Finally, I've got reliably working strategy of defeating deity AI on archipelago maps ("Play Now" settings).
Good nations to play are financial+organized, financial+industrious,financial+philosophical,financial+expansive,organized+industrious etc...
They first key goal is to get Great Lighthouse for +2 trade routes. That means initial stage will require researching sailing early on. Last step in beeline is masonry, so that your capital can construct lighthouse while you're researching masonry. First tech to research typically would be mining to let you construct mines around your capital and open way to bronze working and masonry. There's a decision to make whether to chop forests or not. If you've got lucky to get fresh water on your starting island, I'd say chop forests. If not, that's difficult call. If you have good production bonuses around or if forests are on the plain or if I'm industrious, I'd keep [most] of the forests. Otherwise chop. The choice of first city placement is related to this. Getting one or better 2 food sources within capital range is a must, which is not usually a problem. Of course, you also must place capital on the coast, which is really not much of constrain on archipelago. Starting with fresh water will allow you to chop more forests. Secondary consideration is to place the capital so that it's close to the center of your future empire. It's more of a guesswork on the first 1-2 turns, so it's secondary consideration.
Typically, starting build sequence would be worker, fishing boat/warrior, settler,lighthouse,great lighthouse. But it depends on nation you play and commerce/production balance. It takes a bit of micromanagement so that your tech advances and building go in sync. With this plan getting Great Lighthouse is almost certain (I've missed it only once). However, Great Lighthouse is really critical, so if in doubt, put all efforts into it (the capital doesn't necessary have to grow while building it).
I prefer to build a settler before the great lighthouse, but if I'm not industrious and don't have not much production bonuses or forests, I'd skip settler to secure Great Lighthouse. If on opposite, I've started as production powerhouse, I'd build galley/fishing boat (galley if there isn't enough room for another city on my starting island) and go exploring. Depending on timing, the first fishing boat, can spend couple turns looking around before starting to work the resource. The goal of the second boat is to establish foreign contacts and try to circumvent the globe.
Next cities placement. I will often prefer to settle another good island before putting another city on my starting island. Securing resources is obviously important consideration. The goal of initial phase is to have established couple of city that are going to be production heavy and another 1-2 which will concentrate on commerce while having somewhat reasonable production base (so that they can build buildings and national wonders reasonably quickly.
The next priority is to exploit your resources and discover new, which means getting some required technologies (animal husbandry, iron working etc).
Meanwhile, your galley/boat has gathered some info and that's the first moment when things can go really wrong. If you're on isolated cluster with no way to get out by the coast, that's a big problem (and that's the only really bad kind of start for this strategy). Waiting until astronomy is hopeless, I think, because you'll never catch up with AI in time without tech trading and foreign trade routes. So there're 2 options here. The first one is cultural bridge. If you're separated by narrow ocean straight 1-2 tiles wide (sometimes can only be deduced by guesswork) you can place the city on the shore and build obelisk which will result in a cultural bridge reasonably soon. This implies that you should consider possibility of this situation when placing your cities and to explore in such way to recognize this setup as soon as possible. If this doesn't work, you will have to switch to cultural race strategy.
The following phase is development of your empire. 2 production cities should build barracks and start to build military. First way is of the cheapest kind, to provide lone defenders to your new cities. Then they can switch to some better units that you'll use in later wars. Few archers, more catapults, swordsmen (if you got iron) are good investment. Naval power is going to be important, so you also need to build few galley. Early on, 5-6 galleys should be enough to sink enemy invasion if one happens. Those galleys should patrol on likely approach routes (so that you have time to gather all your galleys together before attacking the enemy fleet). In some cases AI may actually declare war without any invasion force. In this case just protect your fishing resources. But with this strategy AI will probably not attack you at all. All this time keep expanding and build new cities. With the great lighthouse, the coastal city with lighthouse and harbor will be making decent amount of commerce, so no reason not to build them. Especially, if you can get couple of sea foods and hill or two. Even tiny 1-tile islands with 2 sea foods around can sustain a good town. Just use slavery to convert food into buildings. If you play organized, build courthouses quickly as well to cut down on the maintenance. In any case, maintenance at this stage is going to be high, so be prepared to drop research rate down to 30%, 20% or worse. There's no reason to worry here, as your cities grow you'll be in much better shape.
Diplomacy. At this phase I'm trying to maintain decent relations with everybody, trade resources (those many small cities should have secured you plenty of extra resources which can be sold to AI for gold) and technologies. Keep open borders running on maximum. Foreign trade routes are really profitable. I don't adopt any state religions (and I don't research religious techs until I need them for something else).
