I had a fun game with HGB, testing out the Aztec vs German dilemma. I said before,: for Aztecs a lot depends on the horse-rush, if that works for them, they are well ahead, if that fails, they are out of tricks...
So, I played Germans, HGB Aztecs. We started fairly close but not too close.
My cap had 3 trees (moved settler by 1 tile to get that, although I only had 1 water this way). I made 3 warriors sent them out in different directions, killed 3 barbs and got 100g quick. I found his warrior and saw the border of his cap, attacked 2:1.5 (hill to hill) and won. I saw a perfect spot for my 100g city: 5 forests, 1 grass, 2 sea one of them with fish, city on a hill. Sent my settler in that direction and ended my turn next to a jaguar warrior -- NOT GOOD

Next turn HGB was faster than me and captured my settler, I couldn't run away. That was a major set-back. Now he had 3 cities with his 100g and mine, while I only had my cap. Plus, I knew his horse army was going to come soon, because he already killed my first warrior with a horse. He moved towards the hill where I wanted to settle, I had my warrior up there and attacked his 2:1.5 but I lost this time. He made the city in the same spot where I wanted to. I rushed warriors every turn in my cap (which was 3 pop at this point, I grew after I made the first 3 warriors). HGB came with a warrior army from one side, trying to bait me to attack out while he attacks with his horse army from the other side. I did not take the bait, instead I attacked his horse army with my vet warrior army 4.5:4.5 and I got lucky and won, also got a Blitz upgrade from it. Next turn I stepped back before he could attack (although I had another single warrior in the cap) and won against his warrior army and got a great general. I tried to attack the city on the hill but he already had an archer army there. I also made an archer army (bought BW from the Russian AI), then I went and warrior rushed the Moscow, getting ABC. In the meantime I built a settler from cap and settled to another nice spot with 5 forest + 3 water, one of them with fish.
I pushed out another settler from cap and 1 from Moscow, then I teched to medieval. I built 2 barracks (cap + 5tree city) and started producing elite warriors. Aztecs were waaay ahead in tech at this point.
HGB tells me in the chat lobby: "4 turns and you are dead" -- he was getting knights and had 300g to rush them. So, I switched my tech to Iron working and timed it to be ready just in 4 turns for counter attacking (I had some archer armies). I had 7 elite warrior armies when he came with 3 knight armies to attack Berlin. I lost 1 legion army, but managed to kill 2 knight armies. Next turn I killed the 3rd one, getting a 2nd great general. HGB said he would come back again soon, so I shouldn't be too happy

I finished COL at that point (was very slow teching, not enough cities no gold). I pushed out 4 settlers (1 from each city) as fast as I could, then 2 more shortly after, settled with 4 dye tiles, including an island. I started teching faster, went for Monarchy, then Feud. HGB had like 5 archer armies in my hill-top city, but I took them all out with my elite knight armies with GG support. He went into democracy then and teched even faster. I knew it would be dangerous to attack his cities with my knights. So I also teched democracy, gunpowder, steam and stole a GS from the Roman AI and used it for combustion. Then I went for Religion, and attacked with 4 triple elite tank armies, all had inf+blitz, 2 had GG. HGB had walls and rifle armies (multiple per city), but could not stop me. He killed one of my armies with a cannon army, but then his first city fell. After that I quickly rolled throw 2 more. Tenochitlan took some time, he started to get elite modern infantry units there, but it still wasn't enough to stop the ninja+GG tank armies. He said he only needed 2 more turns to get Leo's to turn all his rifleman armies into MI armies, so my timing was lucky.
So, first I should have lost to his horse-rush, then I should have lost to his knight rush, but I managed to come back from way behind in tech. He got over-confident with his tech lead and did not press me enough...
He was surprised how I got to 20 techs from like 7 in a few turns -- well I backfilled everything when I went into democracy with 10 cities 4 of them with libraries. He had 26 techs at that point.