From my experience, 3 military is good enough for average defense, it allows you to hold out till you can reinforce.
But for your style of play, perhaps 5-10 would be better, you don't want to many as it causes slow down in tech etc..., but then you don't want to get crushed. You should have more on the outer cities and reinforce from your inner ones, I try to always have 3 minimum in all cities, but doesn't always work, then any bigger cities up it to 4-5.
If you notice your enemies normally attack you with massive stacks, the only way to counter those are with a large stack yourself. Have 1 large stack that walks between cities and does the attacking, then leave 3 units in all your cities for normal defense, remember if you suddenly get attacked at a choke point (hopefully you have one) you can always reinforce from your other cities, knocking them down to 1-2 stuff like that.
Unfortunately, I do not know exactly how much you must culturally dominate a city for it to switch. That number may well depends on your difficulty level.
However, I think I can help answer your implied question: This city is more culturally mine. Why hasn't it switched to my empire?
First be sure city switching due to culture is turned on.
I assume it is, but this is an option you can set before the game, so its worth mentioning.
The threshold might not be 51%
This is what you supposed, and I agree this might be true. Until someone else chimes in with a number (or several for difficulty) lets assume something else is wrong...
Culture switches are not immediate.
The city will usually have at least one cultural revolt first, i.e. both you and the current owner of the city will see an event like "A [Spanish] revolt is taking place in [City]." This is a great sign for you, and means that you passed the threshold; the city would switch to your empire fairly soon if it had no troops in it. This has the unfortunate consequence that...
The current owner can put troops in the city to slow you down
The longer the city is in revolt in the name of your culture, the more likely it is to switch. So naturally, if the revolt is suppressed by, say, more troops, its less likely to be successful. I think with enough troops the revolts can be prevented altogether. I'm not sure of this, or whether a city can switch without revolting first.
Troops are the only way I can remember the current owner being able to fight you, but there may be others options I can't remember, like particular government choices or wonders?
Consider destroying the troops with espionage
If the troops can slow down the process, then get rid of them. You sound like you want to take the city without war, so spies are the option you have left. But, if you don't care whether you go to war or not...
Consider taking the city with military
If I recall correctly, a city that prefers you culturally will be "liberated" rather than "conquered". Unfortunately, this has the same problem you asked about taking the city cultural: how much is enough? I'm not sure, but I believe if they have revolted for you then its enough.
Liberating a city is effectively "this city is supposed to be mine, the people welcome me", I am certain its what happens when you retake a city you founded but lost, and has great effects:
- The city does not lose a population due to being "conquered".
- The people do not revolt, but begin working immediately.
- Buildings are more likely to survive the transition. (Perhaps all of them do?)
- (Does not apply to your situation but...) The cultural border the city had when you last controlled it are restored.
As a final note, if you could liberate a city, and a third civilization takes the city, they immediately have the option of "returning" it to you.
I feel like I've missed something, I will add it later if I think of it.
Best Answer
Cities are not free.
Each city you add to your empire increases costs by (I can't remember exactly which of these is right, maybe 2/3?) increasing general maintenance costs, increasing the cost of governments, or raising inflation. One of the costs at least is dependent on how far (unit travel wise) your cities are from your capital. Because of increasing costs, its possible to send your empire into an economic depression by expanding too quickly.
Some cities add nothing to your empire.
Early in the game you might take over a barbarian city. Barbarian cities spawn where no one else is, like Tundra, Jungle, and Desert. There's a reason no one else settled there yet, those cities just won't be worth your civilization's hard earned money or even your time controlling them.
Some cities are too dangerous.
Perhaps Egypt is on the way to a cultural victory, and you decide to stop them by taking their capital. Is that one city late in the game really worth the chance of Egypt getting it back and finishing their 3 legendary cities? Burn it to the ground.