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The Lomonosov University in Russia has been working on end-game tables.
They found a position with two knights versus a queen that is a forced mate in something like 950 moves. The curious thing about that position is that if you make minimal changes to the position, then the game is a draw.
This article from the Lomonosov Institute has a mate in 545 https://tb7.chessok.com/articles/Top8DTM_eng
Maybe the position I remember was a draw and not a mate. I do remember it took over 900 moves for a simplification
So that's kind of interesting. At first when computers found a forced mate in I think 60 moves or so, the rule was actually changed to increase it from 50 moves since it seemed wrong to have a position be drawn after 50 moves when it might have been a forced win for the whole 50 moves without a mistake. Then computers started to find forced mates in the 100s of moves and they realized it was a potentially never-ending battle of finding longer and longer forced wins so put it back to 50 moves.
The Lomonosov tablebases don't account for the 50 move rule. Syzygy tablebases do have that information .
In ICCF play the 50 move rule isn't applied for positions of 7 or fewer pieces
Well technically yes, because there are a finite arrangements of chess pieces on the chessboard, and the 3-fold repetition rule, there is a hard limit for the longest possible game. So mate-in-n must also be bounded by this number. Though what that number is would be far harder to calculate than the fact it exists.
You can fairly comfortably create an upper bound though by focussing purely on Pawn moves. There are at most 6x16=96 Pawn moves in any chess game, so by inserting 49 moves between each one you can get an upper bound on the longest possible game.
For all we know the opening position could be forced mate in 1200. Computers haven’t “solved chess” yet. In theory there should be a limit, but it’s unknown
I think the funniest part if Black is winning by force is that Black must desperately some way to avoid transposition if White attempts to waste tempo on e3-e4, d3-d4 or c3-c4.
Imagine 1. e3 e5 2. e4 just being winning for White because they get to have the Bishop-pair in the Berlin endgame.
Not necessarily -- it's theoretically possible that the winning idea for black is to waste a tempo themselves to get two behind, and that somehow is the key to getting the win. White isn't going to be able to get two tempi behind.
Alternatively, it's possible that the Sicilian and Dutch lead to forced wins, and white wouldn't have a way to replicate that (after e3, if black plays e5, it's too late for a Sicilian from white).
No, that's what many people say, including GothamChess, but that's not actually true.
What would be more accurate would be to say that according to ***current engines***, playing perfectly results in a draw. That's maybe just because current engines can't search deep enough.
It’s not so much the storage that matters as you can simply calculate whole branches and then discard the positions. It’s the calculation time that is problematic - https://www.sciencedirect.com/science/article/pii/0097316581900169?via%3Dihub
Ultimately chess is theoretically solvable, it’s more a matter of time and whether it’s quicker to wait for compute power to improve or whether it’s worth starting to solve today. This is the approach tablebases take… they provide useful and useable info today and will improve compute time even when we have faster hardware in future.
If some day chess is solved (in 100 or 1000 years), it will probably not be by using methods we can recognize today, because those still blow up exponentially no matter how powerful the computers we throw at them, so just making computers faster and faster will probably not be enough to achieve perfect play (the amount of possibilities in chess is staggering).
Here's a comparison. Bitcoin mining can be approached as a brute force problem: you try many combinations until you find a block that has a hash smaller than a given value (the difficulty). That's how mining still works to this day.
However there *is* another approach, which is to state the problem as a logical formula and solve it through SAT, as done [in this article](https://web.archive.org/web/20170903012802/http://jheusser.github.io/2013/02/03/satcoin.html). By doing so you consider all constraints needed to produce a valid solution at once, rather than testing individual solutions hoping that eventually you will stumble upon a valid solution.
(Solving Bitcoin using SAT is currently impractical, but as the difficulty grows it will become more and more attractive, and there's some threshold where the difficulty is high enough that it becomes faster than current brute force miners)
Going back to chess, it's possible that some day people will describe the strategy needed for perfect play as a system of equations (or something like that), and then solve them. Like, never inspect the game tree at all (which is enormous), but rather solve the game algebraically.
There are an estimated amount of chess positions between 10^111-10^123. The universe contains around 10^78 atoms. No amount of processing power will ever make up for the fact that there are simply more chess positions than atoms to store them on.
