2 rooks or a Queen?

This is a very controversial question. People posted a lot of discussions on the issue. Basically, it is quite a personal favor and depends on great varieties of the chessboard.

let's just assume there are 2 rooks and a Queen, all pawns are stripped. my opinion is, the queen attack direction is a point source, but 2 rooks can be from totally difference direction(row an columns). The total square covered by a Queen is 7x4+1=29, which is 45% of the board. the 2 rooks, if they are not covering each other, it can cover at almost 7x4-2+2=28, a little smaller. If the 2 rooks are on the same row or column, the covered area reduced to 22, 7 squares lesser, which almost a row. however, since the tools are covered each other, they are not threaten by the queen any more. while a single queen movement is truly restricted.

in order I checkmate, the Queen has to work together with the King. the only way to checkmate is the King pushing the other King in close range. in case of 2 rooks, the checkmate can be done by theirs own as long as they are not on same file. thus, If the queen can forcing the rooks on same files and moving her king toward the other king. possible checkmate.

this is an ideal case, since the 2 rooks can also get help from their king to not occupy the same file by staying close to their king. this also proving a castle for the king to avoid check and forcing draw.

now, we think about checking and avoiding checking in the queen side. to check the queen's king, the rooks have to put on the same file of the king. if the queen is on the same file of the king, the number of possible checking square is 5 for a single rook. for 2 rooks, as they are not threaten by the queen, they can always check, either directly or behind the queen. in fact, the Queen should be avoid to stay on the same file with her king, otherwise, a pinning will loss the queen! thus, the danger square of the queen or the effective cover area of 2 rooks is 28.

In the 2 rooks side, their king can be attacked from any direction if the rook are far away. however, when the rooks are near, the possible attack direction reduced to 1.

OK, i am tried. the last thing we should think about is the possibly of forking a single rook.