2 rooks 2 bishop = queen 2 rooks
I'm not sure about that one ^
2 rooks 2 bishop = queen 2 rooks
I'm not sure about that one ^
It's true! But you need to get all the minor pieces off the board. Your king must be safe so you can his king unsafe.
I don't know about that. Lasker showed that if the sacrificer's pieces can become active it is very easy to overpower the queen. Kasparov obviously didn't trust the instability of the sac. But he didn't trust Lasker's activity = instability in general.
I.e two knights + bishop = Queen
two bishops + knight is slightly stronger than Queen | Cetirus Paribus
Two rooks, if they can work together, are about equal to a queen.
Only if the hostile king is protected against checks from the Queen, otherwice it may seem the Queen may be stronger. Generally speaking the Queen is trifle weaker than two Rooks | Ceteris Paribus.
If the point value is approximately the same, other factors like activity, initiative, king safety if there is enough material on the board, and the potential to make a passed pawn weigh in significantly
If the point value is approximately the same, other factors like activity, initiative, king safety if there is enough material on the board, and the potential to make a passed pawn weigh in significantly
That is true. The material alone isn't enough for positional considerations.
2 rooks 2 bishop = queen 2 rooks
I'm not sure about that one ^
It's true! But you need to get all the minor pieces off the board. Your king must be safe so you can his king unsafe.
This is an interesting manifestation of the 'elephantiasis effect', which is the same effect that makes 7 Knights in general superior to 3 Queens:
Stronger pieces devaluate by the presence of enemy weaker pieces, as the latter interdict access to part of the board for them, in order to avoid 1-for-1 trading. In general, the need to use a trade-avoiding strategy makes a piece less useful. So in general the material balance cannot be computed by simple addition of piece values, but has to take into account these non-linear interactions.E.g. with only black Knights and white Queens you would have
material balance = 11.1*Queens - 3*Knights - 0.7*Knights*Queens
In the Q+2R vs 2R+2B case, the Q suffers from all enemy Rooks and Bishops. And the Rooks that fight with the Queen also suffer from the Bishops. The Rooks on the other side only lightly suffer from the opponnet Rooks, as they have to avoid trading down to Q vs 2B. So the Q+2R side suffers much more devaluation.
3 minors = queen
1 rook 1 piece 1 pawn = queen
2 rooks 2 bishop = queen 2 rooks
What else?