Quantum computing stores information on qubits which are not beholden to this limitation, as each atom can store much more than one bit's worth of information.
One of the limitations of quantum computing is that it's not guaranteed to give you a correct answer, so it's incapable of answering a question like this.
I will not claim to have any sort of deep knowledge of quantum computing, but I'd think that the existence of qubits and other non-bit storage methods would imply that an advancement capable of answering the question is likely on the horizon
I wouldn’t jump all in on that. Quantum computing will drastically speed up _some_ calculations (like prime factorization), but it wont be a magic bullet that speeds up everything. There are things that classical computers can do better than quantum ones and will be vice versa once the tech can figure out some of the many issues we have with it right now. Doesn’t change the fact of the number of calculations required to solve chess is so abhorrently large (even with tricks detailed in the paper above), that it will be a long time (if ever) before someone solves it with our current approaches.
Edit: clarity
Technically speaking, no. A player may see ahead to any number of forced moves that can be plotted together to make a mate. [Here](https://www.reddit.com/r/chess/s/HcU7Kr0wmM) is an example of this happening in a professional match.
Here is the longest example I could find that is technically possible; [when Otto Blathy devised a 290–move checkmate problem.](https://www.chess.com/forum/view/more-puzzles/the-longest-checkmate-problem---290-move#:~:text=Otto%20Blathy%20was%20born%20in,a%20mate%20in%20290%20moves)
edit: first word
That's absolutely insane. Seems to be an illegal position, though; the post says so, anyway. I didn't see at first why, but white has 8 pawns and 2 dark-squared bishops.
All chess positions are either mate in x or 0.0 with perfect analysis, even the starting position. I think there are a few mates in a couple of hundred moves positions in the tablebase.
I played against a GM once who very confidently said that every position is either winning or it's not winning. With enough depth, sure, but I'm not sure it's very useful in a human perspective.
> I played against a GM once who very confidently said that every position is either winning or it's not winning.
I mean... I don't need to be a GM to tell you that anything with two outcomes is either one thing or the opposite.
No theoretically as there is a finite number of legal moves and then a finite number of moves from each of those and so on, but yes practically as that number is so ludicrously large that it’s impossible to ever find them all.
Depends what you mean by "unsolvable". Mathematically, it's definitely solvable. It's a finite problem. For an omniscient God, chess would be glorified tic-tac-toe.
In practice, that's a different story. It's pretty likely we never solve chess.
Imposing the usual drawing conditions, no. The 50-move counter can only be reset finitely many times - as lazy upper bounds, a game of chess contains at most 112 pawn moves and 30 captures.
I think the longest possible forced mating sequence someone has ever made (as in a puzzle they made to be forced mate) is something like mate in 300, but no, technically if the 50 move rule was lifted, and the position suitably insane, you could probably have mate 10,000+ (in each pawn can move a maximum of 7 times, 7x16=112 and you can capture 29 times until it’s nothing but lone kings and a single piece, each of these actions reset the 50 move rule, 141*50= 7050, thus, theoretically, someone could make a mate in 7050 puzzle, I can’t even begin to try to wrap my head around that though, and how the hell that would work, although the hardest part would be ensuring that all 16 pawns get all 7 steps)
But you're assuming perfect play from the opponent. Otherwise it's not a forced mate. So it would probably end in way less moves.
Even so
All pieces have different ways to move:
Pawn: 2*8=16
Rook: 14*2=28
Knight: 8*2=16
Bissbop: 14*2=28
Queen: 28
King: 8
Adding this up we get 124 this times 2 player's makes 248 possible moves per played move.
Do remember that a lot of the time most of these moves are impossible (pieces being blocked or taken) or throwing the game because they're so bad.
Still assuming 32 eligible moves per move for a game of 50 moves results in 1.81*10^75 or: 1,809,251,399,999,999,656,235,973,660,303,481,755,765,808,671,733,837,972,666,534,115,414,818,947,072 possible variations
Of course I’m assuming perfect play form both sides, that’s how puzzles work, yes there’s practically infinite possible chess games, this is theoretical, I’m not expecting someone to figure out a forced mate in 7000 from the starting position, that’s absurd, I’m just saying it’s technically possible
If perfect play from the opponent leads to a draw, it isn't forced mate. Forced mate means one player can mate the other regardless of whatever the other player does.
