Alright this wil be the start of a guide which deals with ways to hopefully improve your micro and shave turns off growth/production/wintime.
the first tip is basic, its the trick of locking production focus in the early game, many players know the way it works, but here it is.
when you grow from size n to n+1 your production is counted after your food is counted, and your growth is inbetween these 2 counts.
Therefore if you set production focus with lets say 5 production and 1 turn to grow with a hill tile, nearby and a grassland tile nearby, then you will make 7 production that turn instead of 5, with the same food amount, same thing goes for gold focus, you can gain slightly more gold if you need 1-2 gold for some reason.
okay, next up is which tiles you work, say you are doing normal tradition opening, and in the beginning turns your cap is 3 pop, with 4 grass tiles and 2 hills, now you are about to build your granary and should you work 3 food tiles or 2 food 1 hill?,
well working the 3 food tiles will give you better growth while building the granary, and more growth total until granary is done compared to working hill, but working the hill tile is often correct.
Since, you will get that granary (i think granary is 60 hammers on standard) in 9 turns instead of 12, lets say that on average you have 1 granary resource, after 12 turns working the hill tile you lost 2 food for 12 turns which is 24 food, but you gained 9 food from 3 turns of granary growth, total food lost is 15.
you need 30 food to grow 1 pop at size 3 so you have lost half a pop.
total production gained is 24. this is equivalent of a scout on standard speed, so now you ask yourself, are you better off going scout then granary than granary and growing ½ pop.
early game the choice should be obvious, a scout is better than ½ population, on average the scout will find ruins which are worth more than ½ pop, and will gain gold from city states, and find wonders, and civs, terrain, the list goes on. You get the idea.
with the granary and the scout up, working 2 2 food tiles and 1 3 food (1 from gran) +2 from gran you have surplus of 5. At this point it will take you 3 turns of growth to reach the food gained from working the 3 grassland tiles, and although there is a snowball effect of the growth of working the 3 grassland tiles which is a bit complicated to explain in detail, then i hope you follow me in the thought that a scout early is a very valuable thing to have, and growth early is not that important if you can catch up later, and generally you should be aware that early production is important and production is more important than growth in the very early game, of course things change when you get to civil service.
TL;DR: prio early production
Next up is what your workers can do
the optimal strategy for deity is worker stealing, instead of producing, i hope everyone will agree with me on this point.
Now a mistake that alot of players will make IMO is that they will make farms too early. You have a nice wheat tile with a granary, and you stole 2 workers, what is the best thing to do?
usually you will have to calculate when you get your settlers out, i like to do tradition/liberty mix, and therefore i know that i will make settlers when i get the free settler policy, so if i see that there is say 8 turns to that policy, then its simply not worth it to make a farm yet.
The amount of food you will get before you have to produce settlers is not worth it, and you are better of making a mine, even probably 15 turns before, if you dont have 2nd worker.
Because ideally you want to work at least 2 improved mines when you kick settlers out, and then you probably would also like to chop into settlers, which require time also, then when you can see that you cannot improve another mine before like 3 turns before your last settler, this is the time to make farms, because now your capitol can grow a bit.
TL;DR: make mines early, not farms.
then there is the question of when to chop forests.
as you can probably see, its very essential to get mining early, its the best tech for workers. is it a good idea to chop out a granary? Yes, the chops here are well spent, you gain a slight amount of food in addition to getting faster through your opening buildings/units.
it is almost always a good idea to chop forests early, and definately not worth saving them for lumbermills (in some specific cases maybe, but for general play this holds) consider that a forest early on is 20 produciton, and your cap is producing maybe 5-7 production a turn, and much less for expos. now consider that production is very important early game, and that one chop is equivalent of 3-4 turns of production. imagine later in the game when you have lets say 100 production, that forest chops would provide 300-400 hammers for a chop, that would be pretty huge right? well it pretty much scales down, shaving 4 turns off your granary/settler/worker is alot.
though you dont wanna chop into buildings when you cant build important buildings, example could be chopping a market, instead of saving for university (if you dont have the cash to buy).
TL;DR: chop early
which brings me to my last point for now, the very small micro gains.
you should realize that some units/buildings are more important to get out early than others, say you are building a scout and you are producing at 6/turn, a scout is 25 production, you end up at 24 in 4 turns, here you should be looking to work a tile with one more hammer for one turn, even if it costs you a bit of food, its just better to get the hammers in the scout and get it one turn faster, than overflowing into the next build, seeing that the first scouts you get is always more important than the latter, and the sooner the better, same thing goes for shrine, you want to make sure that you dont have too much production overflow, if at all possible try to hit the amount required for a shrine, unless you have awesome food tiles.
say you are building a university and you have a choice of getting it in 5 turns or 6, with the latter having just a few more points in food, and alot of production overflow, and you know that your next building is a market, the optimal thing here is to get the uni 1 turn faster.
notice that on quick speed, a scout is 16 hammers, and such you will often be in a situation where you work a 2 food tile, for a production total of 5, needing 4 turns for initial scout, you should work a plains or hill for one turn to get it out faster, if you work a hill, you will overflow with one production into the next scout, giving that 3 turns aswell. These things matter mostly in the first 20 turns of the game.
