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I am a beginner in chess and I am following the tutorials on Chess.com and reading The Complete Idiot's Guide to Chess. In the tutorials about capturing pieces, it is common to count the points in trading pieces.

For example, say I can capture a rook with my knight and the knight will also be captured by my opponent. In that case, because the rook is worth 5 points and my knight is worth 3 points, I will gain 2 points. In most of the tutorials I use, this kind of play is advised.

I am wondering why points matter in trading pieces. Does the fact that the knight is worth 2 less points than the rook make it less valuable?

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    The point system (or material count) is the most basic of tools in your arsenal to evaluate which side is better in a given position. Although it's not the only factor that matters in a position (far from it, in fact), it is by far the easiest factor to learn to use consistently while playing. – Scounged May 17 at 14:09
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    It matters, but it's not the only thing that matters. Ideally you want both more points than your opponent and a better position than your opponent. But if your position is good enough, the points matter much less. After all, having your pieces in a place where they can actually accomplish something makes them more valuable than pieces that are hidden behind pawns or otherwise locked up. – Mast May 18 at 9:57
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The point system in chess gives a rough indication of how strong each piece is. So the short answer to your question is, yes, a rook is more valuable than a knight, and so in the vast majority of cases, if you can trade a rook for a knight, you should do it.

This does beg the question, however, about why a rook is considered more valuable. At its best, a rook can control long files (columns) and ranks (rows). While the knight's tricky movement can sometimes be an advantage, in general we consider it to be inferior. One way to demonstrate the value of a rook is to try the rook and king vs king endgame. (I would definitely recommend looking it up first.) Note that there is no way of checkmating just with a knight and king. In fact, the game would be drawn by insufficient material. This is just a fancy way of saying that neither player has enough firepower to achieve checkmate. As you progress, it will become clearer to you why rooks are more valuable than knights. At some point, you might even be able to notice when a knight is better than a rook! But for now, concentrate on the points system—it's a great way of knowing who is ahead in the game.

Edit: it's worth noting that the points system is not part of the rules of chess. The bottom line is that you are trying to checkmate your opponent's king. But having more material (i.e. points) is a key way of getting closer to this goal.

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    Just a minor remark (I agree with your main points, +1): “This is just a fancy way of saying that neither player has enough firepower to force checkmate.” I think that “force“ is the wrong term here. Even with help from the opponent, one player cannot checkmate the other, hence it is drawn. In KRB-KR on the other hand, it is also impossible to force a checkmate but the game is not immediately drawn. – Keba May 18 at 14:22
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    @Keba Thank you for your comment. I agree, and I have changed it to 'achieve checkmate'. – Joe May 18 at 17:58
  • It doesn't beg the question. It would only beg the question if you tried to answer "Why a rook is more valuable" with "because it has more points." – corsiKa May 19 at 7:30
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    Other things to note: Rooks have "global" range, whereas Knight's are only influential in their close proximity. A pair of Rooks can cover each other, just as a pair of Knight (unlike a pair of bishops, which would be on different colors and can never cover each other). But there's a difference: knights that cover each other can't move (or they'll break each others' cover), whereas rooks can move and continue to protect each other. On the flip side, forking pieces with knights is nice. – Alexander - Reinstate Monica May 19 at 13:22
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Just to put a point on this:

Does the fact that the knight is worth 2 less points than the rook make it less valuable?

This is looking at it upside down.

What matters in an exchange is getting some gain. The points are only a simple tool for estimating that gain.

If an exchange that would be a point-wise loss gives you the opportunity to checkmate the opponent regardless, then it should be obvious that the points have no meaning and the exchange should be made. However, most situations aren't like that, so counting points can be a useful heuristic for the future prospects of the game.

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    An example of a point-losing trade is a mating line that includes a sacrifice. Sometimes a rook or queen is traded for a pawn or even just a move, but the result is checkmate so the trade is worthwhile. – Adam May 18 at 23:46
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    Yes, I think the quoted sentence is exactly backwards: The fact that the knight is less valuable than the rook is why it is assigned a value 2 points less than the rook. – Steve Bennett May 19 at 11:46
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All other things being equal, a material advantage is normally sufficient to win the game. I should mention that the value of a piece is directly related to its strength, i.e. to how many squares it would control on an open board, which is why the rook is worth more than the knight. If you then traded down equally into an ending, your advantage under most circumstances would be sufficient to win, assuming it was mating material like a rook. You probably would need more than one minor piece to accomplish the same thing if pawns are excluded. Winning even just a pawn would be enough to win in the hands of a skilled player, which is how the great Masters like Capablanca played. This could then ultimately be promoted to a stronger piece, normally the queen, to effect the checkmate. Knowing the value of the pieces lets you keep track of this during the game. This is a greatly simplified explanation of course, but is essentially accurate. From this perspective, the game is like a great scale which is initially in balance but on which you try to create a favorable imbalance. Of course there are other factors that must be taken into consideration to determine this, such as position - how much of and what part of the board you control- but a good player weighs them all together when deciding how he or she stands and how to proceed.

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Even though it is quite a useful guidline for beginners, the actual value a piece is assigned to inherently depends on the prevailing board constellation.

Similar to "In closed positions knights ought to be stronger than bishops", we could show countless positions where the standard valuation would be refuted. For instance, in some cases two pawns can indeed be far stronger than a queen.

And still, its important to note that most of the time the standard valuation works. It is so, because it comes from endgame-analyses. The more pieces are alone without coordination, the more the standard valuation holds. If you exchanged a bishop for a rook, you might not perceive the advantage immediately in the middle game, when a lot of pieces are still on the board, but you can try to force more trades and you would be left with an endgame with a rook against a bishop, which is more favourable for you!

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Some other factors can also affect piece values, such as it’s position, and what other pieces it’s paired with. Many people agree that a bishop pair is worth much more than simply the sum of their individual values. You can read more about piece values here: http://en.wikipedia.org/wiki/Chess_piece_relative_value

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