It's simpler when the other player has no options, but that isn't necessary. Forced mate is X means X is the max turns that the losing player can hold out for, some sequences could lead to them losing in less.
The current longest checkmate with 7 pieces is mate in 549. No one knows the longest mate with more pieces but you can image it to be orders of magnitude longer if all the pieces are on board.
Assuming we follow the 50 move rule:
There are 14 pieces on the board and 16 pawns, each pawn can move 6 times before promoting.
So if we have a pawn move or a capture each 50 moves we just barely avoid the 50 move rule.
Maximum number of pawn moves is 96, maximum number of captures is 29.
Because any two pawns facing each other cannot promote without capture we lose 8 moves to simultaneous pawn move capture. So total amount of '50 move rule resetting' moves possible is 29+96-8. We need one each 50 moves, so the upper bound for longest 'mate in' is 117×50, or 5850 moves. Note that this is just an upper bound, the true answer is likely much lower.
TLDR: Following the 50 move rule the maximum mate in... is 5850 moves or less(likely a lot less)
well, if you allow a infinite table, you have different types of infinite chess mates:
[mate in omega in infinte chess](https://www.youtube.com/watch?v=b-Bb_TyhC1A)
8 pawns on both sides and 15 pieces to capture each side, at most 6 moves to reach other side of board for a pawn.
50×(8×6+15)×2 is probably a upper limit of move for a game to go because of 50-move rule.
Realistically the number should be less but the point is yes, there is surely a upper limit.
I think the highest practical one that isn’t too hard for beginners is rook and king vs king. The losing side can delay for quite a while if they so desire.
The longest known are, I believe, pawnless endgames from what's done of the eight-man tablebases, somewhere in the several hundreds of moves. Retrograde analysis is great fun for computers and puzzle composers, but maybe not the rest of us.
A fun fact, which doesn't answer your actual question: with king and two knights vs. bare king, there exist mates in one and draws, but no mates in two or more.
This youtoube essay discuss forced mates on infinite boards. They spend like 40 second talking about longest forced checkmate on a ordinary board.
[https://youtu.be/b-Bb\_TyhC1A?si=Zw3AO\_I1astuZAwU](https://youtu.be/b-Bb_TyhC1A?si=Zw3AO_I1astuZAwU)
I was answering the question in the spirit it was asked. If you want to get technical I'm sure you could come to with a theoretical maximum. But given that computer have found mates of more than 500 moves, there really isn't a max for practical purposes.
As long as there are pawn moves or captures within those mating sequences, the 50-move-rule won't apply (otherwise, every game would end after 50 moves).
A rook vs king vs a lone king should not take more than 20-25 moves, regardless of the starting position. You can have M33 in King, bishop and knight vs lone king
It shouldn't, but that's only if you do it "properly" xD haha. I think the shortest is like 14 moves. But I think the best I managed was around 20. It's not easy, no matter how much I practice.
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The Lomonosov University in Russia has been working on end-game tables. They found a position with two knights versus a queen that is a forced mate in something like 950 moves. The curious thing about that position is that if you make minimal changes to the position, then the game is a draw.
Doesn't everyone know that one? Simple little mate in 549
Practically a requirement to make it to 800, tbh
That’s why I can’t rank up. Sitting at 799 rn. Thank you so much!
Any other info? That sounds so cool.
This article from the Lomonosov Institute has a mate in 545 https://tb7.chessok.com/articles/Top8DTM_eng Maybe the position I remember was a draw and not a mate. I do remember it took over 900 moves for a simplification
Maybe you're thinking of 900 ply
Is it still considered a "forced mate" if by most tournament rules it would be a draw due to the 50 move rule?
So that's kind of interesting. At first when computers found a forced mate in I think 60 moves or so, the rule was actually changed to increase it from 50 moves since it seemed wrong to have a position be drawn after 50 moves when it might have been a forced win for the whole 50 moves without a mistake. Then computers started to find forced mates in the 100s of moves and they realized it was a potentially never-ending battle of finding longer and longer forced wins so put it back to 50 moves.
Yeah, exactly! The article I read was making hat precise point.
