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I'm an amateur chess player.

I was reading an article about how f7 is such a vulnerable square and how castling makes the king safe and attacks on F7 no longer worrisome. But looking at it, I am wondering, is this really that much better for the king?

Sure, originally F7 is only protected by the King himself. But after castling (king side) it has only one additional protector, the rook (compare that with the four protectors the E2 pawn has at the beginning of the game). Secondly, that rook is unlikely to stay there anyways and protect the F7 pawn, as it's likely to move to an open file early in the game. It would be a waste a five point piece to keep there just to protect the pawn. Lastly, we now also have the additional concern of backrank mate in this position.

Can someone explain to me why castling is so important for king safety?

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The f7 pawn is really only a concern for beginners. It is not easy to attack for white with many pieces and is easily defended.

Generally (in the opening/middlegame) you want to surround your king with pieces or pawns for protection. Usually you don't want to bind your pieces to the protection of the king as they have other (attacking) duties. This leaves you with hiding the king behind pawns.

You want those protective pawns to be difficult to attack and difficult to exchange for other pawns as this would open files and diagonals, leaving your king without protection. A typical motif in chess (particularly with opposite side castling) is a pawn storm where the attacking side pushes its pawns forward in order to open lines around the enemy king. Obviously this is most difficult to achieve if the pawns are far away, i.e. close to their original position.

Another way to attack the protective pawns would be with pieces. This is often easier to do in the middle than towards the border where there are fewer squares available for the attacking pieces.

Now in the opening both sides fight for control of the center; basically in order to gain space to operate the pieces and because pieces can easily move to either side of the board from the center. In order to achieve this central control the players typically move one or two central pawns and concentrate piece activity around the center. This means that often the situation in the center is very dynamic and lines can be opened, pieces exchanged... (another typical motif: ''open lines in the center against an uncastled king''). You don't want to find your king among all this action in the middle of the board.

Taking all of this together in many cases hiding the king behind pawn chains on the side of the board after castling is usually a good idea for king safety. Another added advantage is that castling joins the rooks, i.e. the castled rook can easily get to the central files (c-d-e-f) where there are often open or half open files to occupy.

There are also cases where players don't chose to castle (e.g. in some Sicilian and French opening lines), usually in positions with static, blocked centers and easily to attack king-/queen-sides.

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    The threat of f7 is a concept in many openings, including say the Italian Game.
    – qwr
    Commented Sep 19, 2022 at 19:12
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Can someone explain to me why castling is so important for king safety?

Kings are safest behind pawns that have not moved from their starting squares, because it's harder to create open files and diagonals against such a pawn formation. Once pawns have moved forward, they can be attacked more easily by other pawns, which can make them move even more.

In most good openings, one or more central pawns are moved at the start of the game on each side.

Castling lets you put your king behind the untouched pawns on one wing.

Additionally, it's usually harder to direct one's pieces against a side of the board rather than the center, because the edges of the board are a natural space constraint.

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Most chess activity in the opening is through or related to the centre. With your king still in the centre, you overtly expose him to attack. Castling makes safe your king, in general.

Most openings try to get the king safely tucked away ASAP. But many openings delay castling to the edge of safety for the sake of tempo or central play and piece development. There are many a classic chess game where black delayed castling by 1 move too many and succumbed to a violent attack through the centre.

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