Some things I learned during last game:
1. You can't spread culture the same turn you gift the city. When it's gifted, it claims all surrounding inner tile rings until end of turn and spreading culture is not available as a valid espionage mission. I was quite confused when this first happened, but don't worry if it happens to you. The next turn you get back the surrounding tiles and can use the spread culture mission.
2. I think relocating your capital and gifting away the old one should always be worth it. Your capital usually has the most passively generated culture, because of palace and usually being the first city with a library. Then there's also Great Wall and possibly some other wonders built with bureau bonus. In addition, your spies teleport to the capital after a successful mission. If you don't have enough spies to make all 3 cities legendary at once, which you probably don't, then after you're done with the second city, finish Palace in another city close to capital (probably the spot you'd otherwise use as 3rd gift city) and give away your capital. This saves you at least one turn of spy movement.
If you do gift your capital, beware that it will probably give some tiles back to the other cities you gifted earlier, which might make a difference for you when you capture them back. It also gives them tiles to work to build more defenders, so better grab the other 2 legendary cities back quickly after gifting the capital. In my game I gifted the capital, declared and took back both other cities on the same turn. Next turn old capital was made legendary with spies and recaptured.
3. The AI does not look for the fastest possible way to get a garrison to the city. I had quite a nice layout in my game:
The whole western world is Jewish (and I captured the Jewish shrine in my first war
), in the east Victoria and De Gaulle are Buddhist. I gave Vicky a bridge city in the middle of the jungle that was within 9 tiles from both the legendary cities I planned to give her and one of her cities in the east. I did this quite early to make sure this would work, so that I could adjust my plans if there was something about city gifting mechanics I didn't understand. By the time I gifted her the first gift city, she had 3 units in the bridge city, but she still sent garrisons from her core, which meant it took 12 turns for the first (and only) sword to arrive to that city. Same for the second gift city, she sent a longbow from her core, which only made it to my border in the north before I declared to take the cities back.
4. I never got any trade route bonus for my espionage missions despite having open borders and not being in Mercantilism.
How does that work?
5. The bonus for Espionage Point Spending is really for how much you've spent over the course of the game. I thought it was for how much EP you currently have gathered on all the other AI, and that it would decrease as you spend EP on spread culture missions. It didn't decrease. This is one reason why I played it safe and ended up with >4000 unused EP in the end.
6. Stone is important. My capitol was on PH marble, but I lacked stone. Not only do you need it for TGW, but walls and castles as well. I only found out after trading maps that there was unclaimed stone on a large island in the south, and didn't even realize immediately that I should grab it for walls and castles. When I finally did, I sent a settler, but it was one turn late, as Freddy got a settler in place that would have grabbed it had I not settled one turn eariler with stone in 2nd ring. This delayed hooking it up a lot and most of my important cities had castles already by the time it was up. (The southern island also had 4 unpopped huts, which I guarded until I got an Optics trade, but no Astro
.)
7. Lib->Constitution was a prime example of not thinking clearly and just doing stuff the way I'm used to doing them. Would have been so much cheaper and faster to tech constitution instead of going all the way to lib...