Chess will never be solved, here's why

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I went to Yugoslavia a number of times, always hitch-hiking. The only objection was that it was illegal to be asleep in a public place. That included sleeping out at night. I became adept at choosing half-built houses and they were always clean and gave protection from rain. I liked Dubrovnic very much and often went. Had a friend there. Climbed a bit in the Albanian Alps and travelled with some Austrian hippies who were exploring religious centres of the old Serbia, right up near the Albanian border, formed before Serbia contracted. I loved Yugoslavia and of course it was one country, very diverse. Never got to the Novi Sad area but that's more or less the only bit I didn't see. Liked the Macedonian people and those up North, around Maribor and Zagreb. In fact, everywhere.

In Bulgaria while hitch-hiking somewhere near Plovdiv, was very tired indeed and found a big field with a lot of small clusters of undergrowth. Walked right to the middle of it to get away from people and hid near a small copse and slept for the night. In the morning was woken by some noises. Noticed some Russian soldiers about 300 yards (metres) away. Got my stuff all together, packed up as fast and quietly as I could and started to walk back to the road. A sleepy looking Russian came out of a bit of undergrowth and we were face to face, so we sort of ignored each other and carried on. Then some of the bits of undergrowth started to move, shedding bits of tree behind them. Making a clanking sound, these trees were.

I had spent the night right in the middle of a Russian tank battalion and all the clumps of undergrowth were very well disguised Russian tanks .... about 20 of them.  1969.

Avatar of haiaku
Optimissed wrote:
haiaku wrote:

The core point is that without an exhaustive proof, there is no doubt that no scientific theory can be guaranteed to hold true in any possible case. Galilean relativity, Newton's law of gravitation and classical mechanics are golden examples. They were thought to be always true, "unbeatable" so to speak, and they were consistent with centuries of experiments. There was no evidence that they might produce quite inaccurate predictions. We all know how it went: they fail miserably under some circumstances.

Not at all. They produce perfectly accurate results that are suitable for the environment in which they were conceived.

😦? They were thought to be universal and they are not.

Optimissed wrote:

You seem to be wanting to introduce a fallacy ... that of assuming that there are mysterious circumstances that alter the characteristics of chess [ . . . ] The rules do not allow for weird, relativistic effects within chess, so you're wrong again.

Is this a straw man? wink What I and others are saying is that there might be yet unknown lines which could disprove the assumption that chess is a draw. While we could safely ignore that Newton's law of gravitation is very incorrect under some circumstances and happily live with that (GPS satellites would not work properly, but...), for a solution a single unexpected line can make all the difference.

Optimissed wrote:
haiaku wrote:

In game theory, "optimal" is not a casual attribute. For chess, it means that an optimal player would be unbeatable in a match with an even number of games: if the game value is a draw, the optimal player would at least draw every game; if it's a win for either colour, the optimal player would always force the win with that colour. Therefore, the optimal player cannot score less than 50% of the points. Without a mathematical, exhaustive proof, a player cannot be guaranteed to be optimal, exactly like a scientific theory, without an exhaustive proof, cannot be guaranteed to always hold true.

This is confused. The first part is unnecessary. At least we know what we mean by "best play" or perhaps, "optimal", because we've been talking about it, in various threads, for about four years now and we did reach a consensus. Off the top of my head, optimal play is that which doesn't alter the game result negatively, for the player who made that move. Some like to say "from the game-theoretic value" but that's unnecessary, because it doesn't add anything useful. Just an illusion of grandeur.

What about the second part?

Optimissed wrote:
haiaku wrote:

This is not what people expect, when they read something like "the game xyz has been solved". They think about a definitive solution, that nobody will be able to disprove, ever.

You could never be sure that there wasn't a mistake in the analysis, due to a glitch of some unexpected kind. So wrong again, I'm afraid.

That is a point already made by @MARattigan. In fact, I said that people do expect a definitive solution, not that they can be 100% sure that a computer-assisted proof is correct. But the point is: is a statement like "chess is a draw because... [unproven motivations]" as acceptable and reliable as a statement like "a computer-assisted proof by exhaustion established that chess is a [draw, win]"?

Avatar of stancco

Great experiences. I admire you, indeed. Wish I was there!

