
...
So just 4 x 10 ^ 44. Much better. Or maybe '44th power number'
...
If you're going to round the index it should be 10^45 not 10^44. But only in basic rules chess.
++ The 114 draws out of 114 games in the ongoing ICCF WC Finals ...
I've already explained why at least one of those draws was an example of sub-optimal chess from White (the 15-move draw that you linked to), and therefore of dubious quality.
A 15-move draw from White suggests that White is not playing the best possible moves. The best moves from White delay the draw as long as possible, by introducing the most complications and challenges for Black to survive.
...
I think @tygxc usually means perfect, i.e. blunder free, by "optimal".
In that sense optimal moves in draws are just moves into drawn positions and (since @tygxc involves practical games in his arguments) making and accepting draw offers.
If the starting position is drawn, which is quite possible and @tygxc assures us his big red telephone confirms it, then an optimal game in that sense can be any length.
Understood.
Though, I feel I've made a decent argument for the possibility that the human competitors may be pressing their thumbs on the scales of some of these games for their own reasons.
I believe this is a valid point to make, because tygxc points to these games as examples of the pinnacle of chess, as if the humans and engines have combined with a common goal to strive to play the strongest chess possible.
I don't think that's the case, with many of these games. I think the human element is quite apparent ...
So I suppose the main point is: how we can trust in these games as shining examples of optimal chess, when the humans involved may be intentionally guiding the play toward risk-minimizing draws, in the interest of self-preservation? ...
@12147
"A 15-move draw from White suggests that White is not playing the best possible moves."
++ Optimal play is play without errors. You could subjectively rank optimal moves as more or less suited to help the opponent in making an error. 1 e4 is more testing than 1 a4, but both draw. These ICCF players start by analysing all games of their opponents, looking for some undervalued or overvalued elements, like bishop's pair, isolated queen's pawn... You could say a move that has less responses that do not lose is a better move than a move that has more responses that do not lose, but that is subjective.
"The best moves from White delay the draw as long as possible, by introducing the most complications and challenges for Black to survive." ++ That is subjective. In that game white opted for a sideline. The main line delays the draw for longer, but a draw it is just the same.
This for example is a mainline game that ends in 48 moves.
https://www.iccf.com/game?id=1360252
"The longer the game goes before reaching a draw = stronger (more accurate) chess from White." ++ Not necessarily. Prolonging the draw has no merit in itself. Enticing the opponent to err has merit, but is subjective: depends on the opponent.
"The quicker the draw is secured = weaker (less accurate) chess from White."
++ Not necessarily. If white has 12 reasonable moves and only 1 draws quickly and all others lose, then that might be more accurate than if white has 12 reasonable moves that all draw.
"If it's mate in 22 and the winning player delivers mate in 23, then that player, by definition, has played inaccurately and therefore did not play the strongest possible chess."
++ No, a win is a win. There are no bonus points for a shorter win. It may be safer to take a longer win.
"if White allows Black to draw earlier than needs to be, then White has played inaccurately and therefore did not play the strongest possible chess ..." ++ Not necessarily. A 15 moves draw with 5 theory moves is essentially as long as a 40 moves draw with 30 theory moves.
"the player who had White in that game is the lowest rated player in the current ICCF WC field"
++ ICCF rating is no longer accurate because there are so many draws.
Most of the higher rated earned their rating earlier, when there were still many decisive games.
"As White, there are obviously more testing lines that can be played"
++ With much more theory moves and draws just the same.
"I'm not sure you understand tournament strategy" ++ It is the World Championship Finals, they play to become the World Champion, or at least to score a GM or SIM norm.
"the player in question appears to be allowing quick draws in particular situations"
++ Maybe to reduce tournament load: number of simultaneous games.
Anyway, the opponent complied.
'What is your ideology of playing black?' - ' I always play to win.' - Dronov
"This makes many of the draws in the ICCF WC suspect."
++ No. I do not see any possible improvement on any game.
"this then weakens your argument about ICCF WC games being the strongest chess on the planet" ++ It is. 15 ICCF (grand)masters who qualified through Preliminaries, Semifinals, Candidates, twin servers 90 million positions/s, 5 days/move average.
This is way stronger than any human competition including Classical World Championship Matches (human vs. human, 3 min/move) or TCEC engine vs. engine.
We are not discussing "weak chess" or "strong chess", but rather whether the game is a win for white, a draw, or a win for black if every move is played perfectly. "Weakly solved" is an attempt to find a strategy that will yield at worst a draw no matter what the opponent does, in the openings and variations that centuries of play have shown to be the best. "Strongly solved" would mean analyzing every possible continuation from every possible opening move all the way to a decisive result or a proven drawn position.