stop @Oswald192325
Chess will never be solved, here's why
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Apr 5, 2025
0
#16523
playerafar wrote:
StandStarter wrote:
Elroch wrote:
ok, to create tablebases (i.e. a strong solution) you start with the next size down tablebases and with all the positions in the new tablebase (but with no knowledge of the value of those positions).
You find which of these new positions are terminal positions (actually I think you can ignore the stalemate ones until later), and add the information from retrograde moves that lead to smaller tablebases (captures that lead to a position whose value you know).
Then you do iterative retrograde analysis generating information about value by finding all the moves that lead to positions whose value you have information about. There are two separate types of step:
(1) if a position has a move which leads to a position where the other side is mated in N, the position is mate in N+1
(2) if all the moves {m_i} from a position lead to positions where the other side is mating in N_i, with the max over i of {N_i} being N, then it is a losing position, getting mated in N.
It is easy to prove that if you repeat this over and over again, on some step you find you have not found any more new winning or losing positions. If this is the N-th step, it means there are no mates in N (of getting mated in N).
The reason I described that is that the next step is to realise at this point that all the other positions are drawn. The reason is that you can't have any mates of length N+1 or greater if there are no mates in N.
This is a really cool explaination! I think I understand now; tablebase starts at zero and continues until it reaches a value where mate is possible (N+1). If a win isn't possible no matter the moves, it's considered a draw. Am I correct or did I misinterpret?
'tablebase starts at zero' ... zero what?
I like this part:
"The reason is that you can't have any mates of length N+1 or greater if there are no mates in N,"
0 moves. Base game. Sorry for not clarifying.
Apr 5, 2025
0
#16524
Elroch wrote:
The much lower Syzygy number must involve counting only the positions stored, which are then multipled by almost 8 for symmetries on the board. 52234 * 8 = 417872 (an upper bound because of the "almost"). Note that the only moves that reduce the multiple to less than 8 are those where all three pieces are on a diagonal, so that one of the reflections does not affect the position.
Trying to match Syzygy positions to what you always thought were positions is quite awkward.
There's not only the factor of 8 or 2 for board symmetry to take into account but you also have to divide by the factorials of the numbers of sets of repeated pieces of the same colour and type (I'm not sure if there isn't also an extra complication when the repeated pieces are bishops). At any rate you won't get correct adjustment for symmetric positions.
The percentages of wins, frustrated wins, etc. are, I believe very close to correct.
Correct figures are available on the ICGA site for basic rules, but they don't cover the same range as the Syzygy site (no 7 man, no 5-1 and a few other specific missing classifications with < 7). At least that was the case last time I looked.
Add in another factor of 2 for colour to get an upper bound of 835744 which I observe is lower than either number posted above.
Ah, I see now. Your numbers weren't legal positions, as they failed to remove those with a king in check and not to move.
Exactly.
Don't ask me what the point is of counting positions where the side not to move can be in check from a bishop but not by a king. It apparently has something to do with alternate solving.
We still don't have that number of legal positions that is of more interest (to me at least) than the number of diagrams.
The number of legal KBK positions under either basic or competition rules is 934456 (reported semi-legal positions as defined here, but I think in this case "semi-legal" corresponds with "legal").
That can actually be worked out by hand for KBK, but if you want to perform the exercise wholesale youl'd need to write a mickey mouse javascript or something unless you can come up with a simpler expression than I did.
Apr 5, 2025
0
#16525
Magnus-Carlson-ME wrote:
How is THIS a blunder
You failed to find the right thread.
Apr 5, 2025
0
#16526
goodyay123456789 wrote:
playerafar wrote:
There seems to be some debate about the number of positions of K+B verus K.
(which is the same as the number of positions with K+N v K and for K+R and K+Q too but not for K+P versus K - which is less and more complicated.)
The number I got was for any of the first four was 904,704.
Derivation: 3648 x 62 x 2 x 2 = 904,704.
Is there something special about bishops that would make that wrong?
I don't think so.
You can place a bishop of either color - on any of the 62 squares with either side to move.
Yes some of those are illegal - but is somebody going to get very excited about that?
That's included. Deliberately. Because it should be.
Again. Deliberately.
--------------------------------
Or is it the 3648 that's under debate?
---------------------------------------------
Is there anything special about bishops and illegal positions?
