You use too complicated language - it's not good for people who don't speak English as their first language. It would be easier to get your point across without such flowery prose.
Also, this is not quite true - top masters don't use any particular heuristics - in half the positions they see, they can know the best move in one second because they have really good intuition from experience. At the weak master - beginner level, this may be correct.
You make assumptions about things that are not proven. With best play, White's advantage of the first move may lead to a forced win.
Consequently 1 e4 may lead to a forced win with perfect play, where 1 f3 weakens the lead enough to force a draw.
Nevertheless, you are clearly right that "We cannot simply take this conception of Caissa as the ideal that we must seek to emulate, for we would run into a snag: humans are not omniscient." There are moves humans make because they know it leads to a win whereas another move may lead to a faster win or greater gain in material, but it's a complicated position and the human doesn't want to take a chance on overlooking something, so he takes the simple move he knows leads to a sure win. The simple move is obviously the correct choice in the situation.
For example here is a position from a live game of mine, here at chess.com, where I am White to move and Black can't push his pawns or the result will be another passed pawn for me:
For me, the human, the ONLY correct move is follow the Principle of the Opposition. If I move my King so that it is my opponent's move and the Kings are opposite each other with an odd number of squares between, he basically has to move his King out of my way so I can Queen my passed pawn. As a result 1. Kf5! is THE winning move - which is what I played and resulted in my Queening the Pawn and winning.
But Stockfish 8, the closest to a chess god we have now, says that 1. f5 is a better move! Maybe it's better, but only if you can be sure you are unerringly looking far enough ahead to see the win. But if 1 f5 Kg7 - giving my opponent the opposition, it wouldn't be clear to me how to win. So 1 Kf5! is better for me because I know from the Principle of the Opposition that I will win.
You use too complicated language - it's not good for people who don't speak English as their first language. It would be easier to get your point across without such flowery prose.
Also, this is not quite true - top masters don't use any particular heuristics - in half the positions they see, they can know the best move in one second because they have really good intuition from experience. At the weak master - beginner level, this may be correct.
I would consider the intuition of Masters to be the result of the subconscious execution of heuristics - most notably, perhaps, pattern-recognition based upon the thousands of games that they have analyzed. Also, point taken about the prose - thank you.
Very interesting post.
all I see in the rather long post from a practical point of view, is that humans have to play "safer" moves than a computer, or if you will, God- because a human is likely to make mistakes in some tense, difficult to play position- where god would find a way but a human mind would likely err.
I agree
Sorry about the length of the post, I'll try to be more succinct in the future. What I'm really getting at is that chess is, fundamentally, nothing more than a game tree, and every position has one of three values as its evaluation. However, certain patterns emerge when we look at which branches of the tree lead to which results; therefore we can gather useful heuristics to guide us. In a sense, the human way of playing and studying chess is similar to the principle of inductive reasoning: we look at the world, and we see that it behaves in certain ways, so we generalize those rules and apply them to new situations. We look at branches that end in certain results, and we start to notice patterns emerging: those branches which end in any given result tend to contain patterns describable in certain terms, which become our guiding heuristics. I'm really just pointing out the obvious, but this kind of fundamental theory, which underpins the material put forth in beginner chess books (i.e. the actual heuristics themselves), is not so commonly discussed.
I have a vague memory of reading something similar to this somewhere. Could be mistaken. I disagree with one comment. It was very well written.
I have a vague memory of reading something similar to this somewhere.
Could be the case. I didn't plagiarize this, but it's like I said, this stuff is pretty simple. I'm not touting anything profound. Also, which comment did you disagree with?
There are actually 3 as I see it:
1) The ultimate evaluation (white wins, draw, black wins)
2) The principled evaluation (the 5 basic evals e.g. +/= or the engine number)
3) The practical evaluation (it may be an obvious draw, but one player's moves may be more difficult to find, or one player may have less time to find a few difficult moves).
You seem to combine 2 and 3, but there are no heuristics that define ease of play. A person can be winning under 1 and 2, but nearly lost under number 3 (even if the clock isn't a factor).
