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
Cultural borders are determined by culture producing buildings in your city. For instance, the Obelisk adds +1 culture per turn. At certain milestones the city borders will expand to enclose a larger area.
If your city is on a border between you and a neighboring Civ, you'll have to have a higher cultural rating in order to maintain control of the tiles that both cities' borders would normally contain. You can hover over a tile to see what percentage control you have over a particular tile.
The more culture your city is producing, the more likely it is that you will push their borders back. Build culture-producing buildings in border cities to maintain control of your tiles. Culture producing buildings have a small purple "note" icon and usually a number denoting how much culture they produce per turn.
Certain World and National wonders also produce culture, and after researching Drama, you can put some of your Civ's economic output towards culture across all cities. Additionally, Great Artists can produce a Great Work in a city, which adds an immediate culture bonus. This effect is sometimes referred to as a "culture bomb" because it tends to push the borders of the city outward rapidly.
You may also be interested in this article on Cultural Victory, which contains a pretty good list of ways to make your Civ produce more culture.