bumpity bump bump
Chess will never be solved, here's why
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Dec 26, 2022
0
#5183
Who put the bump in the bump in the bump bah bump bah bump?
Who put the ram in the rama lama ding dong?
Dec 26, 2022
0
#5184
At last we're getting some sensible posts after all that @tygxc crap!
Dec 26, 2022
0
#5186
Squid wrote:
BoardMonkey wrote:
Squid wrote:
bumpity bump bump bump
You trying to outbump me?
bumpity bump bump bumpity bump bump bump
That's it! 10^44 bumps!
@6879
"where did you get the number 10^44?"
++ Here: https://github.com/tromp/ChessPositionRanking
"Furthermore how did you get it down to 10^17 ?"
++ The vast majority of the 10^44 positions makes no sense and cannot result from optimal play from both sides. See the displayed 3 random samples: more than 3 rooks / bishop on each side.
A better estimate is 10^37 https://arxiv.org/pdf/2112.09386.pdf
However a random sample of 10,000 such positions show none can result from optimal play from both sides either. That leaves 10^37 / 10,000 = 10^33 positions.
Now multiply by 10 to accomodate also positions with 3 or 4 queens that do arrive with optimal play by both sides, as we know from ICCF. 10^33 * 10 = 10^34
To weakly solve Chess we only need 1 strategy for black to draw against all white opposition.
So instead of w white moves with each w black responses, we only need to look at w white moves with 1 response each. So instead of w*w positions only w*1 = w = sqrt (w*w) positions. Thus Sqrt (10^34) = 10^17 relevant positions.
"I was taking mostly about weakly solving but strongly solving is harder than weakly solving"
++ Strongly solving needs all 10^44 legal positions,
weakly solving only 10^17 relevant positions.
"it doesn’t take computers 5 years to solve chess"
++ It does take 5 years to calculate 10^17 relevant positions.
"otherwise they would have already done it." ++ So far nobody has put up 3 million $ to rent 3 cloud engines and hire 3 grandmasters during 5 years.
"Every so often there is an “engine tournament”, different chess engines are playing chess games against each other, beginning from a set of known starting positions." ++ TCEC, every year. They impose slightly unbalanced openings between 0.3 and 0.7 to avoid all draws.
'If it is possible to weakly solve chess in 5 years, it is possible to solve for each of those positions in about 5 years" ++ No. Weakly solving Chess only needs 1 strategy for black to draw.
Many of the imposed openings fall outside of that. If black can draw with 1 e4 e5, then 1 e4 c5 may draw as well or not.
"someone just needs to have about 20 computers working in the background for 5 years and the competition is gone?"
++ 3 cloud engines of 10^9 nodes/s or 3000 desktops of 10^6 nodes/s.
"it is not possible in such a small time, again, otherwise someone would have already done that."
++ 3 powerful computers of 10^9 nodes/s and 3 grandmasters during 5 years is a huge task, which costs 3 million $. Nobody has funded or started such a project.
"5 years of what computer"
++ 5 years of three 10^9 nodes/s cloud engines, or 5 years of 3000 desktops of 10^6 nodes/s.
"I am not familiar with the term 7-men endgame table base”
https://en.wikipedia.org/wiki/Endgame_tablebase
"I assume this means to the end of the game or to a solved position"
++ All positions of 7 men or less have been strongly solved.
"it is not what it is coded to do"
++ It is. In TCEC the engines hit their 7-men endgame table bases.
"it is coded to give you the probability best move in a reasonable amount of time"
++ If you give more time it gets deeper and hits the 7-men endgame table base.
"is enough time 2 years or 10^20 years?" ++ Enough time is 5 years on three 10^9 nodes/s cloud engines or on 3000 desktops of 10^6 nodes/s.
"so theoretically a computer could solve any positions" ++ No, any legal position would mean 10^44 positions, that is strongly solving or a 32-men table base and that would be too much.
tygxc wrote:
@6879
"where did you get the number 10^44?"
++ Here: https://github.com/tromp/ChessPositionRanking
"Furthermore how did you get it down to 10^17 ?"
++ The vast majority of the 10^44 positions makes no sense and cannot result from optimal play from both sides. See the displayed 3 random samples: more than 3 rooks / bishop on each side.