When it comes to Russians btw, they are well known for ignoring their enemies 😁

Avatar of Optimissed
stancco wrote:

Great experiences. I admire you, indeed. Wish I was there!

When it comes to Russians btw, they are well known for ignoring their enemies 😁


Let's hope so. My instinct was just to look as if I had as much right to be there as he did. Gave him a very slight nod.

It's good to make your acquaintance. It was, indeed, a lot of fun.

Avatar of Optimissed
haiaku wrote:
Optimissed wrote:
haiaku wrote:

The core point is that without an exhaustive proof, there is no doubt that no scientific theory can be guaranteed to hold true in any possible case. Galilean relativity, Newton's law of gravitation and classical mechanics are golden examples. They were thought to be always true, "unbeatable" so to speak, and they were consistent with centuries of experiments. There was no evidence that they might produce quite inaccurate predictions. We all know how it went: they fail miserably under some circumstances.

Not at all. They produce perfectly accurate results that are suitable for the environment in which they were conceived.

😦? They were thought to be universal and they are not.

That really is not the point. People not anticipating Relativity cannot possibly have a bearing on this. Chess is a confined and fully known paradigm. It is only complexity which makes it difficult and not unknown elements.

Optimissed wrote:

You seem to be wanting to introduce a fallacy ... that of assuming that there are mysterious circumstances that alter the characteristics of chess [ . . . ] The rules do not allow for weird, relativistic effects within chess, so you're wrong again.

Is this a straw man? What I and others are saying is that there might be yet unknown lines which could disprove the assumption that chess is a draw. While we could safely ignore that Newton's law of gravitation is very incorrect under some circumstances and happily live with that (GPS satellites would not work properly, but...), for a solution a single unexpected line can make all the difference.


There's no reason to assume there is one, That's due to the equalising tendency, which I've mentioned. It isn't going to happen.

Optimissed wrote:
haiaku wrote:

In game theory, "optimal" is not a casual attribute. For chess, it means that an optimal player would be unbeatable in a match with an even number of games: if the game value is a draw, the optimal player would at least draw every game; if it's a win for either colour, the optimal player would always force the win with that colour. Therefore, the optimal player cannot score less than 50% of the points. Without a mathematical, exhaustive proof, a player cannot be guaranteed to be optimal, exactly like a scientific theory, without an exhaustive proof, cannot be guaranteed to always hold true.

This is confused. The first part is unnecessary. At least we know what we mean by "best play" or perhaps, "optimal", because we've been talking about it, in various threads, for about four years now and we did reach a consensus. Off the top of my head, optimal play is that which doesn't alter the game result negatively, for the player who made that move. Some like to say "from the game-theoretic value" but that's unnecessary, because it doesn't add anything useful. Just an illusion of grandeur.

What about the second part?

Please see below.

Optimissed wrote:
haiaku wrote:

This is not what people expect, when they read something like "the game xyz has been solved". They think about a definitive solution, that nobody will be able to disprove, ever.

You could never be sure that there wasn't a mistake in the analysis, due to a glitch of some unexpected kind. So wrong again, I'm afraid.

That is a point already made by @MARattigan. In fact, I said that people do expect a definitive solution, not that they can be 100% sure that a computer-assisted proof is correct. But the point is: is a statement like "chess is a draw because... [unproven motivations]" as acceptable and reliable as a statement like "a computer-assisted proof by exhaustion established that chess is a [draw, win]"?>>

I can't remember who made that point first: whether it was MAR or I. MAR has some good ideas occasionally. And it holds, too. It means that you have no reason to believe that there will ever be a reliable proof. All analyses will be impossible to check. Even if you ran them twice, the same glitch could conceivably occur. This means you are no nearer absolute knowledge than you are at the moment. It will only be somewhat more confirmed. It's confirmed enough already because people will doubt that chess is a draw ad infinitum. You will never obtain closure, doing it your way. That's why you have to drop the deductive syllogism which runs as follows:

If we had a full and completely trustworthy analysis of chess then we would know definitively whether chess is a draw.

All analyses completed by SOFTWARE-WRITER-X are fully trustworthy.

We can get an analysis by SOFTWARE-WRITER-X in 1000054 years.

Therefore it will be trustworthy and so we will know whether chess is a draw.