That could be added to computers knocking out another big chunk out of the 10^45 number?
Yes!
Bishops have some access problems.
So how could you have a position with a white bishop at h8 and a black King at g7 with black to move?
Yes its illegal with white to move but that's a more general case.
'Black to move! Illegal!!' Rush to Judgement!
It could be a promotion bishop. Uh oh.
illegal? Wait - that could be a promoted bishop! Lol.
But there wouldn't seem to be anything corresponding - for knights and rooks and queens.
This wouldn't impact the 904,704 number.
And note a deficiency in the diagrams.
There doesn't seem to be a way to include who is to move.
if it promoted how is it black to move? it would be draw
white pawn at h7 pushes to h8 and promotes to bishop. WIth check.
Its Black's move. He has to get his King out of check at g7.
And its legal in that case. If its a promotion and then black to move.
If its white to move its already illegal. White can't be checking and be on move.
Its also illegal if the bishop isn't a promotion bishop. even with black to move.
Because there's no way for that bishop to get there.
That's a thing about bishops on corner squares.
A result of corner squares only having one diagonal.
But pawns seem to generate more illegal positions than bishops do.
Illegal unless the bishop is a promotion bishop with black to move.
Apr 5, 2025
0
#16527
StandStarter wrote:
playerafar wrote:
StandStarter wrote:
Elroch wrote:
ok, to create tablebases (i.e. a strong solution) you start with the next size down tablebases and with all the positions in the new tablebase (but with no knowledge of the value of those positions).
You find which of these new positions are terminal positions (actually I think you can ignore the stalemate ones until later), and add the information from retrograde moves that lead to smaller tablebases (captures that lead to a position whose value you know).
Then you do iterative retrograde analysis generating information about value by finding all the moves that lead to positions whose value you have information about. There are two separate types of step:
(1) if a position has a move which leads to a position where the other side is mated in N, the position is mate in N+1
(2) if all the moves {m_i} from a position lead to positions where the other side is mating in N_i, with the max over i of {N_i} being N, then it is a losing position, getting mated in N.
It is easy to prove that if you repeat this over and over again, on some step you find you have not found any more new winning or losing positions. If this is the N-th step, it means there are no mates in N (of getting mated in N).
The reason I described that is that the next step is to realise at this point that all the other positions are drawn. The reason is that you can't have any mates of length N+1 or greater if there are no mates in N.
This is a really cool explaination! I think I understand now; tablebase starts at zero and continues until it reaches a value where mate is possible (N+1). If a win isn't possible no matter the moves, it's considered a draw. Am I correct or did I misinterpret?
'tablebase starts at zero' ... zero what?
I like this part:
"The reason is that you can't have any mates of length N+1 or greater if there are no mates in N,"
0 moves. Base game. Sorry for not clarifying.
Its fine. We get to discuss chess here.
I think you probably know this next thing:
You know that tablebases don't start from the opening.
Right?
Now I can't be 100% sure that when you say 'base game' you don't mean the opening.
But I think you mean ... zero reverse moves. From very simplified endgame positions.
That whole business of generating positions by adding material to two kings ...
I don't know how they do that in the tablebase projects.
Except that it starts from simplified positions like two Kings only on board.
There's a lot of ways that could be done. And again - there's parallel processing.
Which is constantly a big factor.
-----------------
I like the idea of adding material objectively - without having to have a reverse capture.
Then separate the illegal positions that result from that.
Then separate the checkmates and the stalemates.
And the 'checkmates in 1' and stalemates in 1.
But for 'hopeless draws' it gets harder. Because there will be 'helpmates'.
For example K+R versus K+R is a very different class of position ...
Apr 5, 2025
0
#16528
MARattigan wrote:
Elroch wrote:
The much lower Syzygy number must involve counting only the positions stored, which are then multipled by almost 8 for symmetries on the board. 52234 * 8 = 417872 (an upper bound because of the "almost"). Note that the only moves that reduce the multiple to less than 8 are those where all three pieces are on a diagonal, so that one of the reflections does not affect the position.
Trying to match Syzygy positions to what you always thought were positions is quite awkward.
There's not only the factor of 8 or 2 for board symmetry to take into account but you also have to divide by the factorials of the numbers of sets of repeated pieces of the same colour and type (I'm not sure if there isn't also an extra complication when the repeated pieces are bishops). At any rate you won't get correct adjustment for symmetric positions.
