Tournament - poll.

The third installment is objectively the best.

Actually, I also think the fifth game is good, but... Compared to the third, it has two fundamental problems: battles and a rather dull AI. The warfare is incredibly monotonous and encourages a lot of micromanagement, although it looks prettier. Overall, there seems to be a little more tactics, but much less strategy. The fifth game has the advantage that other ways to win are better expressed, but for me, it still looks worse. In the third game, there was a literal conquest; not a single piece of the map remained unclaimed, while here, even on medium-sized maps, there is always a lot of unexplored land. Also, I subjectively liked the eras and civilization-specific features more in the third game.
In essence, the fifth game is probably better for multiplayer, while the third is better for single-player. But even with that, there's a problem: it's too old, and I played it a lot last year.

By the way, if we're being serious, I would play tournament duels in the fifth game or some other games, but if you think about it, all sorts of problems still arise. For a normal connection, it's best to play on a licensed copy, but if there aren't any, then there are Hamachi, GameRanger, etc., but, honestly, in 2018, I don't even want to touch that, lol.