A better estimate is 10^37 https://arxiv.org/pdf/2112.09386.pdf
However a random sample of 10,000 such positions show none can result from optimal play from both sides either. That leaves 10^37 / 10,000 = 10^33 positions.
Now multiply by 10 to accomodate also positions with 3 or 4 queens that do arrive with optimal play by both sides, as we know from ICCF. 10^33 * 10 = 10^34
To weakly solve Chess we only need 1 strategy for black to draw against all white opposition.
So instead of w white moves with each w black responses, we only need to look at w white moves with 1 response each. So instead of w*w positions only w*1 = w = sqrt (w*w) positions. Thus Sqrt (10^34) = 10^17 relevant positions.
"I was taking mostly about weakly solving but strongly solving is harder than weakly solving"
++ Strongly solving needs all 10^44 legal positions,
weakly solving only 10^17 relevant positions.
"it doesn’t take computers 5 years to solve chess"
++ It does take 5 years to calculate 10^17 relevant positions.
"otherwise they would have already done it." ++ So far nobody has put up 3 million $ to rent 3 cloud engines and hire 3 grandmasters during 5 years.
"Every so often there is an “engine tournament”, different chess engines are playing chess games against each other, beginning from a set of known starting positions." ++ TCEC, every year. They impose slightly unbalanced openings between 0.3 and 0.7 to avoid all draws.
'If it is possible to weakly solve chess in 5 years, it is possible to solve for each of those positions in about 5 years" ++ No. Weakly solving Chess only needs 1 strategy for black to draw.
Many of the imposed openings fall outside of that. If black can draw with 1 e4 e5, then 1 e4 c5 may draw as well or not.
"someone just needs to have about 20 computers working in the background for 5 years and the competition is gone?"
++ 3 cloud engines of 10^9 nodes/s or 3000 desktops of 10^6 nodes/s.
"it is not possible in such a small time, again, otherwise someone would have already done that."
++ 3 powerful computers of 10^9 nodes/s and 3 grandmasters during 5 years is a huge task, which costs 3 million $. Nobody has funded or started such a project.
"5 years of what computer"
++ 5 years of three 10^9 nodes/s cloud engines, or 5 years of 3000 desktops of 10^6 nodes/s.
"I am not familiar with the term 7-men endgame table base”
https://en.wikipedia.org/wiki/Endgame_tablebase
"I assume this means to the end of the game or to a solved position"
++ All positions of 7 men or less have been strongly solved.
"it is not what it is coded to do"
++ It is. In TCEC the engines hit their 7-men endgame table bases.
"it is coded to give you the probability best move in a reasonable amount of time"
++ If you give more time it gets deeper and hits the 7-men endgame table base.
"is enough time 2 years or 10^20 years?" ++ Enough time is 5 years on three 10^9 nodes/s cloud engines or on 3000 desktops of 10^6 nodes/s.
"so theoretically a computer could solve any positions" ++ No, any legal position would mean 10^44 positions, that is strongly solving or a 32-men table base and that would be too much.
Just remember that every time Tygxc says something that tries to sound as if it is derived from some theoretical solutions agreed upon by others, he's full of crap. He's the only person that believes his made up numbers. Everything bolded above, that he tries to pass off as accepted possibilities, are just things he has conjured himself.
- His reduction to 10^33 is inconclusive and non-scientific.
- The "only one Black strategy is required" assertion does not hold up.
- Even the square rooting is conjecture based on Checkers, not a proven reduction that can be made for Chess as well, it's a guess/an assumption.
- Tygxc's "nodes" is a unit of measure that does not carry over to his pet theories, he's counting apples and giving us misleading results in oranges.
Any one of these collapses his whole house of cards, so being wrong about all of them...well...
To be honest what is the point of chess being solved because it doesn’t make much difference to human play it will just change similarly to how engines have. For engines it will make chess tournaments pointless because the best engine will never lose and will always draw similar engines. No one cares about engine tournaments as much as human ones
There are 400 ways the first move from each side can be played and although a lot of them will be losing for a side many will not. Humans might be able to remember Rui Lopez main line down to a draw but other things will be played and people will lose
@6896
"it doesn’t make much difference to human play"
++ It probably does. If one human player has access to say 10,000 perfect games with optimal play from both sides, then that would give him an advantage.