Personally I wouldn't trust it! happy.png

Avatar of tygxc

#3864

"From what I've heard not every game at the highest level is a draw."
++ That is right. It is human to err.
Even in ICCF correspondence they sometimes mix up the move order and blunder a piece.

"if almost all chess games are draws that means chess is a draw"
++ No, the higher the level, the more draws. For every win we can pinpoint the error, usually the last move. For the high level draws we cannot pinpoint any error.

"If chess has been proven to be a draw, why are there wins?"
++ Because ultra-weakly solved is not weakly solved. Chess is known to be a draw, but not yet known how. I know for sure 1 e4 e5 2 Ba6 is a black win. Black is up a bishop. If you believe 1 tempo is convertible to a win, then you surely accept 1 bishop is convertible to a win even more. However I do not have a complete game tree up to checkmate. I believe with enough time I can win that as black against Carlsen or against an engine, but I might err at some move.

"There must be some reason not everyone agrees."
++ All stong players agree. Not everyone agrees on scientifically proven facts either.

"I could just as easily say because white has a first move advantage, AND the percentage of white wins at the highest level goes up, that's proof chess is a forced win for white."
++ The win % goes down with level. Chess is a draw, but the path to the draw is wider for white and narrower for black. So black has more ways to err than white.
White can afford to lose a tempo, then white just becomes black. Even black can afford to lose a tempo and white can afford to lose 2 tempi. Black cannot afford to lose 2 tempi: then he gets 1 pawn equivalent behind and that is enough to win.

"Until all games are draws it's evidence, not proof."
++ Yes, it is evidence and not a formal proof. Checkers has been solved to be draw. Checkers is still played and not all Checkers games end in draws. There is still human error especially at the lower level. The proof tree for Checkers has 10^7 positions. Nobody has these memorised.

Avatar of tygxc

#3867

"Do you ask a person riding a roller coaster to design roller coasters?"
++ Weakly solving chess is not designing, it is using existing software on existing hardware.
The best person in the world to ask about that was GM Sveshnikov. Others are Kasparov, Kramnik, Carlsen, Karjakin, Caruana, Nepo, Dokhoian, Kazimdzhanov, or any ICCF grandmaster.

"GMs have made statements about draws, and when pressed they always hedge their bets."
++ Nope, see #3854 and #3856.

"Any number you stick in front of "accuracy" here is garbage, because the calculations that derived them are flawed." ++ That is besides the point. The accuracy cannot determine if play is perfect, but it can tell play is not perfect. It is like a modulo 3 primality test: it can determine that a number is not a prime, but it cannot determine that said number is a prime.

"If you eliminate a single position from evaluation based on your fuzzy criteria, your solution fails on the spot."
++ You still do not get it. The accuracy is not used in weakly solving chess. It is only used in defining sensible positions so as to assess the number of sensible positions that intervene.

"my calculations on current supercomputer capabilities and what it would take using current technology to solve chess are dozens of orders of magnitude more accurate"
++ You still do not understand the difference between weakly solving and strongly solving.

Avatar of Optimissed
tygxc wrote:

#3867

"Do you ask a person riding a roller coaster to design roller coasters?"
++ Weakly solving chess is not designing, it is using existing software on existing hardware.
The best person in the world to ask about that was GM Sveshnikov. Others are Kasparov, Kramnik, Carlsen, Karjakin, Caruana, Nepo, Dokhoian, Kazimdzhanov, or any ICCF grandmaster.

"GMs have made statements about draws, and when pressed they always hedge their bets."
++ Nope, see #3854 and #3856.

"Any number you stick in front of "accuracy" here is garbage, because the calculations that derived them are flawed." ++ That is besides the point. The accuracy cannot determine if play is perfect, but it can tell play is not perfect. It is like a modulo 3 primality test: it can determine that a number is not a prime, but it cannot determine that said number is a prime.

"If you eliminate a single position from evaluation based on your fuzzy criteria, your solution fails on the spot."
++ You still do not get it. The accuracy is not used in weakly solving chess. It is only used in defining sensible positions so as to assess the number of sensible positions that intervene.

"my calculations on current supercomputer capabilities and what it would take using current technology to solve chess are dozens of orders of magnitude more accurate"
++ You still do not understand the difference between weakly solving and strongly solving.


A GM may not be the best person to ask about solving chess. I'd much rather ask a Digital Intelligence expert.

