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    Jan142017

    The Best World Champion, According to the Computer, Is...

    Magnus Carlsen, according to Chess.com's "CAPS" (Computer Aggregated Precision Score), with Vladimir Kramnik #2, Garry Kasparov #3, Bobby Fischer #4, and on it goes. It's a bit interesting, but the concept seems rather a lot like IM and computer science professor Ken Regan's Intrinsic Performance Ratings (IPRs), which have been well-known for years now - see this profile, for instance. (I didn't see any mention of him or his work either in that article or in this one, which is really surprising.)

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    Of course this approach assumes that "best" can be meaningfully ascertained by, as Regan says right upfront in his publication, "[judging] skill based on the quality of decisions made rather than the outcomes of contests". But I think a more useful definition of "best" is "always finding a way to beat the opponent in front of you" -- which can include playing deliberately sub-optimal moves if you know they'll elicit an incorrect response.

    To put it differently, these games weren't played against computers, so the decisions these players made were designed to beat a specific human opponent, not a silicon one. Psychologically-minded players like Lasker and Tal would have taken a completely different approach against non-human opposition. Judging them according to CPU evaluations is assuming a set of priorities -- finding the "correct" move in all situations -- which were not at all theirs, and comes dangerously close to faulting a broom for not being a good mop.

    To think that "[removing] all abstract and non-measurable features of evaluating a chess game or player's strength" is a refinement is a fundamental fallacy, seen too often: "If we just get rid of the stuff we don't know how to quantify, everything works perfectly!" Well, the reality is that the stuff that's difficult to quantify is often where the truth lies, and the easily quantifiable information is often trivial.

    But we talk about the latter because that path leads to publication, tenure, and the like, whereas being honest about how little we know and how reductive our frameworks really are is...less fruitful. Quantify the arts, and argue their value based on how they serve STEM fields or reflect their values, and you're temporarily protected from the scalpels of powerful people who think STEM is real and everything else is decorative (except fame, that's usually popular too).

    All that said I don't doubt that Carlsen is the most "correct" player in history, and it's nice to see a chart that values the tactical acumen of Tal as highly as it does. But there are some assumptions being made here that I just can't accept -- assumptions that I think exemplify the problems of a culture that's put its faith in the quantitative and is unable to see how reductive those models often are.

    [DM: Actually, the model accords pretty well with results and what I'd take to be common sense, with only mild surprises. And as top players who have examined Lasker's and Tal's games have recognized, the romantic tales of their winning with psychology have proved to be myths. They had objective strengths that were underestimated and minimized by opponents and commentators who often didn't realize just how far ahead of their peers they actually were, at least when it came to their strongest points. As Fischer said, "I believe in good moves."]

    January 14, 2017 | Unregistered CommenterP.

    My problem isn't with the results of the model (which are perfectly reasonable), but the assumptions that underpin it. As for the "myth" of Tal's psychological savvy, the fact is that he knew perfectly well that moves like his famous 6. gxf3 (for example) weren't the best move on the board, but would lead to unbalanced positions and probably unsettle Botvinnik.

    [DM: You're changing my words: I said nothing about the myth of "Tal's psychological savvy". I agree with you that Tal sometimes took psychological factors into account - but then so did players like Karpov. What is a myth is that Tal (and Lasker) made a practice of selecting second-best moves as a sort of psychological ploy. As has been confirmed by both computers and later grandmasters, many of their allegedly second-rate, purportedly psychologically-based ideas were in fact entirely sound. Tal and Lasker were simply better than their peers in assessing complicated, "irrational" positions.]

    Believing in good moves is fine, but just as in tennis, the greats know how to "win ugly" as well by neutralizing the strengths of a specific opponent, or avoiding opening prep, and consciously used suboptimal moves to do so (Carlsen's whole approach to openings, Fischer's 5. Nc5 in the Caro-Kann which certainly and deliberately wasn't the best move in the position, etc.). And even now, the only real chance a human has to draw a computer is to choose moves that the CPU deems suboptimal, in order to bait it into positions it can't fully comprehend (e.g. certain fortresses computers still miss because of the horizon effect). Knowing how to make your opponent play badly is part of chess greatness.

