There are no more than 218 ways to interpret this title

I seriously thought they meant "it's not possible to have a chess game with more than 218 moves"

The right™ order is to check the comments before the article, but to read the article before commenting.

Thanks for that link! I was looking for that answer a few years ago, but I couldn't find anyone who had carried it out all the way through (with the cost of "switching control" fully accounted for), nor many people who were even aware of the 75-move rule.

how can the longest game have half a move???

The 50 moves rule doesn't have be considered as it is optional. The players may claim, but they don't have to. So the game can continue.

The 75 move rule is the exact same thing but mandatory. That has to be considered.

(same thing is true for 5 times repetition vs 3 times).

Captures also reset the counter, not only pawn moves.

> And you can derive an easy upper bound from that as 50x8x8x2 (basically each 50 moves you make a pawn move)

This is not high enough, because the 50 move rule also resets when a piece is captured.

The 50 move rule is a rule of chess so it must be considered.

The 3 repetition rule is an opportunity for one of the players to declare a draw, but games can continue beyond that. The mandatory draw rule is 5 repetitions. In any case, the 50 move rule is far more limiting as to the number of moves in a game, since repetitions are necessarily neither pawn moves nor captures (the whole point of the 50 move rule being limited to those is that they are irreversible).

The 3 repetition draw rule has no bearing on the number of possible chess positions. And for the number of possible moves in a game the 50 moves with no capture or pawn move rule is a much more stringent limit.

BTW, the 3 repetition rule only comes into play is one of the players invokes it ... games can legally have more than 3 repetitions, but not more than 5 repetitions.