Wonder when the powers that be will start looking at all this in a much more efficient manner that gets away from this ridiculously antiquated and clumsy set of labels. It takes someone who can think incisively (like me) and who has influence (not me).
Chess will never be solved, here's why
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MARattigan wrote:
haiaku wrote:
Careful. According to Allis', van den Herik's and other definitions, a weak solution provides the game-theoretic value of the initial position and a strategy to achieve at least that value. ...
My reading of Allis', van den Herik's definition is that the strategy provides that value, not at least that value.
The intention was probably at least that value, but the wording is not.
And the definition also doesn't call for the game-theoretic value of the initial position, only the strategy to achieve the value (which needn't be known).
Allis' definition of weakly solved is:
For the initial position, a strategy has been determined to obtain at least the game–theoretic value of the game, for both players, under reasonable resources.
The game–theoretic value is the highest outcome that can be achieved by force and a strategy suited for a weak solution must be proven to achieve the game–theoretic value of the initial position, from the initial position itself. I concede that Allis' definition is somewhat redundant and using "at least" may be superfluous (it is not possible to achieve by force a value higher than the game-theoretic one, and values not achieved by force do not guarantee that the strategy can achieve the — possibly lower — game–theoretic value).
I too used "at least", though, to emphasize that it is not necessary that an optimal strategy for a weak solution always achieves the game–theoretic value of the current position in a game. This value is higher, if the opponent does not play optimally, than the game–theoretic one at the start; so an optimal strategy, that has only to obtain the game–theoretic value of the initial position, may not be the best, when the opponent makes mistakes that change that value.
Jan 22, 2023
0
#7444
Optimissed wrote:
MEGACHE3SE wrote:
Optimissed wrote:
no thats actually the official stuff, I have known that since before this discussion
Do you mean it's what can be found on Wiki when Googling? I did have the misfortune to be coerced into reading the so-called official stuff and I thought it was so bad and generally out of focus that it needs to be challenged. When I first saw it, I genuinely thought it was a joke, devised by some philosophy professor or other, just to see who would believe it. My subject's philosophy and some of the errors would fail a second-year undergrad essay.
It's mish-mash of improperly related ideas, probably put out by people calling themselves "games theorists" and who probably don't know what games theory really is. Actually, the general definition of games theory, to be found on Wiki, isn't too bad. It's about an application of games STRATEGY to real life situations, to turn those situations into a game simulation model which can be scored; scores being applied to outcomes and jiggled about until something approaching real life outcomes is achieved. Then that model can be applied to different strategies of dealing with those r. l. situations. Obviously, a game itself can become the object of a games theoretical approach, with alternative strategies being scored. This will be the source of the general confusion in the so-called official definitions, especially regarding the specialised meaning of "strategy".
This is the main problem with the practice of referring to the product of a solution of chess as a strategy, because to anyone who understands the ideas involved, assigning scores to positions is the strategy programmed into chess engine algorithms. Whereas the product of a solution of chess is wrongly claimed to be a strategy, it really consists of finding accurate moves, in response to moves made by the opponent. A workable strategy isn't going to consist of finding bad moves or anything else than good moves, which are defined as not changing the game state! However, at the moment, none of the algorithms is accurate enough to base a dependable solution on it.
Some of the types of people here buy straight into this pseudo-intellectualised "games theory approach", of course without understanding the basics. Undoubtedly, where they lead, others follow, because such people spend much of their time building a façade of intellectualism, with which to con others.
no its because I literally studied game theory when I was younger for math competitions and this is the official terms.
@7708
"Allis' definition"
++ Allis was the first to define in his thesis on Connect Four.
Van den Herik improved the wording in his paper on solving games.
Jan 23, 2023
0
#7446
haiaku wrote:
MARattigan wrote:
haiaku wrote:
Careful. According to Allis', van den Herik's and other definitions, a weak solution provides the game-theoretic value of the initial position and a strategy to achieve at least that value. ...
