Can a Position be Better but not Winning?
At first thought, the question looks stupid. Of course a position can be better; if not, chess commentators from world champions on down don't know what they're talking about! On the other hand, further reflection suggests the opposite conclusion. As there are only three possible results to a normal chess game (White wins, draw, Black wins), to say that (e.g.) White is better (but not winning) is to speak falsely. Objectively, either White is winning or it's a draw, and while the annotator may not know which there isn't some sort of in-between result corresponding to his evaluation.
How then should we think about this? Robert Pearson offers some thoughts on this on his blog, and as I immediately remembered when I saw his post, I did too, several years ago, on this very blog. My general argument and approach still seem right to me, although I'm not fully happy with my denial that evaluative terms like "slightly better" are objective. I think they are in a certain sense (they are based on real factors on the board, not mere subjective preference) - it just has to be understood that it's not the board alone that's being considered, but the board together with the abilities of a competent but fallible, finite human player.
How then should we think about this? Robert Pearson offers some thoughts on this on his blog, and as I immediately remembered when I saw his post, I did too, several years ago, on this very blog. My general argument and approach still seem right to me, although I'm not fully happy with my denial that evaluative terms like "slightly better" are objective. I think they are in a certain sense (they are based on real factors on the board, not mere subjective preference) - it just has to be understood that it's not the board alone that's being considered, but the board together with the abilities of a competent but fallible, finite human player.
Posted by Dennis Monokroussos on
Tuesday January 6, 2009 at 2:30pm
I would like to clarify one thing from the post of mine that you linked--my second paragraph may have give the wrong impression that I thought the position cited from Jackelen-Gallagher was "better" only in an emotional or psychological sense. I think it is actually a good illustration of all of your "SAs", 1, 2 and 3. That's why I chose to highlight it. And I followed up with some moves and diagrams to show that in the real-world struggle White didn't play perfectly and so Black need not have lost.
Anyway, your comments are helpful to my thinking about how to be a clearer and better writer. Thanks again!
Similarly, it's likely that there exist positions such that it would seem, in the real world, to all the best analysts now and forever in the future that white has a winning advantage, but in which there exists (platonically) a super-subtle draw for black.
We can't, of course, give specific examples of this. But we can reasonably extrapolate from the most surprising wins and draws that composers have exhibited.
In the first kind of case, the best analysts in the real world might assign the notation = . In the second, they might assign the notation + - . Would these notations be (objective, but practically undetectable) errors?
Perhaps the notations do not have a sufficiently determinate meaning to permit an answer to this question.
Perhaps, then, the notations mean a kind of mixture of the objective or apriori facts about the chess position, on the one hand, and the psychological or empirical facts about chess players, on the other hand. Normally this mixture creates no real problem. But in extreme or idealized cases it gives rise to questions with no determinate answer.
But more importantly, those quasi-definitions don't work. White can have a better, even a nearly winning position, but have fewer non-losing moves per turn than Black. (Not every move, perhaps, but your definition doesn't make any allowances for this.) Maybe it will be true most of the time that there are fewer such moves, but it's extremely easy to present natural positions contradicting the alleged rule. (Consider it an exercise to the reader to find such positions.)
To paraphrase Orwell maybe "Some positions are more += than others." For me to feel better in a game of chess I feel like I need to have saddled my opponent with the burden of proving that he is not lost. For me to feel worse about a position I have to either have the burden of proving that I'm not lost or lack of any feasible plans.
If one side as a higher statistical probability of fatally erring I would say that side is worse from a pure game theory point of view. From a purely academic point of view if you were to take a theoretically drawn position and were to give it to a large enough sample of chess players and one side won more often than the other, I would say that the side that won is "better".
Of course, as you say, we want to say that one side has an advantage even if we don't want to claim that it's enough to win, but the trick is in making sense of such a claim. Some attempts might work (I hope the ones in my earlier post, which I linked to, above, are successful), some clearly won't. Material is in the latter category, because a side that's up material can be equal, worse or losing; while there can be other positions with material equality that are better or winning for one side. Material is only one factor of many in evaluating a position.
Maybe, one might say, a player is (non-winningly) better if and only if he has more material or a space advantage or a lead in development or a better pawn structure or more mobility or...etc. But that won't help either, for at least two reasons. First, what if one player has several of the advantage and the opponent several others? Second, the point of the exercise is to explain what it means for one side to be better - what "better" means in a position that is in fact drawn from a God's-eye view, not to explain the particular factors that make this or that specific position better.
I'm afraid you're misunderstanding the goal of the inquiry, but fortunately your last reply gives me a helpful way of clarifying it. You write that "better" means, roughly, that which makes a position better. Notice the circularity there. We're trying to figure out what "better" means (when it doesn't mean "winning"), not trying to determine what factors make a position better.
Specifying "better position" rather than "better" alone doesn't change things. I'm asking what it means to say a position is better (when it's not winning), not what it is in virtue of which (say) White's position is better.
One last try to make the point clear. Let's say White has more material. Fantastic, but why is his position better if the game is still objectively drawn? It's better because...
R vs N, or R+B vs R is better, but not winning
DavidM: While SA1 and SA2 could be used as explanations of SA3 (note that I didn't claim they were mutually exclusive definitions), I don't think either necessarily reduces to SA3. They could be given independently, and I give a reason why that might be the case for SA2.
Also, SA1 and SA2 aren't given as definitions of "better" per se, but as ways to understand a player's being slightly better. And I'm not sure why they can't work as at least possible ways of glossing that phrase.
I think there's less person-relativity among the big boys than you might think, but I have no objection to your general point about SA3. It shows only that defining "true peer" requires some finesse.
As for the moral of the story, it doesn't show that one should avoid main lines, of course, but that not all main lines are created equal for every player. If one assumes that one ought to play main lines, then the conclusion is that playing main lines is a necessary but not sufficient condition for reaching a position one can profitably use in practice.
And when it is not a proved fact, then it is subjective.
Thus,
+- may mean: "surely winning IMHO" or "with mate in 2".
while
+/- usually means "most likely winning"
+/= usually means "most likely draw"
= may mean "approximately balanced" or "the dead tablebase draw"
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Dennis Monokroussos responds:
[It's a strange way to do it, but thanks to a flaw in the PowerBlogs system, the only option I have is to piggyback my comment onto this one!]
With the revision you've made, I don't think there's any serious disagreement between us. But I do think the language can be tricky. I agree that evaluations, when they aren't based on positions that are provably or at least obviously won or drawn, are subjective, and in at least two ways.
First, they're person-relative. A position two GMs believe to be overwhelmingly drawish, and that GM praxis would seem to confirm as drawish, might be anything but in a game between 1500s.
Second, they're person-relative in that they are assessments made by, well, persons. (Even computer assessments are ultimately person-relative, in that they are based on valuations in some ultimate way determined by their programmers.)
Despite this, I want to add that subjectivity of this sort does not rule out objectivity as well. Assessments are a sort of hybrid - they're not based on mere subjective preference in the way that one likes vanilla but dislikes chocolate ice cream.
There is much that can be said in elaboration of this, and I've already said a little in earlier remarks. But here's at least a sort of general suggestion to support this claim. GMs and other opening theorists claim to discover this or that about an opening line (even in cases where the result is not a forced win or draw). In the Open Catalan, for instance, it's often the case that if Black achieves ...c5 without anything bad happening to him, then he has basically solved his opening problems. There is thus a specific, objective aspect of the situation that leads to a well-founded judgment of approximate equality. The judgment is made by people, by subjects (and thus subjective in that sense), but is based on objective, though not mathematically conclusive, grounds.