Origin story for Lloyd's of London:
The patrons bet, for example, on whether Admiral John Byng would be shot for his incompetence in a naval battle with the French. He was.
The gentlemen of Lloyd's would have had no qualms about taking my bet on my own life.
Edward Lloyd realised his customers were as thirsty for information to fuel their bets as they were for coffee, and began to assemble a network of informants and a newsletter full of information about foreign ports, tides, and the comings and goings of ships.
His newsletter became known as Lloyd's List.
Lloyd's coffee house hosted ship auctions, and gatherings of sea captains who would share stories.
If someone wished to insure a ship, that could be done too: a contract would be drawn up, and the insurer would sign his name underneath - hence the term "underwriter". It became hard to say quite where coffee-house gambling ended and formal insurance began.
Usually, both. Plus, if you had high expenses they'd actively search for an (even unrelated) pre-existing condition as a pretext to cancel your coverage (recission).
In the case of these massive flooding, it's hard to make the pool big enough. That's why reinsurance companies exist, which can mix the risk pool of different types and locals.