Not need to worry about that for KkB!
The percentages of wins, frustrated wins, etc. are, I believe very close to correct.
I would expect Syzygy to be exactly correct.
Correct figures are available on the ICGA site for basic rules, but they don't cover the same range as the Syzygy site (no 7 man, no 5-1 and a few other specific missing classifications with < 7). At least that was the case last time I looked.
Add in another factor of 2 for colour to get an upper bound of 835744 which I observe is lower than either number posted above.
Ah, I see now. Your numbers weren't legal positions, as they failed to remove those with a king in check and not to move.
Exactly.
Don't ask me what the point is of counting positions where the side not to move can be in check from a bishop but not by a king. It apparently has something to do with alternate solving.
We still don't have that number of legal positions that is of more interest (to me at least) than the number of diagrams.
The number of legal KBK positions under either basic or competition rules is 934456 (reported semi-legal positions as defined here, but I think in this case "semi-legal" corresponds with "legal").
That can actually be worked out by hand for KBK, but if you want to perform the exercise wholesale youl'd need to write a mickey mouse javascript or something unless you can come up with a simpler expression than I did.
Yes, I could either work it out by hand or more likely by computer, or debug Gemini's attempt. 
Apr 5, 2025
0
#16529
Elroch wrote:
MARattigan wrote:
Elroch wrote:
...
I would expect Syzygy to be exactly correct.
...
I believe Syzygy bases the percentages on tablebase entries rather than positions and that overweights symmetric wins, because the full board symmetries shouldn't be applied to those positions. For other positions the same board symmetry and quirky replicated piece factors apply to each position, so the fact that the reported position counts don't match actual position counts doesn't matter in forming percentages.
If you look at percentage wins in Syzygy and as reported by Wilhelm from the Nalimov tablebases (which does correct for symmetric positions) you sometimes see small differences of 0.01 or 0.02 percent. (Also not in KBK, but I was remarking on the general situation.)
Apr 5, 2025
0
#16530
Elroch wrote:
Yes. But before you travel to another galaxy, it's best to first travel to another star.
The first strong solution is of basic rules chess, maybe covering chess with n-move drawing rules as well. Then you can move on to solving the version with repetition rules - which are a second convenient addition for competition.
Good way of putting it.
And I wouldn't have seen the correction of the 3648 ways to arrange two kings if I hadn't been reading Elroch's posts.
When I was calculating that i deliberately didn't use the easier method of just summing for a corner and edge and midboard king - I deliberately wanted more categories and therefore didn't compare with the 3612. So I got the number wrong because of special subtypes of squares and when you multiply by two and when you don't.
If that 3612 is then multiplied by the 62 places for the bishop and then by 2 for either color of bishop and then by 2 again for who is to move - you get the 895776 possible positions for K+B versus K.
And also for the N and the R and the Q. Same number on all four.
But for the pawn its a lower number but more complicated.
------------------------
So far - there's only one way for the K plus a B or N or R or Q to be illegal.
And that's if there's check and the checking side is on move.
For the P that's also true. But there's an extra one.
If a lone King is on move its also illegal if he's in check from the pawn on its original square.
Apr 6, 2025
0
#16531
MARattigan wrote:
Elroch wrote:
MARattigan wrote:
Elroch wrote:
...
I would expect Syzygy to be exactly correct.
...
I believe Syzygy bases the percentages on tablebase entries rather than positions and that overweights symmetric wins, because the full board symmetries shouldn't be applied to those positions.
Yes, of course. I meant the statistic it gives is correct, not a modified one! There's not actually anything more meaningful about the percentage of legal positions versus the percentage of legal positions taking into account symmetries. Both are just about counting things which are of variable importance.
For other positions the same board symmetry and quirky replicated piece factors apply to each position, so the fact that the reported position counts don't match actual position counts doesn't matter in forming percentages.
If you look at percentage wins in Syzygy and as reported by Wilhelm from the Nalimov tablebases (which does correct for symmetric positions) you sometimes see small differences of 0.01 or 0.02 percent. (Also not in KBK, but I was remarking on the general situation.)
