In the body of chess rules, castling is a clumsy protuberance. Once per game, you get to move king and rook at the same time, with a bewildering list of exceptions. (One dreads having to broach these gotchas with a novice opponent who has castled improperly.) Despite its convoluted logic, castling is nothing more than a convenience, and the game could function perfectly well without it.
Five hundred years ago, the rules of chess were still evolving, with significant regional variations. The ‘king’s leap’, a precursor of modern castling, permitted the king to make one move as a knight jump (perhaps from e1 to g2), while in other forms it could step two squares any which way (so, for example, e1 to g3 was also on the menu). If the latter sounds wacky, at least it is congruous with the way in which pawns can jump two squares on their first move. The interleaving of king and rook in modern castling looks peculiarly arbitrary.
The late 15th century saw a seismic shift, when a variant became popular which upgraded the powers of what we now call the bishop and queen, hitherto much less agile pieces. Since the standards of defensive play were lamentable (as they were even in 1850), it must have seemed imperative to secure the king’s position. But perhaps the appeal was even stronger for the gambiteer, who could exploit it to accelerate an attack. In the 16th century, the Italian player Polerio analysed the gambit 1 e4 e5 2 f4 exf4 3 Nf3 g5 4 Bc4 g4 5 O-O, which would lose much of its oomph if White could not castle.
In modern chess, experienced players almost always castle. World-class players learn counters against standard openings with more precision every year, so it is harder than ever to light the touchpaper on a game.

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