I change mine every 6 months. Essentially before and after winter. It's overkill, but I'll tell you why I do it.
I snapped a chain on my old bike in about 2009. i was stood up pulling away from some lights when it snapped and I got dumped on the crossbar. I broke my coccyx and still have issues today. Can't sit in a car for more than two hours without having to stop, and certain chair positions are uncomfortable after minutes.
A few years later and I was trying to make my Brompton chain last a bit longer. Snapped that and while I didn’t come off, I nearly did. In the process of trying to save myself I really twisted my wrist.
Swore after that that I would never try and make a chain last longer than it should.
At that time however, I was cycling 5 days a week (these days it’s only 3) and was doing about 80 miles a week.
6-months at that mileage was just over 2,000 miles. But I guess you could add half again as I’d not gone to 6-month changes by then.
What I would say though, is that at that time I worked near Hyde Park. As part of my commute I’d do laps of the park. But the cycle track was near the horse track for The Hyde Park barracks.
I mention this as the track was sand. This would get kicked onto the cycle track by the horses and flicked up onto the bike.
My bike was always minging. Combination of the sand and oil, and general road grime.
It used to work like a grinding paste and I’m fairly sure led to the early demise of rims as well as chains.
I reckon the absence of the sand plus the fact I’m doing fewer miles means I could definitely get more time out of a chain, but I’m not prepared to risk it when the price of changing chain and sprockets is only £20 or so.
£40 a year is nothing. Especially when you consider every day I don't/can't cycle, I have to pay £10 to park at the station, and then a tube ticket at £10.50. When I broke my coccyx, I was off the bike for three months. At today's prices, 13 weeks or so off the bike at an extra £100 a week is £1300. All because I was trying to save a few pennies making my chain last longer. I could have bought a new bike for that.
So now chain and sprockets get changed every 6-months. I used to also change the chainring each time, but now I just rotate it forwards one spoke of the chainring so any worn teeth are no longer in the ‘power’ zone. Change it every two or three times I do the chain now now.
So in answer to the original question, because I do far fewer miles in those 6 months, I probably now change the chain at about 1,100-1,250 mile intervals.
Standard Brompton 6-speed chain and sprockets, but a Spa cycles 48-tooth chain ring.
Cleaning regime - might run the chain through a chain cleaner every fortnight, but then remove chain, sprockets. chainring and chain pusher to completely degrease and re-oil them once every 4-6 weeks.