Apr 6, 2025
0
#16532
XianyunLi wrote:
Elroch wrote:
MARattigan wrote:
Elroch wrote:
The much lower Syzygy number must involve counting only the positions stored, which are then multipled by almost 8 for symmetries on the board. 52234 * 8 = 417872 (an upper bound because of the "almost"). Note that the only moves that reduce the multiple to less than 8 are those where all three pieces are on a diagonal, so that one of the reflections does not affect the position.
Trying to match Syzygy positions to what you always thought were positions is quite awkward.
There's not only the factor of 8 or 2 for board symmetry to take into account but you also have to divide by the factorials of the numbers of sets of repeated pieces of the same colour and type (I'm not sure if there isn't also an extra complication when the repeated pieces are bishops). At any rate you won't get correct adjustment for symmetric positions.
Not need to worry about that for KkB!
The percentages of wins, frustrated wins, etc. are, I believe very close to correct.
I would expect Syzygy to be exactly correct.
Correct figures are available on the ICGA site for basic rules, but they don't cover the same range as the Syzygy site (no 7 man, no 5-1 and a few other specific missing classifications with < 7). At least that was the case last time I looked.
Add in another factor of 2 for colour to get an upper bound of 835744 which I observe is lower than either number posted above.
Ah, I see now. Your numbers weren't legal positions, as they failed to remove those with a king in check and not to move.
Exactly.
Don't ask me what the point is of counting positions where the side not to move can be in check from a bishop but not by a king. It apparently has something to do with alternate solving.
We still don't have that number of legal positions that is of more interest (to me at least) than the number of diagrams.
The number of legal KBK positions under either basic or competition rules is 934456 (reported semi-legal positions as defined here, but I think in this case "semi-legal" corresponds with "legal").
That can actually be worked out by hand for KBK, but if you want to perform the exercise wholesale youl'd need to write a mickey mouse javascript or something unless you can come up with a simpler expression than I did.
Yes, I could either work it out by hand or more likely by computer, or debug Gemini's attempt.
Bruh why are you guys making each message really long???
We get paid by the word.
Apr 6, 2025
0
#16533
Regarding converting Syzygy numbers to a normal concept of legal position, I would observe that it is a relatively small job to count the number of positions where all the pieces lie on a diagonal. Especially for the simple example of KkB. The bigger job is dealing with the positions where there is a check, so the position can only be with the move for the side being checked.
First on a specific diagonal, there are 8 places for the white king. If its a corner, there are 6 places for the black king, otherwise 5places. Each of these positions permits 6 bishop locations.
So that's (6 + 6 + 6 * 5) * 6 / 2 = 126 Syzygy positions where the division by 2 at the end accounts for the fact that we can flip around the diagonal the positions are not on. It would have been possible to achieve the same by restricting the white king to 4 squares initially.
These are the 126 Syzygy-counted positions that only give 8 diagrams as opposed to 16.
Dealing with which of these are checks so only give positions for one side to move is a lot more work.
Apr 6, 2025
0
#16534
playerafar wrote:
.Illegal unless the bishop is a promotion bishop with black to move.
i.e. 100% legal.
Apr 7, 2025
0
#16535
Elroch wrote:
XianyunLi wrote:
Elroch wrote:
MARattigan wrote:
Elroch wrote:
The much lower Syzygy number must involve counting only the positions stored, which are then multipled by almost 8 for symmetries on the board. 52234 * 8 = 417872 (an upper bound because of the "almost"). Note that the only moves that reduce the multiple to less than 8 are those where all three pieces are on a diagonal, so that one of the reflections does not affect the position.
Trying to match Syzygy positions to what you always thought were positions is quite awkward.
There's not only the factor of 8 or 2 for board symmetry to take into account but you also have to divide by the factorials of the numbers of sets of repeated pieces of the same colour and type (I'm not sure if there isn't also an extra complication when the repeated pieces are bishops). At any rate you won't get correct adjustment for symmetric positions.
Not need to worry about that for KkB!
The percentages of wins, frustrated wins, etc. are, I believe very close to correct.
I would expect Syzygy to be exactly correct.
Correct figures are available on the ICGA site for basic rules, but they don't cover the same range as the Syzygy site (no 7 man, no 5-1 and a few other specific missing classifications with < 7). At least that was the case last time I looked.
Add in another factor of 2 for colour to get an upper bound of 835744 which I observe is lower than either number posted above.
Ah, I see now. Your numbers weren't legal positions, as they failed to remove those with a king in check and not to move.
