user11202: 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.

user2929: 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.

user17: 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.

user-1: 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.

11202: <p>When I was very young I remember learning the point values of the pieces. And then I ran into something very confusing.</p>

<p>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.</p>

<p>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?</p>

<p>I have some ideas for how to express this simply, but nothing concrete. It seems like there should be such an explanation.</p>
 2929: <p>Note, that a Rook alone can block a whole rank or file, enabling the king to get into position alone.</p>

<p>B+B and B+N cannot do this.</p>
 17: <p>Yes, a rook is worth less than two bishops (five versus six).</p>

<p>But a rook offers more <em>concentrated</em> 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.</p>

<p>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.</p>
 -1: <p>King and Rook mate faster because the 2 pieces <strong>coordinate better together</strong>.</p>

<p>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!</p>

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

<p>Note also that the point value system is a <strong>guideline</strong>. 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.</p>