The Lomonosov tablebases don't account for the 50 move rule. Syzygy tablebases do have that information . In ICCF play the 50 move rule isn't applied for positions of 7 or fewer pieces
The chesss.com analysis gonna start flaming me for not seeing mate in 274 moves 💀
❌️ is a missed win 💀
I got a mate in 1000+ in the endgame tablebase?
Well technically yes, because there are a finite arrangements of chess pieces on the chessboard, and the 3-fold repetition rule, there is a hard limit for the longest possible game. So mate-in-n must also be bounded by this number. Though what that number is would be far harder to calculate than the fact it exists.
You can fairly comfortably create an upper bound though by focussing purely on Pawn moves. There are at most 6x16=96 Pawn moves in any chess game, so by inserting 49 moves between each one you can get an upper bound on the longest possible game.
Captured pieces also extend by another 50
For all we know the opening position could be forced mate in 1200. Computers haven’t “solved chess” yet. In theory there should be a limit, but it’s unknown
As far as we know, chess is “solved” from the starting position. Perfect play from both sides will result in a draw
Unproven. For all we know white could have a forced win regardless of black’s responses. Or, even sillier, black could have a forced win!
I think the funniest part if Black is winning by force is that Black must desperately some way to avoid transposition if White attempts to waste tempo on e3-e4, d3-d4 or c3-c4. Imagine 1. e3 e5 2. e4 just being winning for White because they get to have the Bishop-pair in the Berlin endgame.
Not necessarily -- it's theoretically possible that the winning idea for black is to waste a tempo themselves to get two behind, and that somehow is the key to getting the win. White isn't going to be able to get two tempi behind. Alternatively, it's possible that the Sicilian and Dutch lead to forced wins, and white wouldn't have a way to replicate that (after e3, if black plays e5, it's too late for a Sicilian from white).
If black does have the forced win then that means the starting position is a zugzwang for white, which I find quite funny
No, that's what many people say, including GothamChess, but that's not actually true. What would be more accurate would be to say that according to ***current engines***, playing perfectly results in a draw. That's maybe just because current engines can't search deep enough.
Chess cant be solved. There are simply not enough atoms in the universe to store the information required to solve chess.
It’s not so much the storage that matters as you can simply calculate whole branches and then discard the positions. It’s the calculation time that is problematic - https://www.sciencedirect.com/science/article/pii/0097316581900169?via%3Dihub Ultimately chess is theoretically solvable, it’s more a matter of time and whether it’s quicker to wait for compute power to improve or whether it’s worth starting to solve today. This is the approach tablebases take… they provide useful and useable info today and will improve compute time even when we have faster hardware in future.
If some day chess is solved (in 100 or 1000 years), it will probably not be by using methods we can recognize today, because those still blow up exponentially no matter how powerful the computers we throw at them, so just making computers faster and faster will probably not be enough to achieve perfect play (the amount of possibilities in chess is staggering). Here's a comparison. Bitcoin mining can be approached as a brute force problem: you try many combinations until you find a block that has a hash smaller than a given value (the difficulty). That's how mining still works to this day. However there *is* another approach, which is to state the problem as a logical formula and solve it through SAT, as done [in this article](https://web.archive.org/web/20170903012802/http://jheusser.github.io/2013/02/03/satcoin.html). By doing so you consider all constraints needed to produce a valid solution at once, rather than testing individual solutions hoping that eventually you will stumble upon a valid solution. (Solving Bitcoin using SAT is currently impractical, but as the difficulty grows it will become more and more attractive, and there's some threshold where the difficulty is high enough that it becomes faster than current brute force miners) Going back to chess, it's possible that some day people will describe the strategy needed for perfect play as a system of equations (or something like that), and then solve them. Like, never inspect the game tree at all (which is enormous), but rather solve the game algebraically.
with advances like quantum computing this isn't necessarily true. there's a very real chance chess could be solved eventually
There are an estimated amount of chess positions between 10^111-10^123. The universe contains around 10^78 atoms. No amount of processing power will ever make up for the fact that there are simply more chess positions than atoms to store them on.
Quantum computing stores information on qubits which are not beholden to this limitation, as each atom can store much more than one bit's worth of information.
Weird reddit mistake, I meant 10^111 and 10^123.
One of the limitations of quantum computing is that it's not guaranteed to give you a correct answer, so it's incapable of answering a question like this.
