I wonder if the Bishop and Knight that start out on the same color square as the opponent's King, is worth more than it's twin on the other flank. And if that is of significance when making choices about pawn structure and piece exchange in the early game.

White's King starts out on and castles to dark squares, so Black's King's side dark Bishop can check white, or use the King as a pinboard, or win a tempo when the King moves to avoid that. For the Knights, it takes both sides' King's side Knights 4 moves to give a check, but only 3 moves for the Queen's side Knights, regardless which way is castled.

Is this enough to say that from the onset, the King's side Bishop is (a potential tempo) better than the Queen's side Bishop, and vice versa for the Knights?

Should one transfer one's Queen's side Knight to the King's side, on a 3-move path towards check, and thus possibly win a tempo later on? And also not trade the King's side Knight against the opponent's Queen's side Knight early on?

There is no doubt that the value of a piece depends on where it is on the board, but the difference between b1 and g1 or between c1 and f1 is going to be very small and probably not worth worrying about for human players. (Position-dependent piece values are much more sensitive to the rank and centrality of the square, neither of which change in this case.)

One way to try to measure this would be to ask the all-wise Stockfish. :-) What does it say if you remove one of these pieces? Here's what I got using the Lichess analysis board to default depth (these are the evaluation scores after removing the white piece):

  • Queen's knight: -3.8
  • King's knight: -3.6
  • Queen's bishop: -4.7
  • King's bishop: -4.8

So if we are to believe Stockfish, the queen's knight is worth 0.2 more, and the King's bishop is worth 0.1 more than their counterparts. Seems like a relatively small difference to me, and it is probably dependent on depth. Still, for whatever it is worth, the small differences at least went in the same direction as your hypothesis!

  • Good idea! Handicapping a piece on the King's side, I would think, should have the small compensation of facilitating a quicker King's side castling. But still, keeping that Bishop is evaluated as a bit better. Could it be because it is "faster" to some tactical trick against the opponent's King? What do the engines say if one player starts out without its King's side Knight while the opponent starts out without the Queen's side Knight? (And Bishops respectively, and combined) – LocalFluff Dec 5 at 18:16
  • I'd like to add to my comment above, that castling quickly King's side is defensive and should be especially valuable when one starts out a piece down. Even so, your computer evaluation says that something makes the King's side Bishop +0.1 pawns more valuable than the Queen's side Bishop. – LocalFluff Dec 5 at 18:27

They don't have different values, but the actual place on the board definitely matters for pieces. Some well-known examples are the octopus knight, positioned on the sixth or seventh rank protected by a pawn or another piece, which is usually worth at least a rook. The relative value of a pawn on the seventh rank is also much more than when it's still on the second rank.

There is no a priori difference in relative value between the pieces in the starting position, but there are certain openings (e.g. French advance variation, King's Indian) which create central pawn structures leading to bad and good bishops. One could think of one bishop being worth 2.5 pawns and the other 3.5, but I don't know of any player who really counts this way.

  • But Bishop and Knight that start out on the same color square as the opponent's King, are one tempo closer than the other, to make a forcing move or tactic involving the King, whether it has castled or not. – LocalFluff Dec 4 at 11:04
  • 1
    That's a nice theory, but practice tells us it doesn't matter at all. – Glorfindel Dec 4 at 11:09

Short answer

You do have a certain point, but it is not meaningful enough in the big picture to truly matter.

Long answer

Indeed, on an empty board, the knight from c1 will reach the square e8 one move faster than the one on f1.

However:

  • The board isn't empty. Your opponent won't simply allow you to march up to their king like that. The opponent's pawn structure will make a lot of squares impassable for your knights, and the kingside knight might have a faster path through that structure than the queenside knight in the end.

  • Checks are not the only way to gain tempo. Your queenside knight is potentially faster to attack the opponent's king, but conversely, the kingside knight is potentially faster to attack the queen, which in 90%+ of cases is just about as tempo-winning.

  • The opponent's king will most likely not even be on e8 anymore anyways by the time your knights come into range.

  • Usually, an invasion across the middle of the board will need some preparation on your part, and you will easily spend more than three or four moves to even enable your knight to give a check in the first place. Winning one tempo on the last move of a plan isn't that useful if the plan was more tempo-consuming than another.

  • In the end, that one check to the opponent's king after a direct 3-move or 4-move path only happens in a small fraction of games. Most of the time, you will need your knights to perform other duties.

  • Even in cases where it happens, that one check will only be a tiny fraction of the "value" of that knight during that game. What it did along the path is much more important (an octopus knight as mentioned in another answer will ultimately be much more useful than one who only gave check once and didn't have much more impact otherwise).

  • Chess is concrete.

  • Keeping the "fast" Knight (from the Queen's side!) on the path to check could be helpful many moves later. A King move after castling is a tempo lost to development. It is a restriction on the opponent to give my "fast" minor pieces other tasks. The opponent might make the mistake to engage my "slow", but early on more nearby, Knight instead. Developing the Bishop of the same square color as the King first is already intuitive and established. Computers haven't solved the "concreteness" of chess from the opening, so valuing different pieces on different squares is what we have to begin with. – LocalFluff Dec 4 at 16:08

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