@6897
"There are 400 ways the first move from each side can be played"
++ Weakly solved reduces this to 20 or less. That is where the square root comes from.
You only need 1 black move that draws for each white move.
"although a lot of them will be losing for a side many will not"
++ Weakly solved does not call for all black moves that do not lose. Only one is enough.
"Humans might be able to remember Ruy Lopez main line down to a draw"
++ The Ruy Lopez down to a draw may entail like 10^15 positions, i.e. about 10^13 games.
No human can remember that. However, 10,000 games i.e. 10^6 positions is possible.
"other things will be played and people will lose"
++ A weak solution of Chess based on Ruy Lopez also has to cope with say Vienna, Center Game, Bishop's Opening, Scotch, Four Knights, Italian,
as well as something against 1 d4, say Queen's Gambit Declined,
something against 1 c4, say Reversed Sicilian, something against 1 Nf3, say Reti...
On the other hand that weak solution of Chess then does not need to handle Petrov, Sicilian, French, Caro-Kann, Pirc, Dutch, King's Indian Defense, Grünfeld Indian Defense, Nimzovich Indian Defense, Queen's Indian Defense, Queen's Gambit Accepted...
Optimissed wrote:
tygxc wrote:
@6897
++ Weakly solved does not call for all black moves that do not lose. Only one is enough.
It might win though!
On the other hand that weak solution of Chess then does not need to handle Petrov, Sicilian, French, Caro-Kann, Pirc, Dutch, King's Indian Defense, Grünfeld Indian Defense, Nimzovich Indian Defense, Queen's Indian Defense, Queen's Gambit Accepted...
Seriously, no-one is going to buy this as any kind of a solution for chess. It isn't adding ANYTHING to what we already know or to chess theory. The entire, artificial idea of "weakly solving", "strongly solving" etc is complete nonsense because in practice, they overlap considerably.
In any case, the supposed definitions that are in use "ie weak solving is a strategy that .... etc" or "an algorithm that .... etc" is also nonsense, since in each case we're discussing series of concrete moves, which is very much NOT a strategy, except that in its simplest form, a viable strategy in chess is "any series of moves which does not contain any move or moves that lose by force".
So the supposed experts here place all their faith in other experts whose conceptions of the strategy of solving chess isn't just archaic but ludicrous. And these people, being called "games theorists", cannot do wrong because of their title, and everyone believes them, even though they obviously come from a bygone age and never thought well and properly on this subject in their entire lives.
Tygxc is pushing this rubbish on the pretext of educating others, tacitly supported by people who cannot see that the entire project is built on sand, because they're only intent on trying to get tygxc to recognise their own very limited objections.
Unless the foundations of "solving chess" are reassessed from ground up, there's no point at all in any of this twaddle. No group of scientists would dream of approaching an area of research without assessing and reassessing it. A reliance on the potentially outworn and useless ideas of others is an obvious and elementary mistake, which makes nonsense of this entire thread.
I understand the frustration (and I do not claim that what tygxc is saying is true) but do not dismiss the whole subject of solving games. This is not some made up concept with no use in the real world, this is a major part of game theory (which is a concrete mathematical field with everything any other field has), the concept of solving games is mathematically defined.
Although, there is a reason very few mathematicians study chess, because there is currently little to no advancements to be made. all the research has pretty much already been done, we know it cannot be solved, there are countless studies on that, and “chess research” is pretty much stuck.
most research is not made on real games, but on theoretical mathematical games, which have clearer rules and are more useful to study, the few games that have been “solved” like checkers is just a proof of concept or a show off for a big company or university.
so
Try again...this is the game theory definition in context for this thread:
https://en.wikipedia.org/wiki/Combinatorial_game_theory
P.S. the other wikipedia entry *is* also about games, and is called game theory because that's exactly where it started before being applied to other "rational agents", but not games like chess. If you have watched the movie "A Beautiful MInd", it is about John Nash and his contributions to Game Theory and the idea of applying it elsewhere to all kinds of systems.
tygxc wrote:
@6879
"where did you get the number 10^44?"
++ Here: https://github.com/tromp/ChessPositionRanking
"Furthermore how did you get it down to 10^17 ?"
++ The vast majority of the 10^44 positions makes no sense and cannot result from optimal play from both sides. See the displayed 3 random samples: more than 3 rooks / bishop on each side.
