user17: I (about a 1500 player) once took White against a 2100 player, and played a Queen's Gambit. I lost of course, but the other player complimented my play. He said, "You played well for about 20 moves, and made a small mistake on the 21st, which I took advantage of."
It certainly helped that I was playing White, which is sort of a form of handicap.
(See Is there a way to use handicaps in chess to bridge the gap between players of different skill levels?)
I don't remember using a "book" variation, but played moves that seemed to follow common sense. Maybe I kept the game simple. Somehow, I managed to play "neck and neck" until I overlooked a combination that gave Black a pawn advantage.
Is it as simple as that, staving off defeat is a matter of not making mistakes? (I finally made one, although it wasn't obvious to me.) Or does the weaker player (with White, anyway) have to do something to keep the stronger player at bay, like seize and hold the initiative (which I tried, but probably failed to do)?
And to reverse the question, suppose you were playing someone of much less rated strength who was playing "even" with you, perhaps as the result of learning some book variation. Should you steer for complications, perhaps away from the book, into areas that your opponent might be less familiar with? Or should you just play your best game and count on him to make a mistake?

user4418: First of all, I really like Andrew's answer apart from the part where he talks about trying to randomize the position against a better player. Better players almost always have better evaluation skills than weaker players and so everything else being equal (including pure calculating skill) they will make better judgments faster than you in random positions as well as calm positions.
No, what I would advise against both much stronger and much weaker players is rather banal. With Spock-like detachment and lack of emotion play the position not the man (or woman). Do not try and play an ELO rating! When it is your turn just try and find the objectively best move and play it.
I have seen master level players come unstuck by playing the ELO rating or the man rather than the position. In one case, knowing that they were a much better endgame player they coasted through the opening and middlegame into an endgame the stubborn weaker player managed to draw. I will dig up an example game and post later.
Preparation before the game is a different matter. If your opponent has a particular known weakness or you have a particular strength then by all means try and steer the game in that direction. Having white can be a big advantage here as it lets you cut down the possibilities but sometimes you can also do this with black. 
When it comes to preparation the randomizing advise can get a chance. If you've played the player before with the same colours and you see a chance to divert the opening the pair of you played last time into a particularly tactical variation then prepare, study and unleash this variation if you get the chance. If nothing else it is very likely to gain you time on the clock and it may just be your lucky day. But ad hoc randomizing during the game is something I would advise against.

user75: Here's another point worth mentioning: you could try to steer the game into a draw by threefold or a tactic-less position (first two draws are not about what I'm saying here):
http://www.chessgames.com/perl/chesscollection?cid=1008234
If you're the much lower rated player I think in the short term this is the best you can do. In the long term, learn more about chess and turn your weaknesses into strengths.

user17: Against a weaker player, figure out why he is weak. Maybe he is playing "strongly" because he has "booked up." So take him out of book lines. Maybe he is strong in strategy and weak on tactics (or vice versa). So steer the game into areas where he is weaker.
In my case, against stronger players, self-administered tests show that my "1500" strength is a composite of 1800 opening and endgame strength and 1400 middle game strength. Against, say, a 1700 player, I would look for variations such as the Exchange variation of the Ruy Lopez that exchanges queens early and gets into an early endgame, bypassing the middle game that I'm weak at.
If a decidedly weaker player (more than 200 points difference) wins (or draws) against a stronger player, one of two things may be happening: 1) The weaker player is having a "good" day and the stronger player a "bad" day or 2) The weaker player has recently gotten strong, but this is not yet reflected in his rating.

user142: While I agree with Quantum Elf's general rule, there is also an advantage to complicating the position for someone much weaker (perhaps this applies to the weaker opponent being <1500). If you're able to calculate possibilities quicker than your opponent, moving into a tactical position intentionally will give you more opportunities to capitalize on any tactical mistakes they make.

user107: The general rule is:

Against weaker opponents, try and simplify the position.
Against stronger opponents, try and complicate the position.