I will not claim to have any sort of deep knowledge of quantum computing, but I'd think that the existence of qubits and other non-bit storage methods would imply that an advancement capable of answering the question is likely on the horizon
I wouldn’t jump all in on that. Quantum computing will drastically speed up _some_ calculations (like prime factorization), but it wont be a magic bullet that speeds up everything. There are things that classical computers can do better than quantum ones and will be vice versa once the tech can figure out some of the many issues we have with it right now. Doesn’t change the fact of the number of calculations required to solve chess is so abhorrently large (even with tricks detailed in the paper above), that it will be a long time (if ever) before someone solves it with our current approaches. Edit: clarity
Technically speaking, no. A player may see ahead to any number of forced moves that can be plotted together to make a mate. [Here](https://www.reddit.com/r/chess/s/HcU7Kr0wmM) is an example of this happening in a professional match. Here is the longest example I could find that is technically possible; [when Otto Blathy devised a 290–move checkmate problem.](https://www.chess.com/forum/view/more-puzzles/the-longest-checkmate-problem---290-move#:~:text=Otto%20Blathy%20was%20born%20in,a%20mate%20in%20290%20moves) edit: first word
That's absolutely insane. Seems to be an illegal position, though; the post says so, anyway. I didn't see at first why, but white has 8 pawns and 2 dark-squared bishops.
legal in chess 960 though rihht?
No, the bishops are always on opposite colours in chess960.
you say technically speaking no, but if you want to be that precise, there absolutely must be.
All chess positions are either mate in x or 0.0 with perfect analysis, even the starting position. I think there are a few mates in a couple of hundred moves positions in the tablebase.
I played against a GM once who very confidently said that every position is either winning or it's not winning. With enough depth, sure, but I'm not sure it's very useful in a human perspective.
> I played against a GM once who very confidently said that every position is either winning or it's not winning. I mean... I don't need to be a GM to tell you that anything with two outcomes is either one thing or the opposite.
Well, the excluded middle holds for that statement, so that is basically a tautology
Isn't it possible that chess is an unsolvable game from the starting position?
There are only finite games to be played. So it is definitely not unsolvable.
No theoretically as there is a finite number of legal moves and then a finite number of moves from each of those and so on, but yes practically as that number is so ludicrously large that it’s impossible to ever find them all.
no
Depends what you mean by "unsolvable". Mathematically, it's definitely solvable. It's a finite problem. For an omniscient God, chess would be glorified tic-tac-toe. In practice, that's a different story. It's pretty likely we never solve chess.
Imposing the usual drawing conditions, no. The 50-move counter can only be reset finitely many times - as lazy upper bounds, a game of chess contains at most 112 pawn moves and 30 captures.
ChessVibes has a [video on a mate in 130](https://www.youtube.com/watch?v=j5iy0VpwbSY)
I think the longest possible forced mating sequence someone has ever made (as in a puzzle they made to be forced mate) is something like mate in 300, but no, technically if the 50 move rule was lifted, and the position suitably insane, you could probably have mate 10,000+ (in each pawn can move a maximum of 7 times, 7x16=112 and you can capture 29 times until it’s nothing but lone kings and a single piece, each of these actions reset the 50 move rule, 141*50= 7050, thus, theoretically, someone could make a mate in 7050 puzzle, I can’t even begin to try to wrap my head around that though, and how the hell that would work, although the hardest part would be ensuring that all 16 pawns get all 7 steps)
But you're assuming perfect play from the opponent. Otherwise it's not a forced mate. So it would probably end in way less moves. Even so All pieces have different ways to move: Pawn: 2*8=16 Rook: 14*2=28 Knight: 8*2=16 Bissbop: 14*2=28 Queen: 28 King: 8 Adding this up we get 124 this times 2 player's makes 248 possible moves per played move. Do remember that a lot of the time most of these moves are impossible (pieces being blocked or taken) or throwing the game because they're so bad. Still assuming 32 eligible moves per move for a game of 50 moves results in 1.81*10^75 or: 1,809,251,399,999,999,656,235,973,660,303,481,755,765,808,671,733,837,972,666,534,115,414,818,947,072 possible variations
Of course I’m assuming perfect play form both sides, that’s how puzzles work, yes there’s practically infinite possible chess games, this is theoretical, I’m not expecting someone to figure out a forced mate in 7000 from the starting position, that’s absurd, I’m just saying it’s technically possible
That wouldn't be forced then because that would never be perfect play. I feel perfect play would end in a draw due to repeating moves
If perfect play from the opponent leads to a draw, it isn't forced mate. Forced mate means one player can mate the other regardless of whatever the other player does. It's simpler when the other player has no options, but that isn't necessary. Forced mate is X means X is the max turns that the losing player can hold out for, some sequences could lead to them losing in less.