To the last point, a weak solution is an overall verdict on what has been called the game- theoretical value. Could also be the optimum result.

That can't be obtained without a full solution of all possible and relevant games, each explored to the point where it's obvious what the result will be. It would probably be impossible to store all these results and correlate them together. btickler's calculations will be the more accurate.

Avatar of tygxc

#3883

"I'd much rather ask a Digital Intelligence expert." ++ No not at all. Top grandmasters, their seconds, and ICCF grandmasters know most about chess and chess analysis.

"a weak solution is an overall verdict on what has been called the game- theoretical value."
++ No. You still do not get it.
Ultra-weakly solved means that the game-theoretic value of the initial position has been determined.  In layman's terms: it means a formal proof that chess is a draw.

Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
In layman's terms: it means that a way to draw for black has been found against all reasonable white moves. That would need to visit 10^17 positions, can be done in 5 years.

"strongly solved is being used for a game for which such a strategy has been determined for all legal positions." In layman's terms: a 32-piece table base. That is all 10^44 legal positions, beyond the capability of present engines.

"That can't be obtained without a full solution of all possible and relevant games, each explored to the point where it's obvious what the result will be." ++ A solution tree of 10^17 positions would lead to a proof tree of about a billion positions, i.e. about 10 million perfect games.

"It would probably be impossible to store all these results" ++ No, 10 million perfect games are not that much more than existing data bases holding millions of games.

"btickler's calculations will be the more accurate" ++ No, he has no clue. He still does not understand the difference between weakly solving and strongly solving.

Avatar of Optimissed

We've had this conversation before didn't we, so it's really only an irresolvable difference of opinion? I would say that GMs know about over the board analysis.

Avatar of DiogenesDue
tygxc wrote:

#3883

"I'd much rather ask a Digital Intelligence expert." ++ No not at all. Top grandmasters, their seconds, and ICCF grandmasters know most about chess and chess analysis.

"a weak solution is an overall verdict on what has been called the game- theoretical value."
++ No. You still do not get it.
Ultra-weakly solved means that the game-theoretic value of the initial position has been determined.  In layman's terms: it means a formal proof that chess is a draw.

Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
In layman's terms: it means that a way to draw for black has been found against all reasonable white moves. That would need to visit 10^17 positions, can be done in 5 years.

"strongly solved is being used for a game for which such a strategy has been determined for all legal positions." In layman's terms: a 32-piece table base. That is all 10^44 legal positions, beyond the capability of present engines.

"That can't be obtained without a full solution of all possible and relevant games, each explored to the point where it's obvious what the result will be." ++ A solution tree of 10^17 positions would lead to a proof tree of about a billion positions, i.e. about 10 million perfect games.

"It would probably be impossible to store all these results" ++ No, 10 million perfect games are not that much more than existing data bases holding millions of games.

"btickler's calculations will be the more accurate" ++ No, he has no clue. He still does not understand the difference between weakly solving and strongly solving.

I apparently understand the definitions better than you do.  Weakly solving means solving against all moves from the initial position, not just "reasonable" moves.  Trying to change the definition of weakly solved to fudge your numbers doesn't help your case, it just makes you look desperate enough to mislead people willfully...

Ultra-weak

Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides. This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any moves of the perfect play.

Weak

Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game.

Strong

Provide an algorithm that can produce perfect moves from any position, even if mistakes have already been made on one or both sides.

Your premise is a bastardized dilution of weakly solved.

Avatar of tygxc

#3886

"I apparently understand the definitions better than you do."
++ Your toilet paper calculation shows otherwise.

"Weakly solving means solving against all moves from the initial position"
++ Cutting out unreasonable moves based on knowledge is allowed per van den Herik.
I know 1 e4 e5 2 Ba6 loses for white, so I do not need to calculate to checkmate.
I know 1 a4 cannot be better than 1 e4 or 1 d4, so I do not need to calculate 1 a4 to a draw.

"Trying to change the definition"
++ I do not change the definition. I replicate the definition verbatim.
I just explain in layman's terms as some people complain they do not understand jargon.

"Weak Provide an algorithm that secures a win for one player, or a draw for either,
against any possible moves by the opponent, from the beginning of the game."
++ It is not an algorithm, but a strategy.
Such a strategy can entail a proof tree, but also a set of rules, or a combination.
Allen has weakly solved Connect Four by brute force
and Allis has independently weakly solved it by a set of 7 rules. 