The reasoning is that a strong player will falter more in a complicated position than he would in a "dry", boring position. Against much higher rated opponents, go for wild tactical melees and crazed positions. 
In a "normal" game, the stronger player will simply wait and improve his position until the weaker player gives him something. As just an example, after a equal position after N moves, let's say that the 2100-rated player castles kingside "N+1" moves into the game, and then the next move by the 1500-rated player castles queenside, with the notable difference that no pawns are moved in front of the 2100's king, and the 1500's king has the a6-pawn sticking out. Bam! You just gave him something. The 2100 player would roll the queenside pawns forward and "hook" that a6-pawn. All things being equal you can count on the 2100 player's attack crashing through first.
I will emphasize that no matter who the opponent, that chess is a mix of prophylaxis (e.g. preventing counterplay) and aggression. Take time to study your plans, but don't forget about your opponent. Q: When should you be on the lookout for your opponent's possibilities? A: Every move.

user12: Statistically speaking, a 600 point rating disadvantage means that you have about a 3.07% chance of winning.  If you want to improve that, your best bet is to play a position that you are familiar with.  
This part of the answer might be more pertinent to a 2000 player playing a 2200 player
One way to do this is to play an opening that you know intimately.  If you have a pet line, this is the time to play it.  Especially if you've analyzed an unusual opening with a computer, this will shorten the odds.  Basically, the 3200+ rated computer will be playing your opponent for you.
Ok, that's it for opening preparation
One common suggestion is to randomize the position if you are the weaker player.  This makes a lot of sense.  Chances are that the stronger player is also better at endgames.  So you don't want to get to the endgame unless you will win easily.  I've frequently beaten lower rated players from an equal endgame or even an endgame where I'm a little worse.  
In a "randomized" position, usually multiple pieces are hanging, one or both kings are weak, and most of the pieces are still on the board.  Now, unfortunately, truly good players thrive in these positions, and they will work out all the complications.  But you're probably not playing a 2600+ grandmaster, so this is still not a bad idea.  In these random positions, both players will be forced to use most of their time to make their way along the "narrow path".[1]  Once the players are deep in time pressure, anything can happen.[2] 
This is NOT to say you should make bad moves.  If at any point you make inferior moves, well, the stronger opponent will probably take advantage of them.  Instead, just keep pieces on the board.  One trick you can use to complicate - when a piece is attacked, instead of moving it or defending it, just attack one of your opponent's pieces.  This is much easier said than done, but this will quickly complicate even a mundane position.

Ok, if you've made it this far, just a few more general thoughts.  The easiest way to beat a stronger player is to just get lucky.  Everyone has a bad day from time to time, you just have to be playing someone who happens to make a mistake and take advantage of it.  The key to this is to not make any terrible mistakes.  If you can stay in the game and not lose material, you can always win - even if you have a bad position.  
Double check every move before you make it.  If you see a move that you think wins, spend more time than usual, don't make this move quickly.  If you're right, being behind on the clock won't really matter.  If you're wrong, you won't make an inferior move.  One saying that I've always found helpful is "never play a blunder quickly" (source unknown).  
Personally, I'm not convinced that the right plan is to just complicate the position and hope.  While this is a good plan of last resort, everyone plays with the same 16 pieces.  Make solid moves, calculate everything you need to, and be inspired to play well.  Even if you lose, you'll learn far more from a well played game that you just barely lost than a game where one of the players blundered on move 12.

Lastly, some rules that have helped me against lower rated players in the past:  

Don't be afraid of endgames, even if it should be drawn with best play
Similarly, don't be afraid of equal positions
A small advantage is often enough to win, but even if you are down material, swindles are often possible, so don't give up.
Finally, as a stronger player, I've had good luck in complicated positions.  As likely as it is for a stronger player to blunder, it is even more likely for the lower rated player to also blunder.  


[1]: David Bronstein: "When you play against an experienced opponent who exploits all the defensive resources at his command you sometimes have to walk time and again, along the narrow path of 'the only move'."
[2]: Lev Alburt: (paraphrased from http://www.amazon.com/Chess-Rules-Thumb-Lev-Alburt/dp/1889323101) "Having 15 minutes when your opponent has 5 is worth 200 rating points."