    My point is that OTB chess is about the result, not the correctness of one's moves. Generally speaking these players were playing for titles, trophies, cash, and victory, not accuracy in and of itself. Of course it's gratifying when their moves are also proven to be the best and soundest available, but we should be cautious about evaluating players based on goals that weren't their own. They weren't trying to play "correct" chess, but winning chess, and while there's a lot of overlap between those two things the one shouldn't be mistaken for the other.

    January 15, 2017 | Unregistered CommenterP.

    It is pretty silly to compare Carlsen with a team & computers to Morphy with no team &no computers. A better measure, and one that has long been understood, is comparison with contemporaries. By that measure Capablanca & Morphy stand out, as do Fischer, Kasparov and Carlsen, but not Kramnik, Anand, Smyslov, etc.

    [DM: It isn't silly at all. It's just important not to confuse different measures of greatness. We can try to assess who was the most dominant player of his era, which is what you seem to be after; *and* we can try to assess who actually made the best moves, which is what IPRs and CAPS are trying to do. They're two different things, and both have their place.

    Take sprinting. Jesse Owens was way ahead of his time, but his best times are mediocre by today's standards. That doesn't diminish his status as a hero to track athletes and fans everywhere, who can recognize his greatness and dominance while acknowledging that for a variety of reasons (including good old Gaussian distribution) today's track sprinters are much better (as sprinters) than Owens and his cohort.]

    January 16, 2017 | Unregistered CommenterJB

    I agree with you that Tal sometimes took psychological factors into account - but then so did players like Karpov. What is a myth is that Tal (and Lasker) made a practice of selecting second-best moves as a sort of psychological ploy. As has been confirmed by both computers and later grandmasters, many of their allegedly second-rate, purportedly psychologically-based ideas were in fact entirely sound.

    "Sound" and "optimal" are two different standards, though. I think Tal was more than willing to select a second-best move if he believed it would elicit a poor response from that opponent. And that's a metric -- selecting the option most likely to make your opponent implode -- that's not effectively measured by these sorts of tests.

    (Otherwise, what exactly did you mean by "the romantic tales of their winning with psychology"? I've never seen a reliable claim that Lasker or Tal made bad moves just to make things interesting, if that's what you mean. But there's zero doubt that they chose objectively suboptimal moves in order to create unbalanced positions in which they hoped to outplay the opponent by taking advantage of his prejudices, or getting him to lose tons of time on the clock.)

    My objection, again, is to the idea that "best" = "most correct". There are innumerable positions where the move that gives the best practical chance is clearly not the objectively best move; though both will ultimately lead to a loss with perfect play from the opponent, the passive move might take 40 moves to checkmate, the active one 30 moves, but the latter gives the opponent far more chances to go wrong. Does this system of measurement have a way of measuring that?

    More than anything, these players were never, ever trying to play the "most correct" move -- they wanted to play the move that gave them the best chances.

    [DM: Yes, I realize that you believe this and have repeated the claim, but the vast majority of the time it doesn't square with the facts. The great majority of their moves - including a large percentage of the ones that have had the "psychology"/"practical" tag stuck on them, were in fact objectively good moves - even the best ones - as assessed by top players like Kasparov and contemporary computer engines.]

    So this system commits the fundamental error of measuring something that the players weren't trying to do: this metric assumes a goal (absolute accuracy) that wasn't theirs. Had they wanted to play the most unimpeachable moves -- had they had that in their head as the main criterion of their play -- they would've adopted completely different approaches.

    Take sprinting.

    Sprinting is not a good counterexample because unlike chess, it's not a zero-sum game in its intrinsic goal (running as fast as possible) -- my time doesn't directly affect yours. Sprinters operate independently from one another, and don't generally adopt different strategies for different opponents. (Different heats, maybe, but that's an issue of energy conservation.)

    [DM: I agree that there are disanalogies between chess and sprinting, but I don't think those disanalogies undermine the point I was trying to make. It seems clear by any objective measure that players are getting stronger over time, because more about the game has been learned and our methods and tools for obtaining and internalizing that information has improved dramatically. So of course today's best players are better than the best players of the past. (I didn't say "more talented", just objectively better, on average, and they can play at a higher level in many more kinds of positions than their predecessors.) So in that objective sense, a Kramnik is stronger than, say, a Lasker or miles and miles stronger than a Morphy. This is compatible with acknowledging that he was not the dominant figure in his time that Morphy was in his. But before we glorify Morphy to the skies, we should note that his competition was absurdly weaker than Kramnik's. There's no good reason to think that Kramnik growing up in the Morphy household wouldn't have been as good as Morphy or even better. Ultimately, we don't know; what we do know is that actual Kramnik was less dominant but about 400 rating points stronger than actual Morphy.]

