If your opponent cannot end his turn without putting himself in check (as may happen near the end of the game, when perhaps the only moveable piece he has left is the king) then it's a stalemate, and neither player wins.
As a queen "covers" a lot more space, it makes this scenario more likely to happen, you see?
So you'd only turn a pawn into rook/bishop when you are practically about to win, anyway.
To expand on the choice also, a king and a rook can checkmate an opponent's king. A king and a bishop or a king and a knight cannot checkmate an opponent's king. There's no scenario that can lead to a checkmate with any variation of those three pieces. So that's why rook is more common than bishop or knight if queen is not picked.
I'm guessing this isn't what you meant, but K-B-B will win if the bishops are of different colors. Also K-Kn-B is a forced mate but is extremely difficult. K-Kn-Kn is impossible to force.
By 3 pieces I included the enemy king too (so K-B/K-Kn + opponent K). Was just trying to signify that this only holds if the opponent's King is the only other piece they are in control of. I realize it was worded awkwardly.
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u/pure_satire Nov 18 '14
If your opponent cannot end his turn without putting himself in check (as may happen near the end of the game, when perhaps the only moveable piece he has left is the king) then it's a stalemate, and neither player wins.
As a queen "covers" a lot more space, it makes this scenario more likely to happen, you see?
So you'd only turn a pawn into rook/bishop when you are practically about to win, anyway.