Age of wars. The first serious war I plan will start when I get Steel (I make it a high priority). At the same time I'm preparing plenty of catapults and some gold reserves to do one turn upgrade. Somewhere along the line I've switched to Vassalage, so that most of them have city raider x 2 promotion and few barrage x 2. Other military units are grenadiers (some with forest defense + 2, others with hill defense + 2) and some melee units with city raider promotions. That means grenadiers has to be built last, and catapult and melee unit recruitment has to be completed earlier. And of course I have navy prepared to carry and protect my army. Next step is to choose the victim. Sometimes, there's no choice, because somebody got a big lead, won't trade anything with you and keep declaring war on you. In more fortunate circumstances you can select some neighbour from whom you can grab some good cities not too far away. But keep in mind that you still need to have good relationships with some AI who will tech-trade with you. Your first goal is to go for islands with good cities and resources (but not AI home islands, those will be too costly to conquer at this stage). Don't upgrade your melee units, but bring them into the war. They may get another city raider promotion cleaning up AI units invalidated by cannons. Then you can upgrade them into grenadiers (who can't get city raider otherwise). The military campaign should be well planned in all aspects, because you want to make your invasions quick and efficient. The window for this wars is rather short, because AI will soon get machine gunners and you'll have hard time to take their cities. Medic ships are useful to heal troops in transit. My navy on this stage consists of Frigates and Galleons. I won't keep going for the same AI. Typically I'd take couple of good nearby cities from one AI, make peace with him and attach another AI for another couple of cities. I don't mind giving them something afterwards to bring relations back to acceptable level (somethinglike cautous). This age ends when AI gets machine guns.
Empire buildup II. At this period I'm running hereditary rule, vassalage and slavery. I still keep producing military units in my production cities, but other cities build infrastructure. Ex-AI cities are usually handled in the same fasion. Rush theatre, rush lighthouse or harbor. This way instead of starving its population brings something useful. This makes those cities pretty good very quickly. One of them may become my shipyard (with drydocks), another can be 3rd production center, others can concentrate on science and money. I keep city defenses to the minimum (1 cheap unit) and just patrol seas with plenty of frigates. At this stage, AI is becoming less and less willing to trade tech, so I mostly rely on my own to research to railroads and artillery. When I get there, it's another age of wars.
Age of wars II. This time I upgrade my cannons to artillery and some of grenadiers with hill/forest defense promotions to machine guns. I still keep building grenadiers rather than machine guns, so that I can choose hill/forest promotions. Then I upgrade them. Now I invade somebody who hasn't got many [any] destroyers. Meanwhile I'm researching for destroyers myself and then quickly upgrade my fleet. Machine guns and infantry can't really protect AI from my army and I rarely lose more than 1-2 artilleries to take the city. At this stage I can take AI's home islands. This pretty much decides the game, because I become by far the biggest and strongest. Here priority becomes to clubber the leading AI to make sure he's not getting anywhere close to his spaceship. My research priorities here are biology and rocketry. My target military goal is to get infantry and SAM infantry. In fact, it's pretty much enough to take anything. City raider x 3 artillery and infantries can take care of offensive and AI can't do much against defenders with +2 hill/forest bonuses. I have to leave strong cities that have no appropriate nearby tiles for later though.
Cultural race strategy. In principle, it's a viable strategy on its own, however my main strategy works much better, so I revert to cultural race strategy only in the case described above, when I'm isolated from the rest of the world.
In this strategy, the 3 cultural cities has to have plenty of tiles around, with choice of production and commerce squares, because you'll want to switch them. It's important to build cottages early here and not rely on sea squares for commerce. Generally, I'd convert mines into windmills later in the game when many buildings are already finished. In this cirumstances you won't get any religions until late, so the goal is to grow those cities large. Research goal in this case is liberalism. You won't be researching far in this strategy. I'm ignoring naval power in this strategy and just build decent amount of troops, so that AI won't attack me. I don't plan to invade with them, so the choice of units is not critical. The main problem here is to get cultural victory before Ai gets space victory. Actually, I've never managed it But I came several times just a few turns short, so it's doable with some more micromanagement or some more luck. As your main cities get to the cap (health/happiness) start adding new cities which you'll need later to build supporting temples when you start building cathedrals. That's where production base in your cultural cities will become important, because you need to build those fast. Strangely enough, I wouldn't worry about cultural cities actually producing culture. Anyway, the bulk of culture points will be made in a final rush, when you have few cathedrals and set culture to 100% (at that time all other cities just build wealth to cover your expenses). Unfortunately, there's no good way to rush cathedrals, because you don't want to sacrifice population and you don't have gold/tech to rush for gold.