A better estimate is 10^37 https://arxiv.org/pdf/2112.09386.pdf
However a random sample of 10,000 such positions show none can result from optimal play from both sides either. That leaves 10^37 / 10,000 = 10^33 positions.
Now multiply by 10 to accomodate also positions with 3 or 4 queens that do arrive with optimal play by both sides, as we know from ICCF. 10^33 * 10 = 10^34
To weakly solve Chess we only need 1 strategy for black to draw against all white opposition.
So instead of w white moves with each w black responses, we only need to look at w white moves with 1 response each. So instead of w*w positions only w*1 = w = sqrt (w*w) positions. Thus Sqrt (10^34) = 10^17 relevant positions.
"I was taking mostly about weakly solving but strongly solving is harder than weakly solving"
++ Strongly solving needs all 10^44 legal positions,
weakly solving only 10^17 relevant positions.
"it doesn’t take computers 5 years to solve chess"
++ It does take 5 years to calculate 10^17 relevant positions.
"otherwise they would have already done it." ++ So far nobody has put up 3 million $ to rent 3 cloud engines and hire 3 grandmasters during 5 years.
"Every so often there is an “engine tournament”, different chess engines are playing chess games against each other, beginning from a set of known starting positions." ++ TCEC, every year. They impose slightly unbalanced openings between 0.3 and 0.7 to avoid all draws.
'If it is possible to weakly solve chess in 5 years, it is possible to solve for each of those positions in about 5 years" ++ No. Weakly solving Chess only needs 1 strategy for black to draw.
Many of the imposed openings fall outside of that. If black can draw with 1 e4 e5, then 1 e4 c5 may draw as well or not.
"someone just needs to have about 20 computers working in the background for 5 years and the competition is gone?"
++ 3 cloud engines of 10^9 nodes/s or 3000 desktops of 10^6 nodes/s.
"it is not possible in such a small time, again, otherwise someone would have already done that."
++ 3 powerful computers of 10^9 nodes/s and 3 grandmasters during 5 years is a huge task, which costs 3 million $. Nobody has funded or started such a project.
"5 years of what computer"
++ 5 years of three 10^9 nodes/s cloud engines, or 5 years of 3000 desktops of 10^6 nodes/s.
"I am not familiar with the term 7-men endgame table base”
https://en.wikipedia.org/wiki/Endgame_tablebase
"I assume this means to the end of the game or to a solved position"
++ All positions of 7 men or less have been strongly solved.
"it is not what it is coded to do"
++ It is. In TCEC the engines hit their 7-men endgame table bases.
"it is coded to give you the probability best move in a reasonable amount of time"
++ If you give more time it gets deeper and hits the 7-men endgame table base.
"is enough time 2 years or 10^20 years?" ++ Enough time is 5 years on three 10^9 nodes/s cloud engines or on 3000 desktops of 10^6 nodes/s.
"so theoretically a computer could solve any positions" ++ No, any legal position would mean 10^44 positions, that is strongly solving or a 32-men table base and that would be too much.
I just read the page you linked to, that was a mess of gibberish. There is no explanation of anything, and they are just throwing numbers and terms from nowhere.
What I did understand is that they tested 2 million random positions, and got 12 legal positions out. I have no clue how they got there, but it doesn’t matter! There are (64!)/(32!) positions just with all the prices on the board, so there are much more without(I don’t remember the formula for items that don’t necessarily exist, but having all 32 pieces is a part of all possible positions so it is at least less). So, there are *more* than (64!)/(32!) possible positions, (about 4.8•10^53) and only 12 out of 2 million are legal. That means that there are more than 2.8•10^48 legal positions. How did they get to 10^44 is beyond me.
there are a ton of flaws in the page, most of them probably would be solved if it was written in English not gibberish.
about the actual mathematics paper you linked: it appears you didn’t read the paper? He is calculating legal positions where pawns can’t promote? These are vastly fewer than the amount of total possible positions? I might be just not understanding, but that seems like what the page is about to me.
there is literally 0 reason for that random division by 10000, they already calculated the legal positions you can’t say that only 0.01% off them are “actually legal” for no reason.
