How do you know you are too far behind to win?

I would only quit if my capital was sacked or we were down to less than 3 human players, and everyone else had already quit and messed up the game. There have been so many times I've lost a city or two to an invasion, but was able to rally back and retake them (defense really is easier) so it bothers me to no end seeing all the limp wristed quitters out there who quit if they lose one stupid unit because they gave up. This game has so much margin of error and so many variables, there really is no point you can decidedly say "it's over" other than pretty much your capital's gone and your army is wiped off the map. In poker all you need to stay in the game is a chip and a chair, in Civ I'd say it's a capital and a unit.

 

My solution is generally TRY to bribe other civs to DoW, not Greece (sometimes Alex has a huge army) but his allied CS. (and I just laugh if Genghis spawns next to Alex... won't have to do a thing)
Once only a few CS are left (I've played games with China Japan Zulu and Monty and they all had their share of allies, once they go to war... WELL. What happens is all the Pangaea CSs get conquered, leaving two island ones) DV is impossible for him (or anyone) at that point.

 

I generally fight to the last man. Only when it's that final death blow that will occur I quit xD

I don't quit even when my capital is under siege only when its' the final deathblow like one more attack and my last city is gone and that melee is ready to attack for win and I have nothing left to stop it.

Cuz u never know when you might manage to come back with vengeance. I once lost 3/4 of my cities in civ 5 vanilla if I remember right, I only had my capital Plus three production cities left.. It was really more of the production starved cities for humans and production cheats for the AI issue but anyways.

China was laying siege on my city of berlin with T-34-85s while I had nothing left but Tigers that barely gets built just in time to replace the dead tigers. It was like 12 tigers vs 30 T-34-85s each turn. They whittle down my defenders at berlin and I ship in reinforcements fresh from factories and the cycle begin all over again. It was nothing but tanks vs tanks, not a single infantry to be seen.

Then someone dow'd china, I forgot who.. that let off the pressure enough for me to gain momentum to take back every last one of my cities and beat up china in revenge.

 

Have I mentioned that I hate Greece? I've been playing a long science game on Immortal and doing pretty good, long had a commanding tech lead. So I'm trying to get the last handful of techs and quickly build the last two SS parts - all the while preventing myself losing to @%!$# Greece. Twice now I prevented Greece from winning Diplomacy despite them having 34-35 delegates the turn before. I sit there watching them take their turn before the vote praying that they don't buy all of their city-states back. I'm having to build up to 5000 gold in each of those 20 turns and sometime it wasn't enough. I don't even touch the +300 ones but anything under +100 seems doable. Another vote coming up in 20 turns and if I did the math correctly (considering rate, few GS and a GA), I should launch about the time of the vote. I dread seeing how many delegates they would have then (hoping Greece is not getting Globalization in the meantime). Of course, no one would even come close to wanting to war on them. Part of me hates this gold exploit that was promised to have been removed but the other part of me hates Greece.