compared to a 1300, an 1800 should have more analytic insight (tactics, postional understanding, etc.)
what's the main difference between a 1300 and a 1800 player?

It could be that your chess style is more effective against weaker players and those of the same strength....
my style also seems more effective against weaker opponents. It seems that I tend to beat lower rated opponenets and lose to the higher rated ones!
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However, the blanket generalisation that you're trying to get away with doesn't work. You're trying to concoct a law of nature on insufficient evidence. On our day, we're all capable of playing very well.
You try and find games between absolute world class players (lets say top 5-10) that are older (lets say 60-80) and <2200 players.
You might not even find any. But if you do let us know. I would be very surprised if any of the <2200 players scored even half a point in all of them.
I'm talking regular chess games of course, not simuls or blitz or something like that.
I don't have the time to do that.
Optimissed wrote: Only one or two? You don't know if it's 1 or 2 ?

It could be that your chess style is more effective against weaker players and those of the same strength....
my style also seems more effective against weaker opponents. It seems that I tend to beat lower rated opponenets and lose to the higher rated ones!
.
.
.

Having a wife OR girlfriend is ok but having BOTH is NOT !
Spoken like one of the chess obsessed. Don Juan, most of the world's kings, and several Popes, may disagree.

Having a wife OR girlfriend is ok but having BOTH is NOT !
Spoken like one of the chess obsessed. Don Juan, most of the world's kings, and several Popes, may disagree.
Spoken like a man with no morals , of which there are many !

500 rating points is a big difference . The 1800 will understand chess better and make far fewer blunders than the 1300 and the severity of the 1800's blunders will tend to be less .

Two things come to mind. First is tactics of course. The 1800 sees many more tactics and much more quickly. This is what will win the game for almost any higher rated player (but especially for 1300 vs 1800).
Second is the 1800 has enough strategic knowledge that he'll always have a general plan his moves are working towards.
In contrast the 1300 will make moves in isolation e.g. I want my knight on e4... why? Because it's a central square. Is it a good square though? I don't know, but it's in the middle so I think it's good. And then the next move may have nothing to do with the last move.
Having a general plan will often automatically generate positions where tactics are available when playing against someone who makes moves in isolation.
As someone that falls below 1300, I can say this response describes me exactly.

Having a wife OR girlfriend is ok but having BOTH is NOT !
Spoken like one of the chess obsessed. Don Juan, most of the world's kings, and several Popes, may disagree.
Spoken like a man with no morals , of which there are many !
I'm over 1800. My wife and girlfriend are the same person.

And perfectly capable of hammering an 80 year old karpov.
You probably never played any world class players and analysed with them after the game.
I did, hundreds of times. And you have NO IDEA AT ALL how incredibly strong they are. Even on automatic pilot.
I felt it through and through and it made me very humble as a chessplayer. Rightly so, btw.
I have never played them either, but I had a GM to analyze my games and teach me some. I was amazed how many oppurtunities he showed me in my games. Games I thought I had lost early was in fact with winning chances. So I can verify that GM´s are on a very high level, so high that ordinary players cant understand it.
Let's look at a couple of recent games. I made no selection : just picked the most recent ones in my database :
(to be continued...)
hicetnunc, in the second example game, couldn't white simply come out of the tactics ahead two pieces by playing 26. Bxc3 instead of 26. Bxe7+?

1300 players tend to have played less chess, but they are coming from behind, and are biting hard.
I have a Norwegian rating at 878, which might be something like 1000-1400 Fide. Saturday I played a rapidtournament and scored 3 of 7 against 1500-1850 Fide. My Sicilian black was not ok. The 1800-players dont have so much openingproblems.
'3' & '8'
Ahuahuahuahua