What you do afterwards with square rooting and multiplying by 10 is nonsense, you can’t do that with no explanation, needing one strategy doesn’t magically square root away your problems.
unrelated to all of this though, this is NOT how you calculate how much it would take to weakly solve chess.
For once, yes you need only one “strategy”, but you need to firstly find it, so you need to go over most of the possible moves, and somehow “decide” which is the best, not which gives you the best position, which will get you the win(if possible) or draw. So it is not just to find one move for each of the other player’s.
(You can ignore this point I didn’t really know how to say this and it came out very confusing) Secondly, this whole idea of finding the total amount of possible positions and then going down from there is broken. You need yo start at the first move, and calculated every move you can make, and run with it until the game finishes(stale mate, win, lose, repeat..) and every position you get to you write down (there is a way to write a chess position as a number, not too complicated), if you get to a position you have already been to, you stop(because you already calculated it) and go back and try a different path. This(and variations of this) is the only way to do it. (Because the game is so complex this is very similar to strongly solving it) this takes too much computer power-time to ever complete. (ignore ends here)
thirdly, even if we somehow agree on this 10^17 number of yours, this is still way too much. if every one of these positions would take just 8 bytes to store, that would take be more information than the whole internet, this is not something a computer “could do in 5 years” (and each of those positions and moves obviously take more than 8 bytes to store).
About the why nobody did it already: you said nobody put 3M$ for that yet. Seriously? Google competes in these events sometimes, Nasa considered joining one time! And do you think no bored billionaire has ever thought “hmm, could I do that?” 3M$ is a lot for normal people, but it is a joke in these terms.
When I said that if you could weakly solve chess you could weakly solve all these positions I ment that in the same way you weakly solve from the starting position you weakly solve from the forced position it is the same exact process.
Optimissed wrote:
EylonShachmon wrote:
Optimissed wrote:
tygxc wrote:
@6897
++ Weakly solved does not call for all black moves that do not lose. Only one is enough.
It might win though!
On the other hand that weak solution of Chess then does not need to handle Petrov, Sicilian, French, Caro-Kann, Pirc, Dutch, King's Indian Defense, Grünfeld Indian Defense, Nimzovich Indian Defense, Queen's Indian Defense, Queen's Gambit Accepted...
Seriously, no-one is going to buy this as any kind of a solution for chess. It isn't adding ANYTHING to what we already know or to chess theory. The entire, artificial idea of "weakly solving", "strongly solving" etc is complete nonsense because in practice, they overlap considerably.
In any case, the supposed definitions that are in use "ie weak solving is a strategy that .... etc" or "an algorithm that .... etc" is also nonsense, since in each case we're discussing series of concrete moves, which is very much NOT a strategy, except that in its simplest form, a viable strategy in chess is "any series of moves which does not contain any move or moves that lose by force".
So the supposed experts here place all their faith in other experts whose conceptions of the strategy of solving chess isn't just archaic but ludicrous. And these people, being called "games theorists", cannot do wrong because of their title, and everyone believes them, even though they obviously come from a bygone age and never thought well and properly on this subject in their entire lives.
Tygxc is pushing this rubbish on the pretext of educating others, tacitly supported by people who cannot see that the entire project is built on sand, because they're only intent on trying to get tygxc to recognise their own very limited objections.
Unless the foundations of "solving chess" are reassessed from ground up, there's no point at all in any of this twaddle. No group of scientists would dream of approaching an area of research without assessing and reassessing it. A reliance on the potentially outworn and useless ideas of others is an obvious and elementary mistake, which makes nonsense of this entire thread.
I understand the frustration (and I do not claim that what tygxc is saying is true) but do not dismiss the whole subject of solving games. This is not some made up concept with no use in the real world, this is a major part of game theory (which is a concrete mathematical field with everything any other field has), the concept of solving games is mathematically defined.
At the very best, "games theory" is one of those soft sciences, at least in its application to the theories and strategies of games. In my understanding, games theory wasn't developed to analyse games or the strategies of games, which is a rather simple subject. It is meant to be used to apply theory of games to real life, "serious" situations, which are not games at all. Most people here seem to have no conception that such is the case.
Although, there is a reason very few mathematicians study chess, because there is currently little to no advancements to be made. all the research has pretty much already been done, we know it cannot be solved, there are countless studies on that, and “chess research” is pretty much stuck.