17: <p>I (about a 1500 player) once took White against a 2100 player, and played a Queen's Gambit. I lost of course, but the other player complimented my play. He said, "You played well for about 20 moves, and made a small mistake on the 21st, which I took advantage of."</p>

<p>It certainly helped that I was playing White, which is sort of a form of handicap.
(See <a href="https://chess.stackexchange.com/questions/4/is-there-a-way-use-handicaps-in-chess-to-bridge-players-of-different-skill-if-n">Is there a way to use handicaps in chess to bridge the gap between players of different skill levels?</a>)</p>

<p>I don't remember using a "book" variation, but played moves that seemed to follow common sense. Maybe I kept the game simple. Somehow, I managed to play "neck and neck" until I overlooked a combination that gave Black a pawn advantage.</p>

<p>Is it as simple as that, staving off defeat is a matter of not making mistakes? (I finally made one, although it wasn't obvious to me.) Or does the weaker player (with White, anyway) have to do something to keep the stronger player at bay, like seize and hold the initiative (which I tried, but probably failed to do)?</p>

<p>And to reverse the question, suppose you were playing someone of much less rated strength who was playing "even" with you, perhaps as the result of learning some book variation. Should you steer for complications, perhaps away from the book, into areas that your opponent might be less familiar with? Or should you just play your best game and count on him to make a mistake?</p>
 4418: <p>First of all, I really like Andrew's answer apart from the part where he talks about trying to randomize the position against a better player. Better players almost always have better evaluation skills than weaker players and so everything else being equal (including pure calculating skill) they will make better judgments faster than you in random positions as well as calm positions.</p>

<p>No, what I would advise against both much stronger and much weaker players is rather banal. With Spock-like detachment and lack of emotion play the position not the man (or woman). Do not try and play an ELO rating! When it is your turn just try and find the objectively best move and play it.</p>

<p>I have seen master level players come unstuck by playing the ELO rating or the man rather than the position. In one case, knowing that they were a much better endgame player they coasted through the opening and middlegame into an endgame the stubborn weaker player managed to draw. I will dig up an example game and post later.</p>

<p>Preparation before the game is a different matter. If your opponent has a particular known weakness or you have a particular strength then by all means try and steer the game in that direction. Having white can be a big advantage here as it lets you cut down the possibilities but sometimes you can also do this with black. </p>

<p>When it comes to preparation the randomizing advise can get a chance. If you've played the player before with the same colours and you see a chance to divert the opening the pair of you played last time into a particularly tactical variation then prepare, study and unleash this variation if you get the chance. If nothing else it is very likely to gain you time on the clock and it may just be your lucky day. But ad hoc randomizing during the game is something I would advise against.</p>
 75: <p>Here's another point worth mentioning: you could try to steer the game into a draw by threefold or a tactic-less position (first two draws are not about what I'm saying here):</p>

<p><a href="http://www.chessgames.com/perl/chesscollection?cid=1008234" rel="nofollow noreferrer">http://www.chessgames.com/perl/chesscollection?cid=1008234</a></p>

<p>If you're the much lower rated player I think in the short term this is the best you can do. In the long term, learn more about chess and turn your weaknesses into strengths.</p>
 17: <p>Against a weaker player, figure out why he is weak. Maybe he is playing "strongly" because he has "booked up." So take him out of book lines. Maybe he is strong in strategy and weak on tactics (or vice versa). So steer the game into areas where he is weaker.</p>

<p>In my case, against stronger players, self-administered tests show that my "1500" strength is a composite of 1800 opening and endgame strength and 1400 middle game strength. Against, say, a 1700 player, I would look for variations such as the Exchange variation of the Ruy Lopez that exchanges queens early and gets into an early endgame, bypassing the middle game that I'm weak at.</p>

<p>If a decidedly weaker player (more than 200 points difference) wins (or draws) against a stronger player, one of two things may be happening: 1) The weaker player is having a "good" day and the stronger player a "bad" day or 2) The weaker player has recently gotten strong, but this is not yet reflected in his rating.</p>
 142: <p>While I agree with Quantum Elf's general rule, there is also an advantage to complicating the position for someone much weaker (perhaps this applies to the weaker opponent being &lt;1500). If you're able to calculate possibilities quicker than your opponent, moving into a tactical position intentionally will give you more opportunities to capitalize on any tactical mistakes they make.</p>
 107: <p>The general rule is:</p>

<ol>
<li>Against weaker opponents, try and simplify the position.</li>
<li>Against stronger opponents, try and complicate the position.</li>
</ol>

<p>The reasoning is that a strong player will falter more in a complicated position than he would in a "dry", boring position. Against much higher rated opponents, go for wild tactical melees and crazed positions. </p>

<p>In a "normal" game, the stronger player will simply wait and improve his position until the weaker player gives him something. As just an example, after a equal position after N moves, let's say that the 2100-rated player castles kingside "N+1" moves into the game, and then the next move by the 1500-rated player castles queenside, with the notable difference that no pawns are moved in front of the 2100's king, and the 1500's king has the a6-pawn sticking out. Bam! You just gave him something. The 2100 player would roll the queenside pawns forward and "hook" that a6-pawn. All things being equal you can count on the 2100 player's attack crashing through first.</p>

