It Helps NOT to Know Opponent's Rating
I think the rating system is terrific, but it's so accurate that often players fall in love with it, rather than worry about their playing strength. I seen numerous games where a lower rated player was winning easily and offered a draw "...because he was higher rated and he ..." 1) was afraid of losing or 2) wanted to gain a minimal number of rating points.
Much worse is the fact that numerous players have stopped playing competitively because they perceived their rating wasn't going to go up without exceptional action. My college roommate quit when he got to USCF 1800 even and never played again, and we could even discuss whether that affected Howard Stern's decision to retire "cold turkey" in Feb 2011. For those reasons I wrote an article about 10 years ago Encouraging Tournament Play (starts at the bottom of the linked page) that urged USCF to "hide" the rating system for the good of the large number of players who take actions based on rating, rather than just trying to have fun or to improve. There are several others who believe something similar, including House of Staunton founder Frank Cammarata and, surprisingly, USCF Rating Committee Chairman, Dr. Mark Glickman.
The following fun story illustrates how one plays differently when the opponent's strength is known:
Back in the early 1970's, when I was at my playing peak (Ooh! It hurts me to write that!), I had a friend who would frequent bars and play chess with his friends. One day that friend said:
"Dan, when I play at the bars we have one guy who beats everyone easily. He's a nice guy but he is really on his high horse from winning all those games. Would you be willing to play him anonymously? It should be fun to see what happens."
So I agreed to play for fun - there was no hustle involved. This was not for money but to see how a good bar player - let's call him Player X - would do against a top tournament player (I won the Philadelphia Open Championship in 1971 and 1976 and the prestigious Philadelphia Invitational Closed Championship in 1973, around the time of this story).
Soon thereafter we met at my friend's apartment and eventually he got around to saying "You two guys both like to play chess - why don't you play a game?" So Player X and I agreed and started to play without a clock (whipping a clock out is usually a give-away of someone who plays seriously).
Player X came at me aggressively, as expected. He was playing rather well. I could not estimate his strength just from a few moves, but I supposed he was about 1500 at best (sometimes my guess for playing strength is wrong and, to be safe, I play everyone the same: Always play with confidence, aggression, and respect for your opponent's moves and ideas).
In that first game I defended solidly and Player X kept coming at me. But of course I wasn't going to fall for any basic tactical tricks and eventually I wore him down - he made a small mistake here or there and I won. So Player X good naturedly offered "Good game! Let's play again."
In the second game the play was similar. He played well and aggressively and I played solid. Eventually his small mistakes added up and his game fell apart and I won again.
"Nobody's ever beaten me two games in a row! Let's play again!" So we started a third game and it was another replay: he played aggressively, but it did no good as I was just too strong for him. After the third game Player X was suspicious: "Wait a minute! Something's up. What's going on here?"
At that point our mutual friend and host confessed "Dan is the Philadelphia Champion and an expert-level chess player. At my request he agreed to play you anonymously for fun to see how you would react!" (Note: In those days the ratings were lower and there was only one or two masters [2200-2399] in Philadelphia; all the other top players were rated expert [2000-2199]. A few years later the ratings would inflate toward the level they are today and the top area players, including myself, were able to make master.)
Upon hearing this Player X was relieved and surprised: "Aha! I knew it was something like that. In that case I would like to play you some more." So we played a 4th, 5th, and 6th game.
But for those games Player X changed his strategy - for the worse. He tried to play "solid" and that turned out to be non-aggressive. You can't play that way in chess and be successful. Even super-positional players such as Philadelphia's top 1970's player IM Bruce Rind, have a strong air of aggression in their positional play. As someone correctly advised me when I began tournament play "If you want to get a draw against a higher rated player, play for a win! If that doesn't work you might draw. But if you play for a draw from the start that almost never works." Good advice!
So now the games were no longer competitive. I won all three games easily. Player X's fear of my game and his "solid" play were the wrong way to go.
In my column The Self-Fulfilling Prophecy I talk about how I beat a master the first time I played one (in Jan 1968 after I had been playing seriously about 18 months). I didn't necessarily expect to win but I did not expect to lose, either. I just tried my best on every move. After I won I asked the top player at our club, later NM Rich Pariseau, how I beat the master and he wrinkled his face and said "That's because you played better!".
Sometimes I ask players how many points they should score against someone rated 100 or 200 points higher if they played a 100 game match (assuming neither player improved during the match). The correct answers are 36% and 24% respectively, but they often "under-guess", thinking the lower rated player has even less chance. If you play without knowing your opponent's rating you won't fear the stronger players and you won't be overconfident against the weaker ones. In both cases this will tend to help you (and your opponents as well - so it evens out, assuming they use the same strategy).
It's worth repeating: Always play with confidence, aggression, and respect for your opponent's moves and ideas. If you do that, and don't go by their rating, your results should improve and you might even have more fun...Good luck!