good points.
Judging skill of players from a single game position?

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Is there any extent to which one can reliably judge the skill of a pair of players simply by looking at a single position from a game?
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Not close to the opening!

Interesting idea: I've never heard of this before.
The first position looks like white is very weak (and presumably black not hugely different, since he hasn't won yet). The other two also looked flawed, but not to the same extent (I infer at least one in each is not very strong).
I expect to be proved wrong in an amusing way.

I think there's a better chance of judging the skill of the person REVIEWING the position - than of the players IN THAT POSITION.

I think there's a better chance of judging the skill of the person REVIEWING the position - than of the players IN THAT POSITION.
Who's reviewing the guard then? Umm... I mean... The... custodian?

Give them de Groot A and have them analyze it verbally and you could probably get people close to the right rating range anyway. But for most general positions probably not.

The deeper the search required to find a clear winning or top move - the greater
the ratings of the players, as a general but strong rule.

This is a good question. I teach chess for a living and have a number of younger students. Their parents will often email me a position and move played from one of their child's games asking me how well I think they are doing. Of course, I cannot do a complete analysis of the child's game without the entire game in front of me. I cannot even begin to answer the question "why someone would ask for an evaluation based on a snapshot of the complete game," but I take a look at the position anyway.
The first thing I do is look at the position, trying to determine what it took to get there. Is the position derived from an open or closed game? Is is a tactical play or is it part of a strategic play? I look at possible move options.
I can roughly determine a basic level of play but it's like trying to determine a movie's plot after seeing two frames of the entire film. Using this analogy, I could say the scene had great lighting, fantastic camera angles and points related to the immediate. Does this tell me that I'm looking at the greatest film ever made? Absolutely not.
I don't think you can get a true read on a player's rating from a single move. You can tell whether or not they possess certain skills that can be used to determine a rough level of play but even then, you're only getting a small glimpse rather than a complete look at the game.

This is a good question. I teach chess for a living and have a number of younger students. Their parents will often email me a position and move played from one of their child's games asking me how well I think they are doing. Of course, I cannot do a complete analysis of the child's game without the entire game in front of me. I cannot even begin to answer the question "why someone would ask for an evaluation based on a snapshot of the complete game," but I take a look at the position anyway.
The first thing I do is look at the position, trying to determine what it took to get there. Is the position derived from an open or closed game? Is is a tactical play or is it part of a strategic play? I look at possible move options.
I can roughly determine a basic level of play but it's like trying to determine a movie's plot after seeing two frames of the entire film. Using this analogy, I could say the scene had great lighting, fantastic camera angles and points related to the immediate. Does this tell me that I'm looking at the greatest film ever made? Absolutely not.
I don't think you can get a true read on a player's rating from a single move. You can tell whether or not they possess certain skills that can be used to determine a rough level of play but even then, you're only getting a small glimpse rather than a complete look at the game.
+1

As for the positions, the first was a Karpov-Kasparov blitz game from their exhibition match in 2009; white resigned in that position. Decided it wasn't that smart of me to take a blitz game (hadn't noticed at first).
The second was the finish of my OTB game earlier in the day, white is 2026 and I (black) am 1999, we agreed to a draw there.
The third is Timofeev-Kasparov from the 2004 Russian championship, white resigned in that position.
I'm not very happy with the rather random games I chose (and that the weaker one was equalish while the others were lost for white), I might try to find a few at move 25 where Houdini gives the position a +- 0.1 score. But I don't have time now.
And yes, the De Groot positions -- does anyone have them? Isn't there some coach who has shown the positions to many many players and has a book about how players of different strengths react to the positions? Heisman?

ha ha. Nice one. Regarding the first one, I reckoned that no strong player would have reached that position without resigning. It is a mate in 4 for black. Obviously in a blitz this is not a valid argument. But I am very surprised at how strong the players were in games 1 and 3.
I conclude that it is rather difficult to detect strength. When a player is dominated (either in rating or just in a particular game) a painfully ugly position can be reached (as in 1 and 3). I wrongly infered white was relatively weak in both cases.

I would agree with this statement. Ugly positions can be reached, for even a GM, when they refuse to resign early. Also, a GM can make an otherwise "good" player look like a patzer.
I don't know if you can judge the skill of a player by the position (unless it's a kid playing and he pushes ALL his pawns, leaving his pieces still in their starting position... I've seen this a lot). However, you might be able to judge if there's an ability gap between the two players. Maybe. A game is a snapshot. It's hard to judge by one game. Let alone, one position.

I think there's a better chance of judging the skill of the person REVIEWING the position - than of the players IN THAT POSITION.
Not quite sure what this meant, but I think my reckless inferences about the strength of the players shows how little I know!

Elroch wrote: Not quite sure what this meant, but I think my reckless inferences about the strength of the players shows how little I know!
At least you saw enough to weave a story around the position ... even it was the wrong story!
Of course you can get a fairly good idea how good two players are by watching them play an entire game.
Is there any extent to which one can reliably judge the skill of a pair of players simply by looking at a single position from a game?
I don't mean necessarily judging their skill relative to each other--I just mean knowing whether you're looking at an amateur game, a grandmaster game, or something in between.
I've got no practical reason for asking this question--it's a purely abstract, philosophical one.
Of course if you see more than one hung piece on the board* you're probably not looking at a grandmaster game. But is there anything more subtle or interesting to say than that?
You might think grandmaster positions tend to be more complicated. But couldn't it be that equally complicated situations typically arise in the games of hopeless amateurs--they just don't have the skill to recognize and deal with the position as such?
On the other hand, precisely because grandmasters know the game so deeply and therefore know how to complicate it in ways undreamed of by amateurs, you might expect that grandmaster games more reliably could be found to have such complications in them--and such complications can be identified within a single position, not just in a sequence of moves.
*Even a grandmaster game is going to have a "hung" piece in place for at least half a move when there is an exchange of pieces being finished off.