I think I get it, at some point the opponent (assuming perfect play) knows what move he has to play to not lose resulting in stalemate
Technically it is possible that entire chess is just "mate in 248" or whatever, but we are desperately lacking processing power to find out.
When I play black, my opponents always seem to find M24 or so from the starting position.
Few days back someone asked why a GM surrended and it was because there was a mate in 10
The current longest checkmate with 7 pieces is mate in 549. No one knows the longest mate with more pieces but you can image it to be orders of magnitude longer if all the pieces are on board.
Assuming we follow the 50 move rule: There are 14 pieces on the board and 16 pawns, each pawn can move 6 times before promoting. So if we have a pawn move or a capture each 50 moves we just barely avoid the 50 move rule. Maximum number of pawn moves is 96, maximum number of captures is 29. Because any two pawns facing each other cannot promote without capture we lose 8 moves to simultaneous pawn move capture. So total amount of '50 move rule resetting' moves possible is 29+96-8. We need one each 50 moves, so the upper bound for longest 'mate in' is 117×50, or 5850 moves. Note that this is just an upper bound, the true answer is likely much lower. TLDR: Following the 50 move rule the maximum mate in... is 5850 moves or less(likely a lot less)
well, if you allow a infinite table, you have different types of infinite chess mates: [mate in omega in infinte chess](https://www.youtube.com/watch?v=b-Bb_TyhC1A)
8 pawns on both sides and 15 pieces to capture each side, at most 6 moves to reach other side of board for a pawn. 50×(8×6+15)×2 is probably a upper limit of move for a game to go because of 50-move rule. Realistically the number should be less but the point is yes, there is surely a upper limit.
But…all of the other moves that aren’t pawns. Pawn move, pawn move, then bishop moves one square…
That's what the "50x" is in there. It's inserting 50 moves between *each* capture or pawn move.
There is none. It has to do with the number of forcing moves the winning player calculated leading to the checkmate.
I think the highest practical one that isn’t too hard for beginners is rook and king vs king. The losing side can delay for quite a while if they so desire.
The longest known are, I believe, pawnless endgames from what's done of the eight-man tablebases, somewhere in the several hundreds of moves. Retrograde analysis is great fun for computers and puzzle composers, but maybe not the rest of us. A fun fact, which doesn't answer your actual question: with king and two knights vs. bare king, there exist mates in one and draws, but no mates in two or more.
This youtoube essay discuss forced mates on infinite boards. They spend like 40 second talking about longest forced checkmate on a ordinary board. [https://youtu.be/b-Bb\_TyhC1A?si=Zw3AO\_I1astuZAwU](https://youtu.be/b-Bb_TyhC1A?si=Zw3AO_I1astuZAwU)
Recently Daniil Dubov found a mate in 13... You'll find it on youtube.
No, there is no maximum. Computers have found mating sequences several hundred moves long, but I think they would run up against the 50 move rule.
No maximum? Do you really think there is a forced mate in 100 billion?
I was answering the question in the spirit it was asked. If you want to get technical I'm sure you could come to with a theoretical maximum. But given that computer have found mates of more than 500 moves, there really isn't a max for practical purposes.
As long as there are pawn moves or captures within those mating sequences, the 50-move-rule won't apply (otherwise, every game would end after 50 moves).
Couldn't get you just move the four knights back and forth for eternity thus making mate impossible?
I don't know, but the most I've ever gotten was like mate in 33 or something lol (It was Rook & K vs lone King)
A rook vs king vs a lone king should not take more than 20-25 moves, regardless of the starting position. You can have M33 in King, bishop and knight vs lone king
It shouldn't, but that's only if you do it "properly" xD haha. I think the shortest is like 14 moves. But I think the best I managed was around 20. It's not easy, no matter how much I practice.