The value of the Knight

I believe knights to be more valuable than both the rook and the bishop. A bishop and a rook are both the same in the sense that they move in a perpendicular fashion, but cannot jump like a knight can. The ability to hop over pieces is absolutely invaluable to my particular strategies, because no matter how fortified and enemy's pawn structure is, it is virtually worthless if you put a knight in the right place. Not even a queen has this ability. A grand fork can be made in the opening of a game if played just right. I would love to hear some discussion and perhaps some notation either supporting or rebutting my claim.

i quite agree, knights are invaluable when your opponent has a very fortified and strong pawn structure

The value of a piece is ultimately determined by the position on the board. There are positions when a knight is essentially the best piece on the board and there are times you'd rather replace that knight with a pawn-it all depends on the position.

knights are usually my sacrificial lambs.

Total squares controlled on an empty board + squares able to control matter. Also how quickly pieces can get to new squares matter.

The knight can only control a maximum of 8 squares, and it's very slow, but the reason it isn't worth much less than 3 is as you've pointed out, they can hop over pieces.

Bishops aren't the same as rooks. Important to realize they can only ever influence 32 of the 64 squares.

Anyway, the relative values are essentially confirmed by years of master play, and recently computer chess programming and even some statistical work by Kaufman.

Kaufman goes into some detail. You may find it interesting:

http://home.comcast.net/~danheisman/Articles/evaluation_of_material_imbalance.htm

"Two knights are better than one''..... Thats all ah got say.

The value of a piece is by definition independent on the board position, as it is defined as the average over all (quiet) board positions.

Detailed measurement shows that a single Knight is worth exactly as much as a lone Bishop, but that a Pair of Bishops is worth about half a Pawn more than a pair of Knights, or Bishop plus Knight.

The concept of piece value is only an approximation; in reality one can only assign a value to a certain combination of material. It would be hard to explain by adding piece values why 3 Queens lose so badly to 7 Knights.

To the OP, what do you think is the value of bishop happily sitting on g7 square in the game posted in this thread?

http://www.chess.com/forum/view/game-analysis/where-did-white-go-wrong3?lc=1#last_comment

The claims of "If a pawn is 1, then a Knight is 3, Bishop is 3, Rook is 5, and Queen is 9" is beginner's hogwash.

Every position must be evaluated individually.  I had a game about 10 years ago where I had a Knight and 7 pawns and my opponent had a Rook and 6 pawns but his Rook was so dominant that my Knight and pawns couldn't survive.  At the same time, I've had other games where the side with the extra pawn and the Knight (or Bishop in some cases) has just dominated the Rook.

I've also had multiple instances in tournament play where two Bishops, with or without and extra pawn, has destroyed a Rook and Knight (i.e. 6 beats 8 or 7 beats 8), and so once you are over 1600, throw the points system out the window, and evaluate the position you currently have on the board.  Many times it's right to "sacrifice" a Rook for a Bishop or Knight, and many other times, you are out of your flipping mind giving up the Rook for the Knight or Bishop.

more often than not, knights are more useful for attacking than bishops IME

With all due respect to Pins and Skewers, you can't beat a good Knight Fork.

I like the position argument. I believe I should clarify that I am refering to the value of piece in chess.com's piece scoring. They are kept the same in every game, regardless of position. If it is such "beginner's hogwash" @ThrillerFan, why then does chess.com use such a system? To add, should we agree that such a system is substandard, shouldn't we then demand a piece scoring system that is more up to our standards? 

The system is a general overview of the material captured by both players, more convenient than counting the pieces by yourself. The system is important for beginners and masters alike, but masters do not follow the systems as blindly as a beginner would, instead sometimes they might sacrifice material to gain other forms of imbalances. Also, remember that the vast majority of players on Chess.com are beginners.

@Whip_Kitten That is also a good point.

I took a quick look at everyone who posted and checked their ratings. I recommend everyone else do the same to gain perspective.

It's just an average over all positions. During a game there is no rigid system "that is more up to our standards."

In a real game not only are bishops and knights not worth the same, but knights aren't worth the same as other knights. Strong players intuitively rank each piece's value relative to the others over and over as a game is played.

That said, the reason the point system is used is that it's approximately correct in most positions. Maybe one reason it's so often right is because of endgames. For example in simplified endgames of knight vs rook and bishop vs rook, the rook usually wins easily. Fortresses for the weaker side are few and can be difficult.

It's all a bit like stocks and shares. As the game progresses, the value of the pieces rise and fall in proportion with the noobiness of the players.

The reason why the knight pair is considered weaker than the bishop counterpart is because of "Redundancy"

“During the analysis, I discovered something very remarkable: the board is simply too small for two Queens of the same color. They only get in each other’s way. I realize that this might sound stupid, but I fully mean it. The advantage is much less than one would expect by counting material.” – Victor Korchnoi

Knight better than rook?  lol.

Here's what a knight is worth:  50 dollars.   Assuming she's also an asian prostitute.

Bishop =3.5 Knight = 3.

I use my knights like the dirty dozen. Remember that old 60s movie? In other words. They will die. Their purpose is to sacrifice themselves at the most cost. They disrupt complacency!

I like my knights! They make the game interesting. However, I sac them because they love to die boldly!