Last time I had a really serious delay (4-ish hours), I left the airport and went home for a few hours instead of hanging around in a boring lounge. Was very certain they wouldn't move the departure time forward, as we were waiting for the aircraft to arrive from Tokyo first.

For "normal" delays of +30 minutes, it depends on whether I've checked a bag or not. If bag has been checked, I'll arrive at the gate at the revised boarding time and will not constantly check departure boards. If no bag checked, will monitor departure boards continually.

It will also depend on which airport I'm in; if it's a large airport and there's loads of walking to negotiate (e.g. FRA), I'll be conservative. If it's at a small airport, not so much as the waiting areas are right next to the gates (e.g. any Greek island).

It's only happened once that a gate agent (in Germany) tried to chew me out because I was, in her opinion, late. I pointed to the departure board which still indicated a departure time some 30 minutes into the future, and suggested that me being on time depended on her updating the departure board - you uphold your end of the bargain, and I'll uphold mine. You fail to uphold your end, that's on you and not me.