user19411: Many years ago, I was on a mountain with some people. I was very young then, between 15 and 17 years old, I think. Some older people came and one of them started to play chess with me.
I cannot recall all the details, but at one moment in the game he captured my queen and I continued to play without it. Besides being without queen, he might have had 1 or 2 of my pawns and a bishop. I also had 1 or 2 his pawns, along with 1 or 2 of his bishops.
Then I started to play very smartly, and, somehow, I manged to capture his queen with a trap made by using rooks and knights. I won the game after that.
Obviously, this is not a question about the particular game I played on the mountain. It is more about, if someone loses his queen at the beginning of the game, what are the tactics to trap and capture the other player's queen?
And also, what is the actual strength of a queen? For example, is it generally better to be without queen or without two knights and a rook but with a queen?
I would like to know more about tactics when some player lost some important pieces, but played so well that he won the game. Are there any tricks that can be used here? I am also interested in such a game in which one player loses their queen, but the other one still has theirs.

user19420: I played a game recently where I lost my queen for a knight early on with no other obvious compensation or counterplay.  I almost resigned, but decided to play on for a few moves to see if I could get anything, and ended up winning.
The approach I used was to try and keep pieces on the board, as mentioned in another answer, as any simplification is usually bad if you're down material.  Other strategies I used were - to keep attacking their queen; and generally favouring development, coordination, disruption of their position, and piece activity, over material (e.g. not capturing the dark square bishop in the game - link below).
https://lichess.org/zlVS5Nhj

user18809: Unless there is a clear chance for counterplay, losing your queen means losing the game. You won that game because your opponent was a very bad player.
With regards to the strength of the queen, there is no definite answer, as every position is different. However, as a general guideline:

Two rooks are slightly more powerful than a queen.
A rook and a minor piece(bishop/knight) is slightly weaker than a queen.
Two minor pieces vs a queen often means a lost position.
Three minor pieces are also slightly stronger than a queen

Some folks will come with a "points system", well, that's just  plain wrong.
Finally, queens are a very bad piece at blocking enemy advancing pawns, so that may be a source of counterplay in "otherwise worse" positions.
NOTE Since my statement about the pointing system was received with controversy in the comments, let me elaborate a bit further (even though this is beyond the scope of the original question, it's still related and interesting):

Any scoring system you can think of will always be inaccurate, because we cannot define a total order relation in the "set of piece tandems" that actually models the "is more likely to be stronger than" relation. Even if we could, it wouldn't work well with addition/subtraction (R+6P - N+8P is more likely a rook-side win, but R vs N+2P is more likely to be a knight-side win)
Piece strength can vary a lot from one position to another, so, even if it were possible to define such scoring system, it would overlook a lot of exceptions and, more importantly, it would give us no criterion about when those exceptions happen.
Finally, a "one-point advantage" grows in importance as the game gets simplified, so we don't get a good reference either about how well/badly the game is going for us (even if we only care about material)

For those reasons, I think every score-system is wrong (not even entering the discussion of which one would be right, since different people have had different opinions). But all of that does not really matter that much, even if we ignore 1 and 3, the second issue would still be there, and it's quite an important one! It you learn to think in terms of a scoring system, you will eventually have to un-learn all of that and, from my own experience, I can tell you that's really hard! The main problem is therefore that the scoring system is not useful in practice! It does not provide any help in your game and it makes progress more difficult.
@user1583209 pointed out that computers use the points system quite succesfully. Well, that's simply not the full story! Computer position evaluation has worked very differently for a long time, and even if it were the case, there is pretty much nothing to learn from computers in terms of "how to think" as a human

user10687: Play the board, not the pieces. Chess is more than just a game of material advantage--much like war. This is why piece sacrifices exist.
Take for example the following game:


[FEN ""]
[White "Fabiano Caruana (2823)"]
[Black "Hikaru Nakamura (2779)"]