Exactly.
Don't ask me what the point is of counting positions where the side not to move can be in check from a bishop but not by a king. It apparently has something to do with alternate solving.
We still don't have that number of legal positions that is of more interest (to me at least) than the number of diagrams.
The number of legal KBK positions under either basic or competition rules is 934456 (reported semi-legal positions as defined here, but I think in this case "semi-legal" corresponds with "legal").
That can actually be worked out by hand for KBK, but if you want to perform the exercise wholesale youl'd need to write a mickey mouse javascript or something unless you can come up with a simpler expression than I did.
Yes, I could either work it out by hand or more likely by computer, or debug Gemini's attempt.
Bruh why are you guys making each message really long???
We get paid by the word.
Hahahhaahah.
Great post !!
😁🤣😎👌
Nobody has offered me the contract so Ill be on a strike until the pay me too. Not a word until then
Apr 7, 2025
0
#16537
When evaluating positions at the beginning of the game many might say :
'That's okay. Just don't make illegal moves to generate positions.'
Others: 'and don't bother to count illegal positions with 32 pieces on board - and 31 pieces and so on.'
But those ideas miss points: And they are 'game tree' ideas.
Point: Does John Tromp's number factor in various illegal positions other than maximum 32 pieces and maximum of 2 opposite-colored Kings and things like that?
I don't know. Maybe the precise derivation of his number 4.8 x 10^44 possible legal chess positions as an upper bound - is very publically available.
Point: The current impossibility of solving chess is based on that number.
And three years of forum conversation here are based on that JT number too.
-----------------
To make progress - maybe its a good time to look at that derivation.
Even if it was looked at before.
No I haven't looked into it. Or not yet. Don't have time for everything.
Point: better ideas about what the real actual number is of legal chess positions to be solved that really have play in them. Instead of the larger JT number.
-------------------------
From the front of the game is much harder.
But generalizations can still be made - and computers can zap positions that need zero ply depth to count them.
A 32 piece position can't have any promotions in it. Its impossible.
Because promotions need captures. As to the ratio - that's not simple.
So 32-piece positions can only have the original material forces as on move 1.
31 piece. For now - zero to three promotions are possible in such positions.
But there are other constraints too on 31-piece. Constraints - again - as to what is legal.
Which computers can use.
-----------------
What might actually be solved before the year 2040?
1) total number of checkmate positions? (including mate in one versus those already mate?)
2) total number of stalemate positions.
3) total number of positions with lone king against king with material. Maybe solved already?
Apr 7, 2025
0
#16538
OctopusOnSteroids wrote:
Nobody has offered me the contract so Ill be on a strike until the pay me too. Not a word until then
Maybe they'll pay you under the table. You didn't know ...??
Apr 7, 2025
0
#16539
Elroch wrote:
playerafar wrote:
.Illegal unless the bishop is a promotion bishop with black to move.
i.e. 100% legal.
Actually - there are illegal checks by a bishp from a corner square.
When I talk to AI about this it makes a million blunders.
But just now during such a talk - I realized it.
How could a white pawn promote at a1 or h1?
Note that the white King is 'out of range' to have 'discovered' the bishop check - which would be also impossible with the black King at b2.
It can't !! So there couldn't be a white bishop checking from those squares because it has no legal way to get to those squares with only three men on board.
Its illegal! As would be black bishops checking from a8 or h8 in various configurations.
So it is a third type of illegality with three men on board.
Peculiarities and limitations of bishops.
(Yes obviously and of course there could be exceptions where the white king 'uncovered' the check - but that's 'covered' in the diagram.)
Anyway - more ways for the solving computer to 'take prisoners'.
More prisoners can be added. Material added that does not block the bishop check or couldn't have unblocked it would also generate illegal positions. Is there an en passant that would 'work'?
I think there is. Black King at f6. white discover checks with P to d5ch.
Black blocks with e7-e5 so white goes P x e6 e.p. 'disappearance check'.
The bishop is still legally checking from a1.
(But that's with more material and is one of a low percentage of exceptions.)
Anyway - another attack on that 10^45 number. (which is 'the fortress')
At first - AI didn't get it about a1. Maybe there's a pun in there somewhere.
gugiugiugiu3qhoiuq1hoi21hoihoihiohoihiohh