1 turn faster scout, is often the difference of 30 gold from CS, or a ruin, definately worth it.
the first tip is basic, its the trick of locking production focus in the early game, many players know the way it works, but here it is.
when you grow from size n to n+1 your production is counted after your food is counted, and your growth is inbetween these 2 counts.
Therefore if you set production focus with lets say 5 production and 1 turn to grow with a hill tile, nearby and a grassland tile nearby, then you will make 7 production that turn instead of 5, with the same food amount, same thing goes for gold focus, you can gain slightly more gold if you need 1-2 gold for some reason.
okay, next up is which tiles you work, say you are doing normal tradition opening, and in the beginning turns your cap is 3 pop, with 4 grass tiles and 2 hills, now you are about to build your granary and should you work 3 food tiles or 2 food 1 hill?,
well working the 3 food tiles will give you better growth while building the granary, and more growth total until granary is done compared to working hill, but working the hill tile is often correct.
Since, you will get that granary (i think granary is 60 hammers on standard) in 9 turns instead of 12, lets say that on average you have 1 granary resource, after 12 turns working the hill tile you lost 2 food for 12 turns which is 24 food, but you gained 9 food from 3 turns of granary growth, total food lost is 15.
you need 30 food to grow 1 pop at size 3 so you have lost half a pop.
total production gained is 24. this is equivalent of a scout on standard speed, so now you ask yourself, are you better off going scout then granary than granary and growing ½ pop.
early game the choice should be obvious, a scout is better than ½ population, on average the scout will find ruins which are worth more than ½ pop, and will gain gold from city states, and find wonders, and civs, terrain, the list goes on. You get the idea.
with the granary and the scout up, working 2 2 food tiles and 1 3 food (1 from gran) +2 from gran you have surplus of 5. At this point it will take you 3 turns of growth to reach the food gained from working the 3 grassland tiles, and although there is a snowball effect of the growth of working the 3 grassland tiles which is a bit complicated to explain in detail, then i hope you follow me in the thought that a scout early is a very valuable thing to have, and growth early is not that important if you can catch up later, and generally you should be aware that early production is important and production is more important than growth in the very early game, of course things change when you get to civil service.
TL;DR: prio early production
Next up is what your workers can do
the optimal strategy for deity is worker stealing, instead of producing, i hope everyone will agree with me on this point.
Now a mistake that alot of players will make IMO is that they will make farms too early. You have a nice wheat tile with a granary, and you stole 2 workers, what is the best thing to do?
usually you will have to calculate when you get your settlers out, i like to do tradition/liberty mix, and therefore i know that i will make settlers when i get the free settler policy, so if i see that there is say 8 turns to that policy, then its simply not worth it to make a farm yet.
The amount of food you will get before you have to produce settlers is not worth it, and you are better of making a mine, even probably 15 turns before, if you dont have 2nd worker.
Because ideally you want to work at least 2 improved mines when you kick settlers out, and then you probably would also like to chop into settlers, which require time also, then when you can see that you cannot improve another mine before like 3 turns before your last settler, this is the time to make farms, because now your capitol can grow a bit.
TL;DR: make mines early, not farms.
then there is the question of when to chop forests.
as you can probably see, its very essential to get mining early, its the best tech for workers. is it a good idea to chop out a granary? Yes, the chops here are well spent, you gain a slight amount of food in addition to getting faster through your opening buildings/units.
it is almost always a good idea to chop forests early, and definately not worth saving them for lumbermills (in some specific cases maybe, but for general play this holds) consider that a forest early on is 20 produciton, and your cap is producing maybe 5-7 production a turn, and much less for expos. now consider that production is very important early game, and that one chop is equivalent of 3-4 turns of production. imagine later in the game when you have lets say 100 production, that forest chops would provide 300-400 hammers for a chop, that would be pretty huge right? well it pretty much scales down, shaving 4 turns off your granary/settler/worker is alot.
though you dont wanna chop into buildings when you cant build important buildings, example could be chopping a market, instead of saving for university (if you dont have the cash to buy).
TL;DR: chop early
which brings me to my last point for now, the very small micro gains.
you should realize that some units/buildings are more important to get out early than others, say you are building a scout and you are producing at 6/turn, a scout is 25 production, you end up at 24 in 4 turns, here you should be looking to work a tile with one more hammer for one turn, even if it costs you a bit of food, its just better to get the hammers in the scout and get it one turn faster, than overflowing into the next build, seeing that the first scouts you get is always more important than the latter, and the sooner the better, same thing goes for shrine, you want to make sure that you dont have too much production overflow, if at all possible try to hit the amount required for a shrine, unless you have awesome food tiles.
say you are building a university and you have a choice of getting it in 5 turns or 6, with the latter having just a few more points in food, and alot of production overflow, and you know that your next building is a market, the optimal thing here is to get the uni 1 turn faster.
notice that on quick speed, a scout is 16 hammers, and such you will often be in a situation where you work a 2 food tile, for a production total of 5, needing 4 turns for initial scout, you should work a plains or hill for one turn to get it out faster, if you work a hill, you will overflow with one production into the next scout, giving that 3 turns aswell. These things matter mostly in the first 20 turns of the game.
1 turn faster scout, is often the difference of 30 gold from CS, or a ruin, definately worth it.