    1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 { Caruana had not expected Nakamura to play the Najdorf. } 6. Bg5 e6 7. f4 h6 8. Bh4 Qb6 9. a3 { Note b2 is a poisoned pawn and trap for black queen. } 9... Be7 (9... Qxb2 10. Na4) 10. Bf2 10... Qc7 11. Qf3 Nbd7 12. O-O-O b5 13. g4 { Notice either push of pawns is easily met with resistance from end pawns. } 13... g5 { Push of g pawn threatens f pawn with potential setup for knight on e5 (see variation). } 14. h4 (14. fxg5 Ne5) 14... gxf4 15. Be2 b4 { Interesting sacrifice of b pawn. } 16. axb4 Ne5 17. Qxf4 Nexg4 { A second sacrifice for black to that will do well for him. } 18. Bxg4 e5 { With this fork, three of white's pieces are threatened. } 19. Qxf6 Bxf6 20. Nd5 Qd8 { More precise is knight to c6 (see variation). } 21. Nf5 (21. Nc6) 21... Rb8 { Nakamura spent 35 minutes analyzing the position and decided on Rb8, preventing white's threat of Bb6. } 22. Nxf6+ Qxf6 23. Rxd6 Be6 24. Rhd1 O-O 25. h5 { White prepares for Bh4. } 25... Qg5+ { In an effort to stall/prevent Bh4. } 26. Be3 Qf6 27. Nxh6+ Kh8 { As we will see, white will play Nxf7, but could have played it now. } 28. Bf5 Qe7 29. b5 Qe8 30. Nxf7+ Rxf7 31. Rxe6 Qxb5 32. Rh6+ { 1-0 Black resigns. } { Possible continuation: } 32... Kg8 33. Rg1+ Kf8 34. Rh8+ Ke7 35. Rxb8 Qxb8 36. Bc5+ Kd8 37. Rg8+ Kc7 38. Bd6+ Kxd6 39. Rxb8 { White is now up a bishop and two pawns. } 1-0


Caruana sac'ed his queen and gained so much space, position, and tempo versus black's side.
Also this game:


[FEN ""]
[White "Rashid Gibiatovich Nezhmetdinov"]
[Black "Oleg L Chernikov"]
[Result "1-0"]
[Termination "Normal"]
[ECO "B35"]
[Opening "Sicilian Defense: Accelerated Dragon, Modern Bc4 Variation"]

1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 g6 5. Nc3 Bg7 6. Be3 Nf6 7. Bc4 O-O 8. Bb3 Ng4 9. Qxg4 Nxd4 10. Qh4 Qa5 11. O-O Bf6 12. Qxf6 Ne2+ 13. Nxe2 exf6 14. Nc3 Re8 15. Nd5 Re6 16. Bd4 Kg7 17. Rad1 d6 18. Rd3 Bd7 19. Rf3 Bb5 20. Bc3 Qd8 21. Nxf6 Be2 22. Nxh7+ Kg8 23. Rh3 Re5 24. f4 Bxf1 25. Kxf1 Rc8 26. Bd4 b5 27. Ng5 Rc7 28. Bxf7+ Rxf7 29. Rh8+ Kxh8 30. Nxf7+ Kh7 31. Nxd8 Rxe4 32. Nc6 Rxf4+ 33. Ke2 { 1-0 Black resigns. } 1-0



Through shear inundation of threat after threat, Nezhmetdinov creates a formidable attack even apart from his queen.
Chess cannot be simplified to just piece/material advantage. There are more elements at play.