My reading of Allis', van den Herik's definition is that the strategy provides that value, not at least that value.
The intention was probably at least that value, but the wording is not.
And the definition also doesn't call for the game-theoretic value of the initial position, only the strategy to achieve the value (which needn't be known).
Allis' definition of weakly solved is:
For the initial position, a strategy has been determined to obtain at least the game–theoretic value of the game, for both players, under reasonable resources.
You are correct: https://cris.maastrichtuniversity.nl/en/publications/searching-for-solutions-in-games-and-artificial-intelligence
The version appearing in the van den Herik paper to which @tygxc refers, and attributed to Allis is not a faithful reproduction.
With Allis' definitions, none of the objections I raised to @tygxc's stated definition in #7692 apply.
The game–theoretic value is the highest outcome that can be achieved by force and a strategy suited for a weak solution must be proven to achieve the game–theoretic value of the initial position, from the initial position itself. I concede that Allis' definition is somewhat redundant and using "at least" may be superfluous (it is not possible to achieve by force a value higher than the game-theoretic one, and values not achieved by force do not guarantee that the strategy can achieve the — possibly lower — game–theoretic value).
I too used "at least", though, to emphasize that it is not necessary that an optimal strategy for a weak solution always achieves the game–theoretic value of the current position in a game. This value is higher, if the opponent does not play optimally, than the game–theoretic one at the start; so an optimal strategy, that has only to obtain the game–theoretic value of the initial position, may not be the best, when the opponent makes mistakes that change that value.
I agree with the above. My objection to dropping the phrase "at least" as in the version quoted by @tygxc was not that it allows solutions that achieve less than highest possible yield against some opposition; rather that it rules out solutions that do sometimes achieve higher yields than the game-theoretic value of the initial position.
Jan 23, 2023
0
#7447
tygxc wrote:
@7708
"Allis' definition"
++ Allis was the first to define in his thesis on Connect Four.
Van den Herik improved the wording in his paper on solving games.
Just what wording did van den Herik improve on from Allis' thesis on Connect Four? I don't believe Allis gave any definiition of "solved" in his thesis.
You could, I suppose, take the view that something is an improvement on nothing, but it does lead to the objections I raised in #7692.
You haven't yet commented on those objections. Do you accept them as valid?
(Not that it has any importance to your project to solve chess of course, because you don't intend to take any notice of any definition of the term, but just out of interest.)
@7712
Victor Allis was a Master student of Professor van den Herik.
@7712
No, I do not consider 'objections' of @7692 as valid.
The definitions by Prof. van den Herik have no flaw at all.
They are carefully worded and improve on Allis' first version on minor points.
"no limit on the time"
++ That is irrelevant. Solved is solved, whether it takes years, or months, or centuries.
"a solution in terms of OP's question" ++ The original poster did not specify whether his question was about ultra-weakly, weakly, or strongly solved.
"the definition doesn't say if the strategy is for one player or both"
++ It does: the game-theoretic value is when all participants play optimally.
"If, for example, the initial position happens to be a win for White and also forced selfmate for Black then a strategy for Black to mate himself would count as a solution"
++ No, the definition calls for all opposition. The selfmate does not oppose to the win.
"if the initial position is a draw then a strategy for one player that achieves a win against some opposition and a draw against the rest would not count as a solution for that player"
++ If you can win, then you can draw as well. This issue was treated in the solution of Losing Chess, which is a win for white.
During the solution they considered draws and wins for black as failures for white.
"the man in the street's idea" ++ The man in the street should read van den Herik's paper to understand the difference between ultra-weakly, weakly, and strongly solving.
haiaku wrote:
MARattigan wrote:
haiaku wrote:
Careful. According to Allis', van den Herik's and other definitions, a weak solution provides the game-theoretic value of the initial position and a strategy to achieve at least that value. ...
My reading of Allis', van den Herik's definition is that the strategy provides that value, not at least that value.
The intention was probably at least that value, but the wording is not.
