Obviously a lot is going to depend on the exact position, but I'm asking if there are any general signposts - e.g. bishops usually get better than knights if the position is open, or in an endgame, but I can't say the same about Q vs 3 minors.
The queen does a good job when there are a lot of weaknesses to attack, especially if the opponent's king is out in the open, so there are a lot of options for double attacks.
The pieces are generally stronger if they can coordinate and the king is still relatively safe. Earlier in the game that's usually the case.
A lot depends on whether there are other pieces involved and the pawn structure.
If you mean positions with Q alone vs three minor pieces then relative king safety comes into play. The side with the Q tries to expose the opponents king and harass it.
The Q alone side may need to create connected passed pawns to make progress since the pieces should easily cope with a single passed pawn by twice covering the square in front of the passed pawn.
However, the side with three pieces may need to only create a single passed pawn to create winning chances.
Also, the three pieces side would find it easier to create fortress type positions at least to avoid defeat.
Personally, I would prefer to play the three pieces for the previous two reasons.
But (there's always a but!) in blitz time formats I would prefer the Q!
(As an aside, I once drew a strong IM in a regular tournament game with only two pieces v Q and equal pawns by setting up a fortress.)
I don't have a chess database but someone who does may be able to research positions with just Q vs three minor pieces and provide some statistics.
Generally speaking the queen is going to be better when the opponent's king is exposed to checks and/or when the position is "loose" ie pieces and pawns hanging, pawn weaknesses etc.
If the side without the queen can hold the position together and push a passed pawn there isn't really anything the queen can do.
For me I belive that the Queen is worth 3 pieces for a variety of reasons,
It combines the functionality of the Rook and the Bishop, the Bishop, which act like snipers in the early-mid game, are very valuable, because of their sniper-like capability, whereas the rook is bad in the early stages of the game, because the board is crammed usually, conversely, in the Endgame, Rooks are better, because they allow you to occupy an area and put up a wall that the king cannot cross, by the definition of a bishop, since they are on a single color diagonal, it requires 2 Bishops to create an inescapable wall for the king, the Queen provides for both of these, by being able to snipe pieces on the outskirts with its bishopesque range, and it can wall of sections of the board at the endgame because it can cross multiple colors like the rook
This is more of an extension of the last point, but its your main offensive tool, overall, Rooks are best in the Endgame, Bishops and Knights are great in the Mid game, but the Queen can function almost anywhere, they also exceed in their ability I call the "Royal Attack" because of its long Range, devastating attacks and multitude of directions, it is often used to attack 3 or more pieces at one, where as the Knight can fork but not pin pieces, and the bishop can not fork but can pin pieces, the Queen combines all the functionality into 1, therefore in most situations, if you lose your queen, unless it was a mistake on you opponents move, thus leading to a delayed trade, or mate, its usually time to resign as most of you offense is gone
The Queen is also great at counter-attack, for example in this trap from the Queens Gambit:
- d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. Nf3 d5 5. Qa4+ Kf8 6. Qxb4+ Ke8
Please see in action the famous games from the grandmasters demonstrating the combat dynamics of a Queen versus three minor pieces. No English language can explain the entire dynamics. You must see it for your self.
I am presuming things such as pawns, bishops and knights count as minor pieces for what my answer will be.
Queen > 3 Minor Pieces
In the case that there is a way that you could get a checkmate, but you need to make a risk with what your opponent will notice and what he/she won't notice. You could try to put 3 pieces to get your opponent to take those helping you to get your checkmate. Then there is the case for AI which takes every place into consideration. For AI it would have to be pawns or perhaps making it be that your opponent is forced to take certain pieces.
For the second for AI 'forcing your opponent to take certain pieces' with that I mean that they are in a check or that piece being there is going to lead to a checkmate.
In the case that you want a minimal risk then I would say it would be best to save your queen and try to keep it because it can help create many forks.
3 Minor Pieces > Queen
With 3 minor pieces there is the obvious case getting 3 pawns to the end to become queens, but I will presume that it would be banned for 2 reasons.
- It is more challenging and move and noticeable.
- It is making a minor piece become a major piece.
- With three pieces there are more combinations that you can use to get a checkmate, or defend your king. If the opponent's king is trapped with their own pieces then you can use just your knight to get a checkmate where as it would be hard to get a checkmate with your queen for it would need lots of setting up.
generally speaking with 3 pieces is good due to numbers
I am not saying that one of them is always better. I am just stating the cases. If I had to pick between the two in a case that I don't know as in I can't see the situation for some reason I would go for keeping 3 pieces instead of losing my queen.
Keep in mind that people have their play style. You might prefer keeping your queen or keeping 3 minor pieces depending on your play style.