user11629: Losing a queen early on without any compensation or counterplay means almost certain defeat against anybody except for absolute beginners. 
There is a certain "point system" which can be used to evaluate a position:
Basically you assign points to certain aspects of the position, like material, piece activity, king safety, space advantage, etc. Adding all those points (with weights depending on the aspects), you come up with a final number, for instance -2. The sign (-) means black is better and the number 2 means that all other things being equal, black could be up by 2 pawns. Of course it could also mean that material is equal and black has much more active pieces, etc.
Just for the material aspect the points assigned to the pieces is usually pawn: 1, knight/bishop: 3, rook: 5, queen: 9 (see this for details) or thereabout.
While this point system is used by computers, for practical play it is not really relevant. I don't know any decent player who would start adding numbers to assess a position.
Still you can use it to answer your question...
Looking at games of top players, within an evaluation of roughly -1 to + 1, i.e. at most a pawn up (all other things being equal), the game usually ends in a draw.
Around +-2, the game would usually be lost/won at GM/IM level, though people might still fight for a while depending on the position.
Around +-3, good players would typically resign immediately.
Of course there are exceptions to this rule and particularly in very tactical/wild positions with open kings and attacking potentials, there could be chances for the losing side.
Still it could give you an idea of what losing a queen (value 9) means...


I would like to know more about tactics when some player lost some important pieces, but played so well that he won the game. Are there any tricks that can be used here? I

The word you mean is "strategy" not "tactics". As outlined above, most people would resign in a situation like you describe. Still, if you think your opponent is weak enough to continue fighting there are a few things you can do to increase your chances:

keep many pieces on the board (don't exchange pieces): this increases the potential for tactics
keep the position complicated: typically this means open positions with lots of piece activity
start a direct attack on the enemy king
if time is limited try to force your opponent getting low on time, e.g. by moving quickly, doing unusual moves, etc.
play for tricks/tactics (you really should never do this in chess because it is not how you play chess beyond a certain level...)


19411: <p>Many years ago, I was on a mountain with some people. I was very young then, between 15 and 17 years old, I think. Some older people came and one of them started to play chess with me.</p>

<p>I cannot recall all the details, but at one moment in the game he captured my queen and I continued to play without it. Besides being without queen, he might have had 1 or 2 of my pawns and a bishop. I also had 1 or 2 his pawns, along with 1 or 2 of his bishops.</p>

<p>Then I started to play very smartly, and, somehow, I manged to capture his queen with a trap made by using rooks and knights. I won the game after that.</p>

<p>Obviously, this is not a question about the particular game I played on the mountain. It is more about, if someone loses his queen at the beginning of the game, what are the tactics to trap and capture the other player's queen?</p>

<p>And also, what is the actual strength of a queen? For example, is it generally better to be without queen or without two knights and a rook but with a queen?</p>

<p>I would like to know more about tactics when some player lost some important pieces, but played so well that he won the game. Are there any tricks that can be used here? I am also interested in such a game in which one player loses their queen, but the other one still has theirs.</p>
 19420: <p>I played a game recently where I lost my queen for a knight early on with no other obvious compensation or counterplay.  I almost resigned, but decided to play on for a few moves to see if I could get anything, and ended up winning.</p>

<p>The approach I used was to try and keep pieces on the board, as mentioned in another answer, as any simplification is usually bad if you're down material.  Other strategies I used were - to keep attacking their queen; and generally favouring development, coordination, disruption of their position, and piece activity, over material (e.g. not capturing the dark square bishop in the game - link below).</p>

<p><a href="https://lichess.org/zlVS5Nhj" rel="nofollow noreferrer">https://lichess.org/zlVS5Nhj</a></p>
 18809: <p>Unless there is a clear chance for counterplay, losing your queen means losing the game. You won that game because your opponent was a very bad player.</p>

<p>With regards to the strength of the queen, there is no definite answer, as every position is different. However, as a general guideline:</p>

<ul>
<li>Two rooks are slightly more powerful than a queen.</li>
<li>A rook and a minor piece(bishop/knight) is slightly weaker than a queen.</li>
<li>Two minor pieces vs a queen often means a lost position.</li>
<li>Three minor pieces are also slightly stronger than a queen</li>
</ul>

<p>Some folks will come with a "points system", well, that's just  plain wrong.</p>

<p>Finally, queens are a very bad piece at blocking enemy advancing pawns, so that may be a source of counterplay in "otherwise worse" positions.</p>

<p><strong>NOTE</strong> Since my statement about the pointing system was received with controversy in the comments, let me elaborate a bit further (even though this is beyond the scope of the original question, it's still related and interesting):</p>