    Tennis or boxing is closer, but there we have the same problem. These are competitive sports whose purpose is beating the opponent in front of you, not hitting some objective metric of quality: the one-time record holder for world's fastest serve (quite an objective metric) also has the distinction of having been returned by Andre Agassi for a winner!

    January 19, 2017 | Unregistered CommenterP.

    Three quick notes:

    1. (in reply to "P.") Indeed, measuring skill at knowing how to make your opponent play badly is the largest part of what I've been after since 2013. The expansion yields some stunningly good fits like this one for 2800+ but also travails recounted in my Election Day article (which was written and posted before returns started coming in).

    2. What are the scientific error bars on the CAPS ratings? Despite having gobs of data, my posts show +-100-200 or wider on IPRs, and I don't claim to have any more than 3-digit precision on anything in my work (hence I round my IPRs to the nearest 05 like FIDE ratings used to do, period). Is there a paper with enough details to evaluate this system?

    3. Chess-DB's Chess Play Quality Index has been around for several years, but if you compare their master Elo correlation chart at that link with my completely linear results here, one of us must be quite wrong. And the polemic point of that article by me is that one of my own two charts must be wrong...though I think either in isolation would pass peer review with authoritative force.

    January 19, 2017 | Unregistered CommenterKenneth W. Regan

    Dennis, I can easily concede (and have never disagreed) that the "great majority" of Lasker and Tal's moves are sound, but that doesn't detract from my basic point. We're not talking about outright blunders here, but about moves like the famous 5. gxf3 (my mistake on writing 6. gxf3 earlier) which were consciously chosen for reasons other than their objective merit. Tal is on record as saying that it leads to equality, while the Queen recapture leads to a slight advantage for White. It's indisputable that he knew it wasn't the soundest move available to him, but chose it anyway for practical reasons.

    [DM: If you're going to insist that although the "great majority" of Lasker's and Tal's moves were sound, your basic point about psychology is unaffected, then I'm going to affirm the same about my point, as I've noted that *every single player* takes psychological factors into account every now and then. Even Svetozar "I play the pieces" Gligoric and Bobby "I believe in good moves" Fischer. Making reference to Tal's experiment with 5.gxf3 - which was *not* typical - proves very little.]

    The CPU would brand 5. gxf3 a mistake, much as it would brand a swindle attempt (or any sort of active play) in a lost position a mistake if it leads to a quicker defeat.

    [DM: About this well-worn example: 5.gxf3 is NOT a mistake. The engine does prefer 5.Qxf3, unsurprisingly, but by less than three-tenths of a pawn. (Update: By the time I finished the paragraph the difference was .11 at depth 32. Incidentally, this supports my contention that Tal's experiments were often much better - objectively - than most people appreciate.) White is not worse after 5.gxf3, so as a one-off idea to create a fresh position on the board it's not a bad choice at all.]

    And it would be correct that those moves are, objectively, mistakes. The error is in extrapolating a player's strength based on those decisions: the passive move that holds out longer but offers no hope of counterplay may be the objectively correct move, but choosing it is an unambiguous mistake in sport. In human vs. human play, it's wrong not to attempt a swindle when the alternative is certain, slow defeat.

    To be clear: computers are wonderful tools for assessing tactical accuracy; analyzing the frequency of blunders in grandmaster play is an entirely worthwhile area of research; and I don't doubt that today's players are, in an overall sense, the strongest who have ever lived -- certainly the best defenders, and with a much deeper and broader chess "understanding", though raw calculating ability may be a different story (I still figure Tal is the best pure tactician to ever play the game).

    But let's not be fooled into thinking that a player's deviation from CPU evaluation is synonymous with that player's strength.

    [DM: In the aggregate? Of course it is. Nothing in our discussion has suggested otherwise, and your admission in the first paragraph confirms the view.]

    Any GM playing a human opponent isn't playing to please the CPU but to beat that opponent, and every decision they make can only be viewed in that context -- anything else is a distortion. If even one move out of every 1000 they made was chosen specifically because they knew it was suboptimal (not "sound" or "unsound" -- that's not the issue -- but suboptimal) but also knew that it would yield more effective results in that particular situation than the "best" move, then any assessment rubric that fails to account for the practical wisdom of choosing that move -- to see the selection of that specific suboptimal move as a testament to the player's strength, not their weakness -- is fundamentally flawed.