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You're right that basic books don't cover this, and eventually most players figure this out (if only intuitively) but I think it's not useful to a beginner who can't yet even see the board. Remember how chaotic a game of chess seemed in the beginning, with pieces appearing out of nowhere to capture your queen, or checkmate you.
This "old cliche" is the product of De Groot's psychological experiments with chess players, it has good explanatory power, and has been repeated and supported since (masters playing with brain imaging devices to see which parts of the brain are most active). You may not like the idea of chess patterns, maybe you prefer to call it something else, but it makes sense. How else can a GM play 50 people at once and win every game? They're certainly not calculating 50 times as much. In fact even 1 on 1, amateur vs GM, GMs calculate less over the course of the whole game.
- I hate posts like this because it is so misleading to newbies - chess is a friggin game - and chess snobs live in a dream world where they do not acknowledge luck - and do not acknowledge random foolish mistaken moves which result in defeat and random foolish mistaken moves that result in victory - people are not perfect - chess is based on mistakes - of the two opponents the one who makes the fewest mistakes wins - like - in middle of the game there might be 15 different possible moves resulting in a kabillion possible out comes and chess snobs make out like they are playing with that precision - o kay I will agree with you ( but silently I won't believe you ) - I have an easy strategy - my whole game is luck = my favorite opening is the king using the screams like a girl war cry - - - oh then the human dynamics - a computer can calculate fifty kabillion moves per second - - and I am playing group games where people need three days to make ONE move - go figure
- I hate posts like this because it is so misleading to newbies - chess is a friggin game - and chess snobs live in a dream world where they do not acknowledge luck - and do not acknowledge random foolish mistaken moves which result in defeat and random foolish mistaken moves that result in victory - people are not perfect - chess is based on mistakes - of the two opponents the one who makes the fewest mistakes wins - like - in middle of the game there might be 15 different possible moves resulting in a kabillion possible out comes and chess snobs make out like they are playing with that precision - o kay I will agree with you ( but silently I won't believe you ) - I have an easy strategy - my whole game is luck = my favorite opening is the king using the screams like a girl war cry -
Intelligent people should agree that, at least when humans play chess, there is luck involved.
But luck to a beginner (or near beginner) isn't the same as luck to an experienced player. To a beginner, luck is randomness due to lack of skill. To an experienced player, it's about educated guesses. They make their best guess based on all the knowledge and skill they have. This is very different from forgetting pawns capture diagonally... (you might laugh at that, but I could show you beginner games where there's really no other explanation for the terrible moves).
Imagine, if you will, an omniscient chess player, whom we shall call Caissa...
To say that chess is a draw is to say that Caissa could never lose a game with either color, assuming she was attempting to win. A highly skilled player could draw her, but not beat her, unless there is a forced win available to black or white - if there is no such win, then Caissa is invincible. Via modus ponens, I deduce that Caissa could never lose a game she was trying to win.
What you wrote is extremelly interesting. (It is also one of the reasons I have proposed a new piece, the Huygens, which I'll explain later).
I think we're just going to call the same thing by different terms. It takes a lot of experience to be a GM. No one just understand it.
I think it's telling that in Carlsen's blindfold clock simuls (!!) he had the most trouble against the player who moved randomly, like a beginner. Carlsen even admitted he forgot where pieces were during the game. If his skill were due to understanding the subtle interaction of the pieces, then why would this be true? If his skill were due (at least in large part) to knowing many patterns, it makes perfect sense to be unable to keep track of the position.
There's also that super hard mate in 1 that took some GM 15 minutes to solve (I solved it by systematically looking at every move that could give check which took just as long).
It's hard because it's nothing like normal positions. None of the interactions make sense.
This sounds quite interesting. However, the distribution of primes may very well be solved at some point in the future.
The phrase "basic chess theory" brings to mind such fundamental concepts as space, material, and endgames, which are taught in every chess primer. However, I believe there is a deeper layer to the study of how humans play chess, one which is not covered in such books. I will dump some of my thoughts here, in case they are of interest to anybody.