And the definition also doesn't call for the game-theoretic value of the initial position, only the strategy to achieve the value (which needn't be known).
Allis' definition of weakly solved is:
For the initial position, a strategy has been determined to obtain at least the game–theoretic value of the game, for both players, under reasonable resources.
That isn't a definition, because reasonable resources is vague and not suited to a definition.
However, the use of "at least" is correct in context. It may seem vague but it's simple to understand what is meant, which is completely clear. Omitting something equivalent to "at least" may be misleading. After all, it certainly confused MAR.
MEGACHE3SE wrote:
Optimissed wrote:
MEGACHE3SE wrote:
Optimissed wrote:
no thats actually the official stuff, I have known that since before this discussion
Do you mean it's what can be found on Wiki when Googling? I did have the misfortune to be coerced into reading the so-called official stuff and I thought it was so bad and generally out of focus that it needs to be challenged. When I first saw it, I genuinely thought it was a joke, devised by some philosophy professor or other, just to see who would believe it. My subject's philosophy and some of the errors would fail a second-year undergrad essay.
It's mish-mash of improperly related ideas, probably put out by people calling themselves "games theorists" and who probably don't know what games theory really is. Actually, the general definition of games theory, to be found on Wiki, isn't too bad. It's about an application of games STRATEGY to real life situations, to turn those situations into a game simulation model which can be scored; scores being applied to outcomes and jiggled about until something approaching real life outcomes is achieved. Then that model can be applied to different strategies of dealing with those r. l. situations. Obviously, a game itself can become the object of a games theoretical approach, with alternative strategies being scored. This will be the source of the general confusion in the so-called official definitions, especially regarding the specialised meaning of "strategy".
This is the main problem with the practice of referring to the product of a solution of chess as a strategy, because to anyone who understands the ideas involved, assigning scores to positions is the strategy programmed into chess engine algorithms. Whereas the product of a solution of chess is wrongly claimed to be a strategy, it really consists of finding accurate moves, in response to moves made by the opponent. A workable strategy isn't going to consist of finding bad moves or anything else than good moves, which are defined as not changing the game state! However, at the moment, none of the algorithms is accurate enough to base a dependable solution on it.
Some of the types of people here buy straight into this pseudo-intellectualised "games theory approach", of course without understanding the basics. Undoubtedly, where they lead, others follow, because such people spend much of their time building a façade of intellectualism, with which to con others.
no its because I literally studied game theory when I was younger for math competitions and this is the official terms.
No such thing as "official terms".
Jan 23, 2023
0
#7453
tygxc wrote:
@7712
No, I do not consider 'objections' of @7692 as valid.
I meant to refer to #7691, but you appear to be addressing that post anyway.
The definitions by Prof. van den Herik have no flaw at all.
They are carefully worded and improve on Allis' first version on minor points.
You give above no reasoned argument against my objections, just your opinion that Allis' definitions in his peer reviewed paper (presumably the one I posted in #7710 rather than anything in the one you quoted in #7709) are inferior to those in van den Herik's peer reviewed paper, without any justification for that opinion.
You do give arguments against some of the points in my post #7691 below which I'll address individually.
Prof. van den Herik attributes the definitions he gives directly to Allis and the Allis paper to which I referred. He makes no mention of any alteration from the original, so I think we can assume the version appearing in the van den Herik paper is simply a faulty transcription.
My objections in #7691 relate only to the version in van den Herik paper. Allis' definitions are essentially identical to the ones I posted myself.
"no limit on the time"
++ That is irrelevant. Solved is solved, whether it takes years, or months, or centuries.
A solution according to either of the above definitions involves determining a strategy.
You have to distinguish between the time it takes to produce the strategy and the time it takes to apply the strategy.
If there is no limit on time on either then the following strategy for a player is a solution (of FIDE chess variants suitably amended to be soluble).
1. If it is not your turn do nothing, otherwise
2. Determine the game states after each possible legal move.
3. Follow Syzygy's algorithm until each of the game states determined in 2 has been assigned a win or frustrated win for you or your opponent or until no further entries can appear with the material in any of the game states determined in 2. Note that this step does not require any external input from a tablebase.