Good nations to play are financial+organized, financial+industrious,financial+philosophical,financial+expansive,organized+industrious etc...
They first key goal is to get Great Lighthouse for +2 trade routes. That means initial stage will require researching sailing early on. Last step in beeline is masonry, so that your capital can construct lighthouse while you're researching masonry. First tech to research typically would be mining to let you construct mines around your capital and open way to bronze working and masonry. There's a decision to make whether to chop forests or not. If you've got lucky to get fresh water on your starting island, I'd say chop forests. If not, that's difficult call. If you have good production bonuses around or if forests are on the plain or if I'm industrious, I'd keep [most] of the forests. Otherwise chop. The choice of first city placement is related to this. Getting one or better 2 food sources within capital range is a must, which is not usually a problem. Of course, you also must place capital on the coast, which is really not much of constrain on archipelago. Starting with fresh water will allow you to chop more forests. Secondary consideration is to place the capital so that it's close to the center of your future empire. It's more of a guesswork on the first 1-2 turns, so it's secondary consideration.
Typically, starting build sequence would be worker, fishing boat/warrior, settler,lighthouse,great lighthouse. But it depends on nation you play and commerce/production balance. It takes a bit of micromanagement so that your tech advances and building go in sync. With this plan getting Great Lighthouse is almost certain (I've missed it only once). However, Great Lighthouse is really critical, so if in doubt, put all efforts into it (the capital doesn't necessary have to grow while building it).
I prefer to build a settler before the great lighthouse, but if I'm not industrious and don't have not much production bonuses or forests, I'd skip settler to secure Great Lighthouse. If on opposite, I've started as production powerhouse, I'd build galley/fishing boat (galley if there isn't enough room for another city on my starting island) and go exploring. Depending on timing, the first fishing boat, can spend couple turns looking around before starting to work the resource. The goal of the second boat is to establish foreign contacts and try to circumvent the globe.
Next cities placement. I will often prefer to settle another good island before putting another city on my starting island. Securing resources is obviously important consideration. The goal of initial phase is to have established couple of city that are going to be production heavy and another 1-2 which will concentrate on commerce while having somewhat reasonable production base (so that they can build buildings and national wonders reasonably quickly.
The next priority is to exploit your resources and discover new, which means getting some required technologies (animal husbandry, iron working etc).
Meanwhile, your galley/boat has gathered some info and that's the first moment when things can go really wrong. If you're on isolated cluster with no way to get out by the coast, that's a big problem (and that's the only really bad kind of start for this strategy). Waiting until astronomy is hopeless, I think, because you'll never catch up with AI in time without tech trading and foreign trade routes. So there're 2 options here. The first one is cultural bridge. If you're separated by narrow ocean straight 1-2 tiles wide (sometimes can only be deduced by guesswork) you can place the city on the shore and build obelisk which will result in a cultural bridge reasonably soon. This implies that you should consider possibility of this situation when placing your cities and to explore in such way to recognize this setup as soon as possible. If this doesn't work, you will have to switch to cultural race strategy.
The following phase is development of your empire. 2 production cities should build barracks and start to build military. First way is of the cheapest kind, to provide lone defenders to your new cities. Then they can switch to some better units that you'll use in later wars. Few archers, more catapults, swordsmen (if you got iron) are good investment. Naval power is going to be important, so you also need to build few galley. Early on, 5-6 galleys should be enough to sink enemy invasion if one happens. Those galleys should patrol on likely approach routes (so that you have time to gather all your galleys together before attacking the enemy fleet). In some cases AI may actually declare war without any invasion force. In this case just protect your fishing resources. But with this strategy AI will probably not attack you at all. All this time keep expanding and build new cities. With the great lighthouse, the coastal city with lighthouse and harbor will be making decent amount of commerce, so no reason not to build them. Especially, if you can get couple of sea foods and hill or two. Even tiny 1-tile islands with 2 sea foods around can sustain a good town. Just use slavery to convert food into buildings. If you play organized, build courthouses quickly as well to cut down on the maintenance. In any case, maintenance at this stage is going to be high, so be prepared to drop research rate down to 30%, 20% or worse. There's no reason to worry here, as your cities grow you'll be in much better shape.
Diplomacy. At this phase I'm trying to maintain decent relations with everybody, trade resources (those many small cities should have secured you plenty of extra resources which can be sold to AI for gold) and technologies. Keep open borders running on maximum. Foreign trade routes are really profitable. I don't adopt any state religions (and I don't research religious techs until I need them for something else).
