Is the fifty-move rule in chess the correct amount?

In chess, pretty much universally, the so-called "fifty-move rule" is applied: If at least 50 moves (ie. 100 half-moves, ie. both players have made 50 moves) have been made without a pawn move and without a capture, either player can declare the game as drawn. (In other words, applying the rule is optional.)

(If the 50th or any subsequent move is checkmate, then it takes precedence over the draw. A player cannot afterwards avoid being checkmated by retroactively trying to claim draw, if a checkmating move was allowed to be made. Curiously there have been cases of chess engines that have been incorrectly programmed to think that the 50-move draw takes precedence over the checkmate, and have lost a drawn game in this manner.)

While applying the rule is technically optional, FIDE quite recently (in 2014) introduced an additional (lesser known) rule for their tournaments that if 75 moves are made without a pawn move and without a capture, the game is drawn automatically (a referee may apply this rule if he sees this happening, and the game is ended regardless of what the players want.)

The 50-move rule might sound like a relatively recent invention, but actually it has a surprisingly long history. It was first introduced into chess by Ruy Lopez all the way back in the 1560's. While other numbers of moves were also suggested, 50 became the de facto standard quite quickly.

As you might imagine, this rule, and the exact number of moves, has been quite contentious over the centuries. After all, 50 is a completely arbitrary number that's not really based on anything. It was originally, and for many centuries, just a nice round number that's "big enough" for the vast majority of known endgames. There's really no reason why it couldn't be 45, or 60, or some other arbitrary number that's likewise "big enough".

With centuries of accumulated chess knowledge, unsurprisingly people started to eventually find endgames with forced wins that took longer than 50 moves. This felt unfair: A player could win the game, but since it took more than 50 moves (without a pawn move or a capture), he could not. Instead, the game would be declared draw, because of this rather arbitrary rule with its arbitrary number.

The rule was attempted to be patched several times. For example in 1928 FIDE amended the rule to state that if a known endgame position required more than 50 moves to a forced win, then the rule would be extended to 100 moves.

Since only a handful of endgame positions requiring more than 50 moves were known at the time, this was considered enough. However, over the decades, and especially after computers were used to analyze positions, more and more such positions were found, some requiring a lot more than 50 moves. (The current record known, as of writing this, is 545 moves to a forced win with optimal play from both players, without a pawn move or a capture.)

Since it became clearer and clearer that the number of such positions was innumerable, and the maximum amount of moves was likewise really large, FIDE decided in 2001 to restore the 50-move rule to be just 50 moves, period, for any position.

Does this rule make sense, given that there are so many positions where a game would be "incorrectly" declared a draw, even though one of the players would have a theoretical forced mate and thus victory? Does it make sense for the number of moves to be that completely arbitrary 50? (Why 50 and not some other amount?)

Rather obviously, the rule exists for practical reasons, especially in tournaments. A game cannot be allowed, for very practical reasons, to continue indefinitely. (While the three-fold repetition rule would stop certain repetitive patterns from going on forever, it's not enough to stop a game from continuing for hundreds and hundreds, perhaps even thousands of moves, without the same position ever repeating three times.) Chess tournaments have an allotted time to be organized, for practical reasons, and a single game just cannot continue for days.

One could argue that chess clocks are for that purpose. This can indeed be the case, but on the other hand, there are tournament formats where each player gets additional time for each move, so theoretically the game could continue indefinitely. (There may also be smaller tournaments, eg. for school students, that don't use clocks at all.)

If we agree that some limit has to be put on games that just don't progress in any meaningful way ("progress" being measured by irreversible moves, ie. pawn moves and captures), then 50 moves is not an unreasonable amount. It's plenty enough for like 99.99% of (pawnless) endgame positions that happen in real life practical games. Engames that are theoretical wins in more than 50 moves (without pawn moves and captures) are extraordinarily rare, especially in actual realistic games.

Given that it's impossible to even prove for most positions whether they are forced wins, and given that the vast majority of players would usually not even know how to win for certain (the likelihood that they will make a mistake and make the game an actual draw, or even a loss for them, is quite high), I think it's completely reasonable to just ignore those extraordinarily rare circumstances, and not try to apply patch after patch to the rule. Starting to list all the exceptions to the rule (which was attempted by FIDE at one point) would be an endless wild goose chase.

I think the 50-move rule makes practical sense, and the number 50 is acceptable, given how rare the exceptions are. It has more practical value than the astronomically rare games where it "wrongly" makes a won game a draw.