"Strong Provide an algorithm that can produce perfect moves from any position,
even if mistakes have already been made on one or both sides."
++ Not an algorithm, but a strategy for all legal positions.
Not only after one or more mistakes have been made, but also alternative drawing paths after one drawing strategy has been found. If 1 e4 e5 is proven a draw, then for weakly solving it does not matter if 1 e4 c5 draws as well or not, but for strongly solving that is needed too.
The essence is that weakly solving needs to visit far less positions than strongly solving.
Weakly solving Losing Chess required 900 million positions, not 10^44.

Avatar of Optimissed
btickler wrote:
tygxc wrote:

#3883

"I'd much rather ask a Digital Intelligence expert." ++ No not at all. Top grandmasters, their seconds, and ICCF grandmasters know most about chess and chess analysis.

"a weak solution is an overall verdict on what has been called the game- theoretical value."
++ No. You still do not get it.
Ultra-weakly solved means that the game-theoretic value of the initial position has been determined.  In layman's terms: it means a formal proof that chess is a draw.

Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition. In layman's terms: it means that a way to draw for black has been found against all reasonable white moves. That would need to visit 10^17 positions, can be done in 5 years.

"strongly solved is being used for a game for which such a strategy has been determined for all legal positions." In layman's terms: a 32-piece table base. That is all 10^44 legal positions, beyond the capability of present engines.

"That can't be obtained without a full solution of all possible and relevant games, each explored to the point where it's obvious what the result will be." ++ A solution tree of 10^17 positions would lead to a proof tree of about a billion positions, i.e. about 10 million perfect games.

"It would probably be impossible to store all these results" ++ No, 10 million perfect games are not that much more than existing data bases holding millions of games.

"btickler's calculations will be the more accurate" ++ No, he has no clue. He still does not understand the difference between weakly solving and strongly solving.

I apparently understand the definitions better than you do.  Weakly solving means solving against all moves from the initial position, not just "reasonable" moves.  Trying to change the definition of weakly solved to fudge your numbers doesn't help your case, it just makes you look desperate enough to mislead people wilfully...

Ultra-weak

Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides. This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any moves of the perfect play.

Weak

Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game.

Strong

Provide an algorithm that can produce perfect moves from any position, even if mistakes have already been made on one or both sides.

 


I completely agree with btickler that tygxc has drastically underestimated the number of lines and therefore positions that have to be examined for a so-called weak solution. This is because the algorithms have to widen the search considerably, in order to eliminate apparently relevant lines that turn out to contain a mistake.

The strong algorithm is irrelevant and indeed, so is the concept. This is because the so-called algorithm to produce a weak solution actually means "produce a perfect chess engine which makes no mistakes and which always plays the best moves". There's a logical absolute identicality. Therefore it's all that's required.

The definition for the ultra weak solution is problematic, since any such strategic argument would have to be proven to be completely reliable and accurate. It is, however, identical in approach to the suggestion I made three or four years ago in another thread, regarding trying to create an algorithm that identifies points of imbalance and recrystallisation in chess games.


Avatar of N1N3TY
Very interesting post.
Avatar of tygxc

#3895

"I completely agree with btickler that tygxc has drastically underestimated the number"
++ So you do not understand the difference between weakly and strongly solving either.
10^44 is the number of legal positions for solving strongly.
Weakly solving requires far less, about 10^17.
Losing Chess has been weakly solved using 10^9 positions, not 10^44.

"produce a perfect chess engine which makes no mistakes"
++ No, that is not weakly solving.
Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
'a strategy' ++ can be a proof tree or a set of rules or a combination of both
"the game-theoretic value" ++ a draw
"against any opposition" ++ white tries to win, black tries to draw, white fails, black succeeds

"points of imbalance and recrystallisation" ++ mumbo jumbo

Avatar of Optimissed
tygxc wrote:

#3895

"I completely agree with btickler that tygxc has drastically underestimated the number"
++ So you do not understand the difference between weakly and strongly solving either.
10^44 is the number of legal positions for solving strongly.
Weakly solving requires far less, about 10^17.
Losing Chess has been weakly solved using 10^9 positions, not 10^44.