4. If a game state determined in 2 has been assigned a win for you in 3 play a move that leads to one with the lowest DTZ. Otherwise if a game state determined in 2 has been assigned a frustrated win for you in 3 play a move that leads to one with the lowest DTZ. Otherwise if a game state determined in 2 has not been assigned a win or frustrated win for your opponent in 3 play a move that leads to one. Otherwise if a game state determined in 2 has not been assigned a win for your opponent in 3 play a move that leads to one. Otherwise play anything.
So if you believe that a time limit on producing or applying the solution is irrelevant, you may as well stop posting your offers to solve chess for us. Syzygy has already beaten you to it.
"a solution in terms of OP's question" ++ The original poster did not specify whether his question was about ultra-weakly, weakly, or strongly solved.
This phrase that you've snipped out of the middle of my post was used in the context of time limitation as discussed above. Nothing to do with the type of solution.
Since it's patently obvious that there is a strategy for producing any type of solution given enough time and resources, it can reasonable be assumed that OP was referring to a solution that could be applied in reasonable time with reasonable resources.
"the definition doesn't say if the strategy is for one player or both"
++ It does: the game-theoretic value is when all participants play optimally.
A definition of game-theoretic value may well refer to both players, though it wouldn't usually refer to a strategy.
Why are you talking about that? It should be clear that the definition I was talking about was your definition of "weak solution".
"If, for example, the initial position happens to be a win for White and also forced selfmate for Black then a strategy for Black to mate himself would count as a solution"
++ No, the definition calls for all opposition. The selfmate does not oppose to the win.
Neither does anything else against perfect play.
It's obvious to anybody not trolling that Allis. van den Herik and myself mean, by "against any opposition", simply, "against any legal actions by the opponent". Nobody but yourself is ever going to take as meaning "against what @tygxc thinks are good moves".
"if the initial position is a draw then a strategy for one player that achieves a win against some opposition and a draw against the rest would not count as a solution for that player"
++ If you can win, then you can draw as well.
OK. Either prove that Black can't win in the position below or post your move to draw.
Black to play, ply count 0
This issue was treated in the solution of Losing Chess, which is a win for white.
During the solution they considered draws and wins for black as failures for white.
"the man in the street's idea" ++ The man in the street should read van den Herik's paper to understand the difference between ultra-weakly, weakly, and strongly solving.
He would get a better idea if he read Allis' paper. You've apparently read both but understood neither.
@7717
Allis wrote in his 1994 PhD Thesis promoted by Prof. van den Herik:
ultra-weakly solved For the initial position(s), the game-theoretic value has been determined.
weakly solved For the initial position(s), a strategy has been determined to obtain at least the game-theoretic value of the game, for both players, under reasonable resources.
strongly solved For all legal positions, a strategy has been determined to obtain the game-theoretic value of the position, for both players, under reasonable resources.
His promotor Prof van den Herik wrote in his 2002 paper:
Here 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 latter paper is later, and is written by the professor, not the student.
It improves on the 'at least' and 'for both players' with the wording 'against any opposition'.
It does away with the vague 'reasonable resources'.
Jan 23, 2023
0
#7455
At least you can now see that "DETERMINED" does not include "Ignore this position because we can make something up on the fly for any continuations arising from it". "Determined" entails "specified".
If you can't I don't know why you haven't claimed you have already solved chess because you can make up a way to draw on the fly (since chess is "obviously" a draw).
tygxc wrote:
@7717
Allis wrote in his 1994 PhD Thesis promoted by Prof. van den Herik:
weakly solved For the initial position(s), a strategy has been determined to obtain at least the game-theoretic value of the game, for both players, under reasonable resources.
strongly solved For all legal positions, a strategy has been determined to obtain the game-theoretic value of the position, for both players, under reasonable resources.