<ul>
<li>Any scoring system you can think of will always be inaccurate, because we cannot define a <a href="https://en.wikipedia.org/wiki/Total_order" rel="nofollow noreferrer">total order relation</a> in the "set of piece tandems" that actually models the "is more likely to be stronger than" relation. Even if we could, it wouldn't work well with addition/subtraction (R+6P - N+8P is more likely a rook-side win, but R vs N+2P is more likely to be a knight-side win)</li>
<li>Piece strength can vary a lot from one position to another, so, even if it were possible to define such scoring system, it would overlook a lot of exceptions and, more importantly, it would give us no criterion about when those exceptions happen.</li>
<li>Finally, a "one-point advantage" grows in importance as the game gets simplified, so we don't get a good reference either about how well/badly the game is going for us (even if we only care about material)</li>
</ul>

<p>For those reasons, I think every score-system is wrong (not even entering the discussion of which one would be right, since different people have had different opinions). But all of that does not really matter that much, even if we ignore 1 and 3, the second issue would still be there, and it's quite an important one! It you learn to think in terms of a scoring system, you will eventually have to un-learn all of that and, from my own experience, I can tell you that's really hard! The main problem is therefore that the scoring system is not useful in practice! It does not provide any help in your game and it makes progress more difficult.</p>

<p>@user1583209 pointed out that computers use the points system quite succesfully. Well, that's simply not the full story! Computer position evaluation has worked very differently for a long time, and even if it were the case, there is pretty much nothing to learn from computers in terms of "how to think" as a human</p>
 10687: <p>Play the board, not the pieces. Chess is more than just a game of material advantage--much like war. This is why piece sacrifices exist.</p>

<p>Take for example the following game:</p>

<pre>
<code>
[FEN ""]
[White "Fabiano Caruana (2823)"]
[Black "Hikaru Nakamura (2779)"]

    1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 { Caruana had not expected Nakamura to play the Najdorf. } 6. Bg5 e6 7. f4 h6 8. Bh4 Qb6 9. a3 { Note b2 is a poisoned pawn and trap for black queen. } 9... Be7 (9... Qxb2 10. Na4) 10. Bf2 10... Qc7 11. Qf3 Nbd7 12. O-O-O b5 13. g4 { Notice either push of pawns is easily met with resistance from end pawns. } 13... g5 { Push of g pawn threatens f pawn with potential setup for knight on e5 (see variation). } 14. h4 (14. fxg5 Ne5) 14... gxf4 15. Be2 b4 { Interesting sacrifice of b pawn. } 16. axb4 Ne5 17. Qxf4 Nexg4 { A second sacrifice for black to that will do well for him. } 18. Bxg4 e5 { With this fork, three of white's pieces are threatened. } 19. Qxf6 Bxf6 20. Nd5 Qd8 { More precise is knight to c6 (see variation). } 21. Nf5 (21. Nc6) 21... Rb8 { Nakamura spent 35 minutes analyzing the position and decided on Rb8, preventing white's threat of Bb6. } 22. Nxf6+ Qxf6 23. Rxd6 Be6 24. Rhd1 O-O 25. h5 { White prepares for Bh4. } 25... Qg5+ { In an effort to stall/prevent Bh4. } 26. Be3 Qf6 27. Nxh6+ Kh8 { As we will see, white will play Nxf7, but could have played it now. } 28. Bf5 Qe7 29. b5 Qe8 30. Nxf7+ Rxf7 31. Rxe6 Qxb5 32. Rh6+ { 1-0 Black resigns. } { Possible continuation: } 32... Kg8 33. Rg1+ Kf8 34. Rh8+ Ke7 35. Rxb8 Qxb8 36. Bc5+ Kd8 37. Rg8+ Kc7 38. Bd6+ Kxd6 39. Rxb8 { White is now up a bishop and two pawns. } 1-0
</code>
</pre>

<p>Caruana sac'ed his queen and gained so much space, position, and tempo versus black's side.</p>