Age of wars. The first serious war I plan will start when I get Steel (I make it a high priority). At the same time I'm preparing plenty of catapults and some gold reserves to do one turn upgrade. Somewhere along the line I've switched to Vassalage, so that most of them have city raider x 2 promotion and few barrage x 2. Other military units are grenadiers (some with forest defense + 2, others with hill defense + 2) and some melee units with city raider promotions. That means grenadiers has to be built last, and catapult and melee unit recruitment has to be completed earlier. And of course I have navy prepared to carry and protect my army. Next step is to choose the victim. Sometimes, there's no choice, because somebody got a big lead, won't trade anything with you and keep declaring war on you. In more fortunate circumstances you can select some neighbour from whom you can grab some good cities not too far away. But keep in mind that you still need to have good relationships with some AI who will tech-trade with you. Your first goal is to go for islands with good cities and resources (but not AI home islands, those will be too costly to conquer at this stage). Don't upgrade your melee units, but bring them into the war. They may get another city raider promotion cleaning up AI units invalidated by cannons. Then you can upgrade them into grenadiers (who can't get city raider otherwise). The military campaign should be well planned in all aspects, because you want to make your invasions quick and efficient. The window for this wars is rather short, because AI will soon get machine gunners and you'll have hard time to take their cities. Medic ships are useful to heal troops in transit. My navy on this stage consists of Frigates and Galleons. I won't keep going for the same AI. Typically I'd take couple of good nearby cities from one AI, make peace with him and attach another AI for another couple of cities. I don't mind giving them something afterwards to bring relations back to acceptable level (somethinglike cautous). This age ends when AI gets machine guns.
Empire buildup II. At this period I'm running hereditary rule, vassalage and slavery. I still keep producing military units in my production cities, but other cities build infrastructure. Ex-AI cities are usually handled in the same fasion. Rush theatre, rush lighthouse or harbor. This way instead of starving its population brings something useful. This makes those cities pretty good very quickly. One of them may become my shipyard (with drydocks), another can be 3rd production center, others can concentrate on science and money. I keep city defenses to the minimum (1 cheap unit) and just patrol seas with plenty of frigates. At this stage, AI is becoming less and less willing to trade tech, so I mostly rely on my own to research to railroads and artillery. When I get there, it's another age of wars.
Age of wars II. This time I upgrade my cannons to artillery and some of grenadiers with hill/forest defense promotions to machine guns. I still keep building grenadiers rather than machine guns, so that I can choose hill/forest promotions. Then I upgrade them. Now I invade somebody who hasn't got many [any] destroyers. Meanwhile I'm researching for destroyers myself and then quickly upgrade my fleet. Machine guns and infantry can't really protect AI from my army and I rarely lose more than 1-2 artilleries to take the city. At this stage I can take AI's home islands. This pretty much decides the game, because I become by far the biggest and strongest. Here priority becomes to clubber the leading AI to make sure he's not getting anywhere close to his spaceship. My research priorities here are biology and rocketry. My target military goal is to get infantry and SAM infantry. In fact, it's pretty much enough to take anything. City raider x 3 artillery and infantries can take care of offensive and AI can't do much against defenders with +2 hill/forest bonuses. I have to leave strong cities that have no appropriate nearby tiles for later though.
Cultural race strategy. In principle, it's a viable strategy on its own, however my main strategy works much better, so I revert to cultural race strategy only in the case described above, when I'm isolated from the rest of the world.
In this strategy, the 3 cultural cities has to have plenty of tiles around, with choice of production and commerce squares, because you'll want to switch them. It's important to build cottages early here and not rely on sea squares for commerce. Generally, I'd convert mines into windmills later in the game when many buildings are already finished. In this cirumstances you won't get any religions until late, so the goal is to grow those cities large. Research goal in this case is liberalism. You won't be researching far in this strategy. I'm ignoring naval power in this strategy and just build decent amount of troops, so that AI won't attack me. I don't plan to invade with them, so the choice of units is not critical. The main problem here is to get cultural victory before Ai gets space victory. Actually, I've never managed it But I came several times just a few turns short, so it's doable with some more micromanagement or some more luck. As your main cities get to the cap (health/happiness) start adding new cities which you'll need later to build supporting temples when you start building cathedrals. That's where production base in your cultural cities will become important, because you need to build those fast. Strangely enough, I wouldn't worry about cultural cities actually producing culture. Anyway, the bulk of culture points will be made in a final rush, when you have few cathedrals and set culture to 100% (at that time all other cities just build wealth to cover your expenses). Unfortunately, there's no good way to rush cathedrals, because you don't want to sacrifice population and you don't have gold/tech to rush for gold.