I'd played Civ3 for years without seriously considering bombard units. After all, the AI hardly used them, so why bother? It was only after reading some threads and going over legendary games that their utility became apparent. (Sulla's win as Iroquois on vanilla Deity, holding off waves of Rooskies by wounding them with massed batteries of artillery, was a real eye-opener.)
Nowadays up to half of my SoD's (Stacks of Doom) consist of bombards, and border towns get their share. That's why Mathematics is such a critical tech; you need it to make Catapults, without which precious Legionaries or Swordsmen are at greater exposure to the tender mercies of the RNG (Random Number Generator). It makes a huge difference between attacking a healthy Spearman and one red-lined. Even at yellow they usually lose. Once you take or raze the town cats can bombard counterattacking units that are invariably unfortified, picking off the most vulnerable with your swords or archers (just be careful not to attack solitary units unless you have horses which can return to the stack afterwards). The other wounded usually retreat so you can beat them off piecemeal, with kill ratios approaching ten to one.
That said, you have to upgrade them or at higher levels you'll find yourself almost uselessly bouncing rocks off Musketmen fortified in cities. Or cannonballs off Infantry, unless they're in the open. There've been cases where about a dozen shots by cats caused only one or two hits on muskets, necessitating suicidal attacks by swords that cost nearly the whole force. (And if you contemplate doing the same against rifles, fuhgetaboutit. Ain't gonna happen, unless maybe there's a single defender.)
Further on the down side bombards aren't lethal or necessarily reliable (I've had cats get hardly any hits against even spears in cities, especially enemy capitals), they drastically slow down a stack with mounted/armored units, they can't go into mountains or wetlands except along roads, they cost as much as regular combat units for upkeep, and the upgrade from cannons to artillery is almost prohibitively expensive (120 gold) unless you're rolling in dough. Some experienced players don't use them for these and other reasons; check out the threads for details.
Anyway that's my opinion. Cheers and good luck.
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