I'll just skip towards the last few turns, which I will bold point.
-I only have 2 cities. My main (capital) city got surrounded by Mongolia because he expanded way too quickly for me to react. The other city was on a small island for away. The only other cities on that island were from Rome and Mongolia.
-Rome randomly declares war on me. Me and Mongolia declare war on Rome (because me and Mongolia are BFFs...at this point).
-I take my carrier (which had 3 atom bombs) and land on Rome's shore.
-Nukes a Roman city, but it was too close to Mongolia's borders, so the radiation leaked over into his territory. Now I'm at war with Mongolia from an epic screw up.
-Remember, I'm completely surrounded (territory wise) by Mongolia, so I have nowhere to run. Oh, and I have no real military because I was focusing on a science victory.
-My main (capital) city has 80ish defense at this point. I got steamrolled by Mongolia in 2 turns. Two. Turns.
-Lost my capital city, which my well, EVERYTHING. It was a freaking uber city with all of my science and culture stuff in it.
-So after my capital got taken, I'm left with +46 science, +9 culture, 3.3K gold, +28 gold per turn, and +9 happiness. At least I was able to keep my gold and happiness up...somehow...
-My last city is on that small island now...along with Rome's city and Mongolia's city, and at this point I'm still at war with both of them.
-Before I could even do anything, Catherine (Russia) swoops in with a science victory and builds all of the spaceship parts in no time.
And ya. That was easily my biggest failure in Civ 5 ever. I accidentally nuked Mongolia and got steamrolled in 2 turns. Guess that's what happens when you accidentally nuke the most powerful army in your Civ match (literally, nobody else even came close). The sad part is that I was doing so well until then, and before that, I wasn't even in a single war, and I was playing for almost 500 turns!
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Put this in the OP.