First of all, in order to understand how humans do and should play chess, we would do well to examine how a god would play the game; after all, perfection is the standard towards which we all aspire (ignoring the Romantic view of chess, which has no place in the quest to optimize our play). Imagine, if you will, an omniscient chess player, whom we shall call Caissa, because I am too lazy to either figure out how to write umlauts or copy-paste from wikipedia.
Now, I assert that chess is a draw. This is fairly uncontroversial, so I don't think I need to justify this premise. To say that chess is a draw is to say that Caissa could never lose a game with either color, assuming she was attempting to win. A highly skilled player could draw her, but not beat her, unless there is a forced win available to black or white - if there is no such win, then Caissa is invincible. Via modus ponens, I deduce that Caissa could never lose a game she was trying to win.
Let us consider, momentarily, Caissa's choice of openings. It is extremely unlikely that 1.f3, as horrible of an opening move as it is, leads to a forced win for black; it is obviously false that 1.e4 does so. Therefore, she would not distinguish between the two; indeed, contrary to the strongest of human intuitions, and even to the opinions of Grandmasters, she might merrily open with her f-pawn. Is it not fallacious of me, then, to call 1.f3 "horrible"? From the point of view of a god, it is as good as any other first move. This brings up an even graver question: if any given position is either a victory for white, a victory for black, or a draw with perfect play, then how can the assessments of analysts be correct? A god's-eye view of the chessboard reveals that a three-valued approach to the appraisal of positions would best capture reality. How can white be "better, but not winning?" How, indeed, is any assesment other than "0.00" and "mate in n" correct?
It is here that we are first forced to consider puny humans. We do not play perfectly; while Caissa may not care about an advantage of a few centipawns, it means something to us. But what is actually being measured when black is said to have a slight edge, or white a considerable advantage? If I knew chess programming, then I could answer this in terms of exact metrics; however, it is fairly obvious even to the layman that what is truly being spoken of is ease of victory/defence. Ultimately, there may be two positions that are both drawn with perfect play, but which differ drastically in how easy they are to hold; in one, white may have a variety of options that maintain the draw, while in the other, he may have to follow a precarious thread of forced moves to come out unscathed.
If we extend Caissa's cognitive abilities beyond the range of chess and into general intelligence - or if we simply envision her as a computer program and have her answer to a programmer - then she could gain a new ability: consideration of her opponent. Were she facing another god, she truly would do no better to play 1.e4 than to play 1.f3; however, were she facing a mere human, she could optimize her chances of victory by always choosing those moves which most restricted his possibilities, maximizing the probability of an error on his part. It would be no trouble for her to do so, considering we have defined her as omniscient regarding the royal game.
We cannot simply take this conception of Caissa as the ideal that we must seek to emulate, for we would run into a snag: humans are not omniscient, as I have stressed, so unlike Caissa, we also care about the difficulty of out own positions to play. Due to this, even if a human were granted omniscience for a turn, unless he had a winning move, he would have to take into account a variety of complex factors, including the skill levels of both him and his opponent. This greatly complicates things, as there is therefore no clearly defined metric by which to judge the quality of human-vs-human play. With this unfortunate fact in mind, I will turn to the next topic of our investigation: how can humans best imitate this, admittedly poorly-defined, ideal?
The answer is heuristics. While the essence of chess from a god's-eye view is mistakes, which change the evaluation from one of three values to another, the essence of human chess is heuristics. This is a fairly obvious truth, but it is rarely stated outright in those terms. Chess can be reduced to a mere tree of moves, albeit a prodigiously massive one; concepts such as tactics, control of the centre, and even material are all heuristics to help humans, and the imperfect computers which we currently work with, to find the best moves without reference to the ultimate truth of the game tree.
It is this upon which those chess primers I mentioned earlier are based. They are designed to instruct beginners about which heuristics are useful, and which are not. There is much literature regarding the optimal algorithm for chess-playing that humans can conveniently execute; all of these algorithms are combinations of heuristics. Grandmasters use higher-level heuristics than Masters, who use higher-level heuristics than amateurs.
All of this is fairly obvious, and most chess players have probably figured it out for themselves; however, as trivial as it may be, I find it fairly interesting, and it is less discussed than other chess-related topics, and rarely written on in the literature.