His promotor Prof van den Herik wrote in his 2002 paper:
Here 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 latter paper is later, and is written by the professor, not the student.
It improves on the 'at least' and 'for both players' with the wording 'against any opposition'.
It does away with the vague 'reasonable resources'.
Here, 'against any opposition' cannot be regarded as an improvement upon "at least". The contexts are different. The addition of 'against any opposition' is completely superfluous and unnecessary, since it is only to be expected that any opposition will occur. However, "at least" did add something to the meaning in that optimal play can lead to win, not just a draw. I call optimal play good play. It's just as well that "reasonable resources" was done away with. That was nonsense.
Regarding "strongly solved", specifying "legal positions" is superfluous and consists of "noise", since it (a solution) is known to refer to chess. Within chess, only legal positions can occur and so illegal ones can't possibly occur. Mr. Rattigan should take note of that.
Jan 23, 2023
0
#7457
tygxc wrote:
@7717
Allis wrote in his 1994 PhD Thesis promoted by Prof. van den Herik:
ultra-weakly solved For the initial position(s), the game-theoretic value has been determined.
weakly solved For the initial position(s), a strategy has been determined to obtain at least the game-theoretic value of the game, for both players, under reasonable resources.
strongly solved For all legal positions, a strategy has been determined to obtain the game-theoretic value of the position, for both players, under reasonable resources.
His promotor Prof van den Herik wrote in his 2002 paper:
Here 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 latter paper is later, and is written by the professor, not the student.
So you think your big brother is bigger than my big brother. Well whoopidoo.
Your big brother's paper states that the definitions are from my big brother's paper.
They're not. They're an inaccurate transcription of the definitions in my big brother's paper. The inaccuracies give rise to the objections I raised in #7691.
It improves on the 'at least' and 'for both players' with the wording 'against any opposition'.
That is the opposite of improvement. That is the reason for my second and third objections in #7691.
It does away with the vague 'reasonable resources'.
That again is the opposite of improvement. That is the reason for my first objection in #7691.
It would also mean you can stop peddling your offer to solve chess because Syzygy has already beaten you to it.
You haven't produced any pertinent points in rebuttal of #7691. Is claiming your big brother is bigger than mine the best you can do?
What sparked the idea to think about this in your mind?
MARattigan wrote
Meaningless and unfocused drivel. It shows clearly where you're at. Just old people chuntering away obsessively and getting nowhere. Making noise according to the rules they invented. Pretending to be something they are not.
I'm probably older than you so you can't get me. Ya!
Incidentally, perhaps if you're wondering why I've lost my patience with you .... it's because I made similar criticisms to yours, in a preceding post; but I give the reasons for my criticisms whereas you give no reasons at all but just repeat irrelevancies. Perhaps if you were to stop believing in your own superiority and try to understand my posts, you would learn something about how to think well. Then again, perhaps not because the people who discuss this in an unfocussed manner are all about the same ability level and they believe improvement is impossible.
the definition also doesn't call for the game-theoretic value of the initial position, only the strategy to achieve the value (which needn't be known).
Well... it needn't be known if it's a win, because if you can force a win then sure, you've solved it.
But let's say we come up with a strategy that always draws in chess... we couldn't call that a weak solution without knowing a better result isn't possible.
I'd agree with the first.
If you come up with two strategies, one for each player that always draw then you've also solved it.
And if you come up with two strategies, one for each player that always at least draw then you've solved it again.
Sure, if you have two independent unbeatable strategies, one for each player, then you know the game theoretic result... maybe in some cases that would be a way to approach the problem of solving a game.
(And I guess for this we're assuming the game has only 3 outcomes, ranked best to worst as win, draw, loss)
As for the last, yes, FIDE need to fix their laws so that is the case and the results for the opponent occur in reverse order. (Without a definite ranking the phrase "at least a draw", for example, makes no sense.)
If you have a strategy that wins for just one player then as you said you have a solution. No strategy is required for the other.
My suggested definitions correspond with what you say for the drawn case.