Reasons why king and rook mate quicker than king, knight/bishop and bishop?

When I was very young I remember learning the point values of the pieces. And then I ran into something very confusing.

I was able to learn king and rook vs king mates pretty easily, but king and 2 bishops was trickier--and bishop/knight took me much longer to learn.

This confused me. B+B/B+N = 6 points > R = 5 points. So I did not understand why the rook did things more quickly. Was it just me seeing things linearly, or was there something about how pieces interacted?

I have some ideas for how to express this simply, but nothing concrete. It seems like there should be such an explanation.

• It gets even more confusing if you add more pieces. KNN can draw against KQ, but KBN and KBB (in generally) do not. But as you probably know KNN only draws against K alone, while KBN and KBB can win. And vs. KRB, KNN lose (even though RB is 8 points and a Q is 9), but KBB draw and KBN as well if the bishops have the same color. Sep 7 '16 at 13:11
• If nothing else, more pieces required to mate means more pieces to move means it gets more complicated (as one of the answers points out, due to coordination) Sep 7 '16 at 15:29
• @Michael very plausible intuitive answer. With R, everytime you move, you improve a value 5 piece. With 2 minor, everytime you move, you improve a value 3 piece, so it takes longer. Sep 7 '16 at 16:07
• Is that an apples to apples comparison? R+R = 10 points. Sep 7 '16 at 21:13
• I guess a king and 4 white-squared bishops should be able to mate even faster than a king and queen? 12 points to 9, right?
– bof
Sep 8 '16 at 6:14

King and Rook mate faster because the 2 pieces coordinate better together.

Recall that the mating procedure for King and Rook is about making a box with the Rook, then making that box smaller. This is quite straight forwards. Compare this to mating with King, Bishop and Knight, which is hard even for masters!

This brings me to discuss your misconception on the point value of the pieces. They relate to trading pieces. So if you trade Rook and Pawn (6 units) for 2 minor pieces (6 units), then on a point only basis, material is even.

Note also that the point value system is a guideline. It is not a cast iron law of the universe. In the example above, which side is better after trading Rook and Pawn for 2 minor pieces depends on the concrete position. But that is a different topic.

• Thanks. Now that you mention it, I remember having no problem accepting that Q&N work better than Q&B, while R&B work better than R&N. But I never put it together. In this case, the B/N are close enough in value I was willing to be more flexible considering what was more valuable, when. Sep 7 '16 at 13:13

Yes, a rook is worth less than two bishops (five versus six).

But a rook offers more concentrated power in one piece. To utilize the "six," you need to move two pieces rather than one. Add your king to both the rook on one hand, and the two bishops on the other hand, and you realize that it is easier to manage two pieces rather than three.

Even if the "three" are worth a little more. This is particularly true when the "third" piece is a knight rather than a bishop. The two bishops control squares of both colors between them, but the knight controls squares of opposite color to the bishop only half the time.

Note, that a Rook alone can block a whole rank or file, enabling the king to get into position alone.

B+B and B+N cannot do this.

• B+B can block two adjacent diagonals, with is effectively the same as a rank or file. Sep 7 '16 at 14:58
• @Glorfindel : not exactly. Maybe similar when the opponent's King is in the center, but not when near the corner. With a Rook you can repeat the same algorithm line after line.
– vsz
Sep 7 '16 at 15:01
• That depends on which algorithm, you need to be careful not to stalemate the King, both with KR and with KBB. The end-phase for KBB indeed more difficult. Sep 7 '16 at 15:04
• @Glorfindel : It's simple if "keep your Rook far away from the opponent's King" is part of your algorithm. :) Not something you can do with Knights, or Bishops near the corner.
– vsz
Sep 7 '16 at 15:18
• Because the R is a long-distance piece, it often does not matter exactly where it is. Anywhere on the proper rank/file will do. As Glorfindel notes the same is true for BB in the early stages. For BN this almost never true. Jan 27 '20 at 3:44

Points are irrelevant.

Points vary all over the place depending on the actual position.

KR vs K has more useful mobility and work together easily to mate.

KBB take more effort as you cannot remove a file/rank from the other kings possible moves so you have to think and envision squares that are covered by the Bs. This takes more effort than visualizing a rook and the squares it covers.

KBN is just the same but trickier as you envision the covered squares. Top GMs see squares covered at a glance. Most weaker players have to work and count them to see what is happening.