<p>Also this game:</p>

<pre>
<code>
[FEN ""]
[White "Rashid Gibiatovich Nezhmetdinov"]
[Black "Oleg L Chernikov"]
[Result "1-0"]
[Termination "Normal"]
[ECO "B35"]
[Opening "Sicilian Defense: Accelerated Dragon, Modern Bc4 Variation"]

1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 g6 5. Nc3 Bg7 6. Be3 Nf6 7. Bc4 O-O 8. Bb3 Ng4 9. Qxg4 Nxd4 10. Qh4 Qa5 11. O-O Bf6 12. Qxf6 Ne2+ 13. Nxe2 exf6 14. Nc3 Re8 15. Nd5 Re6 16. Bd4 Kg7 17. Rad1 d6 18. Rd3 Bd7 19. Rf3 Bb5 20. Bc3 Qd8 21. Nxf6 Be2 22. Nxh7+ Kg8 23. Rh3 Re5 24. f4 Bxf1 25. Kxf1 Rc8 26. Bd4 b5 27. Ng5 Rc7 28. Bxf7+ Rxf7 29. Rh8+ Kxh8 30. Nxf7+ Kh7 31. Nxd8 Rxe4 32. Nc6 Rxf4+ 33. Ke2 { 1-0 Black resigns. } 1-0

</code>
</pre>

<p>Through shear inundation of threat after threat, Nezhmetdinov creates a formidable attack even apart from his queen.</p>

<p>Chess cannot be simplified to just piece/material advantage. There are more elements at play.</p>
 11629: <p>Losing a queen early on without any compensation or counterplay means almost certain defeat against anybody except for absolute beginners. </p>

<p>There is a certain "point system" which can be used to evaluate a position:</p>

<p>Basically you assign points to certain aspects of the position, like <em>material</em>, <em>piece activity</em>, <em>king safety</em>, <em>space advantage</em>, etc. Adding all those points (with weights depending on the aspects), you come up with a final number, for instance -2. The sign (-) means black is better and the number 2 means that all other things being equal, black could be up by 2 pawns. Of course it could also mean that material is equal and black has much more active pieces, etc.</p>

<p>Just for the material aspect the points assigned to the pieces is usually pawn: 1, knight/bishop: 3, rook: 5, queen: 9 (see <a href="https://en.wikipedia.org/wiki/Chess_piece_relative_value" rel="noreferrer">this</a> for details) or thereabout.</p>

<p>While this point system is used by computers, for practical play it is not really relevant. I don't know any decent player who would start adding numbers to assess a position.</p>

<p>Still you can use it to answer your question...</p>

<p>Looking at games of top players, within an evaluation of roughly -1 to + 1, i.e. at most a pawn up (all other things being equal), the game usually ends in a draw.</p>

<p>Around +-2, the game would usually be lost/won at GM/IM level, though people might still fight for a while depending on the position.</p>

<p>Around +-3, good players would typically resign immediately.</p>

<p>Of course there are exceptions to this rule and particularly in very tactical/wild positions with open kings and attacking potentials, there could be chances for the losing side.</p>

<p>Still it could give you an idea of what losing a queen (value 9) means...</p>

<hr>

<blockquote>
  <p>I would like to know more about tactics when some player lost some important pieces, but played so well that he won the game. Are there any tricks that can be used here? I</p>
</blockquote>

<p>The word you mean is "strategy" not "tactics". As outlined above, most people would resign in a situation like you describe. Still, if you think your opponent is weak enough to continue fighting there are a few things you can do to increase your chances:</p>

<ul>
<li>keep many pieces on the board (don't exchange pieces): this increases the potential for tactics</li>
<li>keep the position complicated: typically this means open positions with lots of piece activity</li>
<li>start a direct attack on the enemy king</li>
<li>if time is limited try to force your opponent getting low on time, e.g. by moving quickly, doing unusual moves, etc.</li>
<li>play for tricks/tactics (you really should never do this in chess because it is not how you play chess beyond a certain level...)</li>
</ul>