I would say the opposite. Everything remains to be done. So far, chess bears no relationship to maths, because so far, absolutely zero progress has been made in representing chess mathematically. One mathematician whom I know and trust says that it cannot be done. By that, he probably means that it won't be done in his lifetime.
most research is not made on real games, but on theoretical mathematical games, which have clearer rules and are more useful to study, the few games that have been “solved” like checkers is just a proof of concept or a show off for a big company or university.
Most research will be done on simple games, which can actually be mathematically represented.
Game theory is not a “soft science”, it is a field in mathematics as much as topology and as arithmetics. Please don’t take away the credit for incredible mathematicians because of some people who misused research in an online forum, this is a legit topic with doctors and professors and people who commit their whole life to.
game theory was developed as any other thing in mathematics, not specifically to do something in the real world but to solve some mathematical problems, and after that we find uses in the real world. The name “game theory” is kind of misleading, it is not about “games”, it is called that because of how it started, but it (along with graph theory) is they main tool to mathematically analyse games.
there are many ways to represent chess mathematically, there just isn’t that much to get from it, the only thing you can really do is get closer and closer to weakly solving it, which isn’t that great of a mathematical achievement, and most of the people in the field agree it is basically impossible.
Dec 27, 2022
0
#5199
EylonShachmon wrote:
...
There are (64!)/(32!) positions just with all the prices on the board...
Er, you sure about that? I think I prefer the gibberish.
So long as we're talking about basic rules positions at any rate (@tygxc obviously isn't, which is far more to the point).
MARattigan wrote:
EylonShachmon wrote:
...
There are (64!)/(32!) positions just with all the prices on the board...
Er, you sure about that? I think I prefer the gibberish.
So long as we're talking about basic rules positions at any rate (@tygxc obviously isn't).
No I ment positions in total not legal positions, that is the number if you just put every piece in a random position.
one of the things they check when they check if the position is legal or not is stuff like bishops not on the same colour, pawns not on first and last row, kings not near each other ….
(! Is factorial, it is the number times every integer smaller, so 5! = 5•4•3•2•1=120, 6! = 6•5•4•3•2•1=720, 10! = 10•9•8•7•…•2•1=3,628,800)
@6876
"It looks like some people don’t understand what it means to solve chess."
++ Solved can mean 3 different things.
Ultra-weakly solved means that the game-theoretic value of the initial position has been determined,
weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition,
and strongly solved is being used for a game for which such a strategy has been determined for all legal positions.
"The problem with chess it that there are just too many positions"
++ Chess has 10^44 legal positions, of which 10^17 are relevant to weakly solve chess.
"it will just take a computer larger than the earth longer than the universe has existed"
++ No, you confuse strongly solving with weakly solving.
It takes computers 5 years to weakly solve chess.
"what computers like stockfish do is looking at what move gets you the best position"
++ Computer engines like Stockfish can calculate from the opening towards the 7-men endgame table base if given enough time
where did you get the number 10^44? Furthermore how did you get it down to 10^17 ?? Please clarify.
I am not confusing weakly and strongly solving, I was taking mostly about weakly solving but strongly solving is harder than weakly solving so it doesn’t change what I was saying.
it doesn’t take computers 5 years to solve chess, otherwise they would have already done it.
Every so often there is an “engine tournament”, different chess engines are playing chess games against each other, beginning from a set of known starting positions.
If it is possible to weakly solve chess in 5 years, it is possible to solve for each of those positions in about 5 years, so someone just needs to have about 20 computers working in the background for 5 years and the competition is gone? no, it is not possible in such a small time, again, otherwise someone would have already done that.
Also, what do you mean by “computers”? My laptop at home from 5 years ago isn’t the same power as the google super computer, and speed is just a matter of computer power, so 5 years of what computer.
I am not familiar with the term “7-men endgame table base” but I assume this means to the end of the game or to a solved position, no, it cannot, not because it is impossible but because it is not what it is coded to do, it is coded to give you the probability best move in a reasonable amount of time, not to give you all the move in a few years.
If you are talking about a computer coded to solve the game not about an engine, then ”yes”, because “given enough time” doesn’t mean anything, is enough time 2 years or 10^20 years? so theoretically a computer could solve any positions “given enough time” but that enough time would be billions or trillions of years (or more depending on the power of the computer) in most positions.