    (That doesn't mean it's useless; I'm just calling for a certain amount of humility, is all. The CAPS rankings might well be spot-on -- they're certainly close to what I'd imagine to be the case -- but if they're based on flawed assumptions about the right way to measure player strength, those flaws don't disappear just because the data tell us what we want to hear.)

    January 21, 2017 | Unregistered CommenterP.

    I think that time as world champion is also important (though in Fischer's case it is clearly shorter than his dominance would have allowed). Thus, it seems that Kasparov, who held the crown and dominated for so long, is in a class above Carlsen (for the time being, anyway) or Kramnik, and that Anand, who has a plus score against Kramnik, beat him decisively in a head to head match (2008) and held the classical crown for five years to Kramnik's eight should be pretty much even with him.

    [DM: Without necessarily agreeing with your conclusion I'll strengthen your case for Anand by noting that Kramnik's reign was 7 years, not 8, while Anand's was 6 years, not 5. Mexico City counts, even if it wasn't a match.]

    January 21, 2017 | Unregistered CommenterTEF

    Dennis, let's make this as clear as possible:

    About this well-worn example: 5.gxf3 is NOT a mistake. The engine does prefer 5.Qxf3, unsurprisingly

    We seem to be using different definitions of "mistake". My contention is that, from the CPU's perspective, any suboptimal move is a mistake, and it will ding Tal's estimated "rating" based on that -- with no understanding of why he knowingly chose a move that's not objectively the best (and there's no question that 5.gxf3 is not objectively best!), or how that's actually evidence of his strength. It can't differentiate between a miscalculation (or a failure of strategic understanding) and a suboptimal move chosen to elicit favorable results.

    [DM: A "mistake" is a strong word - you can use "inaccuracy" instead. But I honestly don't understand why this discussion is continuing. If we're speaking about the occasional sub-optimal move used for psychological purposes, sure, of course: I agreed with that from the very start. In fact, even chess engines do this, in the context of the "contempt factor"! (This is a setting that gives the engine a certain amount of leeway in avoiding what it considers the absolute best move in order to avoid a draw.) But this is something that happens only on occasion. For instance, after 5.gxf3 Tal didn't make any further sub-optimal moves on purpose in the opening and early middlegame.]

    If you have proof to the contrary, let me know. Perhaps the CAPS algorithms have been tuned to ignore opening experiments and forgive evaluation changes of <N -- though I still don't see how any CPU will properly see a player's choice of (for example) a complex but unsound swindling line vs. a slower but inevitable loss as what it should be, i.e. a testament to their strength. (And, for that matter, 10-20 evaluation changes of <N can still turn a winning position into a losing one, and often have.)

    Tal's evaluation of 5. gxf3, which I posted earlier, corresponds very closely to the engine's: it's not as good as the main line, but creates an unbalanced and interesting position. But live by the sword, die by the sword: if we look to the CPU to tell us who's strongest, then any suboptimal move (per the CPU) is definitionally a mistake. Not a blunder, not a "bad move", but that's a question of degree, not type.

    So my question, or question-set, is: do we feel comfortable with a CPU adjusting its opinion of Tal's absolute strength downward (even by the minutest amount) because of 5. gxf3, or Fischer because of 5. Nc5? Do we feel comfortable with Marshall's incredibly dangerous, trappy play in lost positions being used as negative evidence of his strength because, against perfect play, they lose a lost position a bit faster? Do we overlook the flaws in a system because "of course" it's correct "in aggregate" and tells us something similar to what we intuitively believe to be true? Would we question the results more vigorously if they didn't tell us what we expected to hear?

    [DM: In general, yes, I'm comfortable with that, thanks for asking. (Especially since cheapos in lost positions and opening experiments are common to almost every player.) These issues come up rarely enough that I don't believe the rating outcomes are significantly skewed. I would add that while I don't know too much about how CAPS works, Ken Regan's IPRs exclude the opening (IIRC, he starts with move 11 or move 13) and also ignores situations where one player has an advantage of +5 or greater, which eliminates some cheapo situations too.]

    January 22, 2017 | Unregistered CommenterP.

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