"produce a perfect chess engine which makes no mistakes"
++ No, that is not weakly solving.
Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
'a strategy' ++ can be a proof tree or a set of rules or a combination of both
"the game-theoretic value" ++ a draw
"against any opposition" ++ white tries to win, black tries to draw, white fails, black succeeds

"points of imbalance and recrystallisation" ++ mumbo jumbo


Quite frankly, I think that the terminology is complete nonsense and is the probable reason why people become confused. It's a bit of a stretch for you to say that "we disagree, therefore you do not understand".

It isn't made any easier by the ridiculous terminology but reading yours and btickler's correspondence with each other, it's apparent that you're talking past each other and that problem can be traced to the terminology, which is not fit for purpose. Its purpose should be to convey meaning but that isn't happening.

<<"points of imbalance and recrystallisation" ++ mumbo jumbo>>

A concept I came up with when I was writing a chess article around 1988. I think that since I used it, I've seen GM chess writers use it so don't be in too much of a hurry. It makes complete sense to me and so it will to any who maybe don't have your intellectually-based disdain for mumbo-jumbo.

Avatar of tygxc

#3989

"I think that the terminology is complete nonsense" ++ I am sorry, that is the scientific terminology in the game theory field. I explained in layman's terms for your convenience.

"we disagree, therefore you do not understand" ++ People disagree because they do not understand. They should read and think before disagreeing. People are better at slinging insults and accusations than at reading and understanding.

"reading yours and btickler's correspondence with each other, it's apparent that you're talking past each other"  ++ btickler does not understand the difference between weakly and strongly solving, that is why about weakly solving he erroneously uses the number for strongly solving.

"the terminology, which is not fit for purpose. Its purpose should be to convey meaning."
++ The terminology is fit for purpose, it applies to any game, not just chess, but it is intended for scientific readers. That is why I have added an explanation in layman's terms and specific to chess for your convenience. 

Avatar of Optimissed
tygxc wrote:

#3989

"I think that the terminology is complete nonsense" ++ I am sorry, that is the scientific terminology in the game theory field. I explained in layman's terms for your convenience.

"we disagree, therefore you do not understand" ++ People disagree because they do not understand. They should read and think before disagreeing. People are better at slinging insults and accusations than at reading and understanding.

"reading yours and btickler's correspondence with each other, it's apparent that you're talking past each other"  ++ btickler does not understand the difference between weakly and strongly solving, that is why about weakly solving he erroneously uses the number for strongly solving.

"the terminology, which is not fit for purpose. Its purpose should be to convey meaning."
++ The terminology is fit for purpose, it applies to any game, not just chess, but it is intended for scientific readers. That is why I have added an explanation in layman's terms and specific to chess for your convenience. 

It's rubbish. The fact that they can't think straight is exemplified by the completely dumb definitions. Maybe game theory attracts people of low ability. Elroch was insinuating or even claiming that they are amazingly knowledgeable and wondrously intelligent. Doesn't look that way, they're completely tangled up & haven't a clue. See how I put the definitions into plainer English. I could do a better job if it was worth the effort..

Avatar of Optimissed

Incidentally, this is not the province of game theory, so there's no need to follow their dopey definitions. It's much more digital intelligence. It's a computing problem. We're talking about using digital intelligence to analyse chess and that's just another problem in computing and software writing; not game theory.

I wouldn't criticise if it weren't so completely obvious the definitions are screwed up. I can think my way around them but if you start with the premise that the definitions are perfect, you're bound to become confused. It's quite comical watching you and btickler talking past each other and that's partly an effect of the confused definitions. If you want, I'll write a careful criticism of them. I don't know if it would help, though, because there aren't many people who seem to be able to understand that they aren't perfect. When I first saw them I thought they were some computing or philosophy professor's joke.

Avatar of Optimissed

<<<Solving chess means finding an optimal strategy for the game of chess, that is, one by which one of the players (White or Black) can always force a victory, or either can force a draw (see solved game). It also means more generally solving chess-like games (i.e. combinatorial games of perfect information), such as Capablanca chess and infinite chess. According to Zermelo's theorem, a determinable optimal strategy must exist for chess and chess-like games.>>>

The strategy for optimal chess consists of finding the best moves and that is all. If you can think of something better than finding the best moves, we'd love to know,