1: What's the failgold

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rate? If you aren't industrious/running organized religion/etc is it ever worth it to build wonders over wealth?
Always 1H = 1G. Any modifiers to hammers will in effect increase the amount of gold you get for a set of amount of raw hammers....but fail gold is only EVER based on
invested hammers. This means you don't really get more fail-gold because of these modifiers, but you simply invest more hammers more quickly in terms of turns elapsed. Does that make sense? So it's definitely a good thing to use those modifiers for fail-gold purposes, especially as the difficulty level ramps up and you have relatively less opportunity to put lots of hammers in a target wonder. This gets to be really relevant when passing a wonder around from city to city to avoid completion as you stack more and more fail-gold into it, hammer modifiers can really improve your total yield.
Second part of the question: depends on the wonder. I would only really draw a hard line on the Great Lighthouse: you always want it if you plan to build it, because it's one of the best wonders (depends on map type), nothing speeds it up except IND, and in the window you have to build it (can go by T60 or so, or earlier, if you are unlucky!) Sailing + Masonry can be a significant detour. It's a very good wonder with a fair amount of opportunity-cost, so you should aim to complete it IF you ever try to build it IMO and is poor for fail-gold purposes. I'd much sooner use Stonehenge, ToA, Oracle, Great Wall, or even Mids (if it's not realistic to get them) for early fail-gold targets.
Other wonders that are consistently good to complete are Mids and Taj.
Arguably Oracle, Kremlin, even Sistine (especially if you win Music anyway) just to keep it away from AIs and to avoid needing Caste/CRE/Monuments in new cities for border pops. Colossus can be good depending on the map but often isn't worth the detour into MC so early required to beat an AI to it (sometimes can be built by T80 on Immortal).
2: Playing an immortal iso game where I fogbusted my whole island, I had 8 cities and wanted to settle 5-6 more. When you have lots of land you can settle safely, is it better to settle all cities at once or one at a time? Usually I go for all cities at once since I get to start growing cottages asap
When still isolated and on one landmass, there's definitely a soft limit to how much you want to expand which is generally dictated by the number of cities you have as there is a sharp drop off in gain vs. upkeep cost once you start piling on # of cities costs...which go up for all cities with each additional city, as well as being applied to each new city itself. Without GLH, island cities, or trade routes to another civ (which in true iso require Astronomy) you probably want to wait lest you see a sharp drop in your economy. You can get away with a little more if ORG or FIN, but on Immortal 7-8 cities is where I usually start to "feel" the expansion without one of these elements to help out.
4: How often does ai trade amongst themselves?
Technically, they always trade as soon as they *can* according to their limitations. The only hard rule is that they can't trade a tech on the same turn they acquire it. It can get very complex. Attitudes, specific AI's monopoly thresholds, preferences for specific techs (based on which tech it is), whether they start to build the unlocked wonder, etc.
Some more insight though:
Attitude - many AIs trade readily at Pleased. All AIs trade at Friendly barring the monopoly rule, 1 turn limit, and if they are building a wonder. Only who has the tech has to meet the threshold, not the recipient. AIs never trade to their worst enemy regardless of their attitude level, even Mansa.
Monopoly threshold - different for every AI, check the Know Your Enemy thread. Ranges from extremes like Toku (never trades to a recipient unless all other players know his tech) to Mansa (always trades all tech unless to Worst Enemy). Also, I'm not sure this even applies to AI>AI trading in the first place.
Tech preference - certain techs are barred from trade because an AI values it more highly, which can modify the exchange (beaker) value. This is affected by AI flavors and simply weighting on the specfic tech i.e. a tech like HBR is valued much more highly than its actual beaker amount. Warmonger values military tech more, Zealots religious techs, etc.
Wonder rule - An AI never trades a tech if they have begun to build the associated wonder unlocked by it, until a certain amount of progress is put in it or one of the other thresholds supercedes it (I'm actually not sure which). I can not actually remember whether Friendly AIs trade wonder techs during construction off the top of my head, as it's a rare situation in most of my games.
In practice, by far the most influential effects are rooted in Attitude and relations the AIs have with each other. Which leads to certain conclusions you can draw by looking at the fields like:
-Similar Peaceweight leaders are more likely to like each other, and thus trade
-AIs in the same religion like each more, and are more likely to trade. Effect is compounded if they also like each other via Peaceweight.
-AIs with differing preferences value certain flavor tech differently, and are less likely to trade with each other
So you can at a glance look at a field and determine the relative likelihood a tech will get traded around. If your field contains a lot of peaceniks like Freddy, Liz, Gandhi (same religion) and Hammi (own 2nd religion) with a Ragnar and Shaka (same, third religion), you can assume that anything you trade to Freddy likely goes to Liz and Gandhi, Freddy/Liz/Gandhi are more likely to trade with Hammi than Ragnar/Shaka, and Hammi may choose to not trade with either group but is less likely to with Ragnar/Shaka. Ragnar and Shaka are likely to trade with each other, especially military techs. Etc Etc.
I've sometimes heard to not trade away good techs since ai could trade it to all other ais, is that something you really need to worry about?
Depending on your goal, yes definitely.
Example: Rifling. Rifling is a highly valued tech and AIs will trade it readily, even if they don't tech toward it that fast due to flavor. Militant AIs *will* tech toward it faster. Once one AI techs Rifling they tend to trade it around quickly, and the jump up from pre-Rifling to Rifles is a huge leap in AIs' defensiveness in cities. It's like a time-bomb waiting to go off. So if you were to run to Rifling for Cavs or mass draft, it would be very prudent of you to not trade it around to anybody until somebody self-teching it is eminent, as it will likely go everywhere. This includes your own vassals, who will merrily trade away key military tech to pick up crap they can't get from you.
Another less sharp example would be holding off on trading something like Nationalism until you have a commanding effort put into the Taj and can't be beaten to it, avoiding trading techs on the Lib path to slow the AI's shot at it, etc.
There's a lot of nuance to trading in general, but a very broad rule would be to not trade anything that grants a key advantage for the player (usually military tech) in order to slow the rest of the field's ability to proliferate it, and thus ride your advantage in war as long as you can. But you should readily trade other things that could speed you up in getting there, or to play catch up (which is the whole essence of a lot of bulbing gambits).