<p>I will emphasize that no matter who the opponent, that chess is a mix of prophylaxis (e.g. preventing counterplay) and aggression. Take time to study your plans, but don't forget about your opponent. Q: When should you be on the lookout for your opponent's possibilities? A: Every move.</p>
 12: <p>Statistically speaking, a 600 point rating disadvantage means that you have about a <a href="http://en.wikipedia.org/wiki/Elo_rating_system#Mathematical_details">3.07%</a> chance of winning.  If you want to improve that, your best bet is to play a position that you are familiar with.  </p>

<p><sup>This part of the answer might be more pertinent to a 2000 player playing a 2200 player</sup><br>
One way to do this is to play an opening that you know intimately.  If you have a pet line, this is the time to play it.  Especially if you've analyzed an unusual opening with a computer, this will shorten the odds.  Basically, the 3200+ rated computer will be playing your opponent for you.<br>
<sub>Ok, that's it for opening preparation</sub></p>

<p>One common suggestion is to randomize the position if you are the weaker player.  This makes a lot of sense.  Chances are that the stronger player is also better at endgames.  So you don't want to get to the endgame unless you will win easily.  I've frequently beaten lower rated players from an equal endgame or even an endgame where I'm a little worse.  </p>

<p>In a "randomized" position, usually multiple pieces are hanging, one or both kings are weak, and most of the pieces are still on the board.  Now, unfortunately, truly good players thrive in these positions, and they will work out all the complications.  But you're probably not playing a 2600+ grandmaster, so this is still not a bad idea.  In these random positions, both players will be forced to use most of their time to make their way along the "narrow path".<sup>[1]</sup>  Once the players are deep in time pressure, anything can happen.<sup>[2]</sup>  </p>

<p>This is <em>NOT</em> to say you should make bad moves.  If at any point you make inferior moves, well, the stronger opponent will probably take advantage of them.  Instead, just keep pieces on the board.  One trick you can use to complicate - when a piece is attacked, instead of moving it or defending it, just attack one of your opponent's pieces.  This is much easier said than done, but this will quickly complicate even a mundane position.</p>

<hr />

<p>Ok, if you've made it this far, just a few more general thoughts.  The easiest way to beat a stronger player is to just get lucky.  Everyone has a bad day from time to time, you just have to be playing someone who happens to make a mistake and take advantage of it.  The key to this is to not make any terrible mistakes.  If you can stay in the game and not lose material, you can always win - even if you have a bad position.  </p>

<p>Double check every move before you make it.  If you see a move that you think wins, spend <em>more</em> time than usual, don't make this move quickly.  If you're right, being behind on the clock won't really matter.  If you're wrong, you won't make an inferior move.  One saying that I've always found helpful is "never play a blunder quickly" (source unknown).  </p>

<p>Personally, I'm not convinced that the right plan is to just complicate the position and hope.  While this is a good plan of last resort, everyone plays with the same 16 pieces.  Make solid moves, calculate everything you need to, and be inspired to play well.  Even if you lose, you'll learn far more from a well played game that you just barely lost than a game where one of the players blundered on move 12.</p>

<hr />

<p>Lastly, some rules that have helped me against lower rated players in the past:  </p>

<ul>
<li>Don't be afraid of endgames, even if it should be drawn with best play</li>
<li>Similarly, don't be afraid of equal positions</li>
<li>A small advantage is often enough to win, but even if you are down material, swindles are often possible, so don't give up.</li>
<li>Finally, as a stronger player, I've had good luck in complicated positions.  As likely as it is for a stronger player to blunder, it is even more likely for the lower rated player to also blunder.  </li>
</ul>

<hr />

<p>[1]: David Bronstein: "When you play against an experienced opponent who exploits all the defensive resources at his command you sometimes have to walk time and again, along the narrow path of 'the only move'."<br>
[2]: Lev Alburt: (paraphrased from <a href="http://rads.stackoverflow.com/amzn/click/1889323101">http://www.amazon.com/Chess-Rules-Thumb-Lev-Alburt/dp/1889323101</a>) "Having 15 minutes when your opponent has 5 is worth 200 rating points."</p>
