Deity level guys citizen management

You set it to production focus, and then lock down the tiles you want to use. (food usually)
 
^This. Lock and relock tiles as circumstances dictate. I stay on production focus 98+% of the time.
 
The focuses are great most of the time. But do require baby sitting and sometimes further interdiction is required when your needs for that city become more specific.
It really depends on whether you're going all or wide though.

Tall: you more often than not have more general citizen management going on in your cities, as the cities themselves exist to fulfill many rolls. Also they grow so often for much of the game it can be hazardous to fiddle with locks. Automated citizens can remain reasonably optimized to changing conditions. Often If I lock in a template for them, I'll forget to update upon gaining population or completing tile improvements, losing more efficiency than I gained by optimizing it myself. If you're really diligent you can generally push the city a little harder with your own tweaking though.
A hammer missing here, or an extra food there are a relatively minor things in a 20 pop city, also nothing is really going to waste when the city has to do everything.

Wide: typically each city will have a very specific purpose. As a result citizen roles and population cap are much more consistent. When playing wide games I generally have every citizen in almost every city locked into place, with avoid growth on just in case.
 
I usually lock my academies and stay on general focus until renaissance then go to food focus.

The only time I use production focus is on building wonders when the AI has tech parity. The constant growth is much desired and after a certain point the hammers will just be there anyway.
 
I'm not a diety player, but I've definitely noticed that the AI default overvalues science and gold in comparison to growth and production. It's easy to see in cities with plantations early in the game, or with specialists late game after going rationalism.
 
as long as you remember to check your cities after they grow, production focus is always best. There is no reason to pass up those free hammers, even if it's a small amount. And yes you should always lock down your tiles manually.

just using the focuses and not microing tiles might be good enough to get the job done even on deity sometimes, but it's not going to be optimal and you might as well give yourself every advantage you can.
 
only important early game anyway; just stay on production and lock food tiles early, midgame go for food, and late game just use default; a size ~40 capitol works almost anything it can anyway.
 
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