[1] - Fires were almost a daily occurrence in Rome, and Crassus took advantage of the fact that Rome had no fire department, by creating his own brigade—500 men strong—which rushed to burning buildings at the first cry of alarm. Upon arriving at the scene, however, the firefighters did nothing while Crassus offered to buy the burning building from the distressed property owner, at a miserable price. If the owner agreed to sell the property, his men would put out the fire; if the owner refused, then they would simply let the structure burn to the ground. After buying many properties this way, he rebuilt them, and often leased the properties to their original owners or new tenants.

> Fire fighters were not paid salaries, however. Each fire company was staffed with 36 residents of the district, serving under the command of two fire masters. Each man appointed had to serve a year or pay a fine of ten guilders.

Not sure about density in urban old Rome or old Amsterdam, but sounds like their "fire brigade" ended up quite larger in Rome unless Amsterdam had a lot of "districts":

> After Egnatius' death, Augustus set up his own fire brigade, which also consisted of 600 slaves, and later, in 7 or 6 BCE the fire brigade was enlarged, now consisting of 3,500 freedmen, the vigiles, who were divided into seven cohorts of 500 men each and made subordinate to a praefectus vigilum. In about 200 CE, their number was doubled to 7,000 men. https://en.wikipedia.org/wiki/Marcus_Egnatius_Rufus