I remember doing some math on the "economics of happy" ages ago. Yes, in terms of maintenance the basic happiness buildings are better than luxuries; but the hammer cost has to be accounted for. In my math I simply settled for having the purchase price of the building as its base cost and then adding maintenance. If a Coliseum is built on T100 in a game that lasts until T250, as an example, it's overall cost is 500 gold + 150 * 2 = 800 gold or 5.3 gpt for those 150 turns; which is slightly worse than a luxury. With a longer lifespan of 180 turns it would be a little less than 4.8 gpt for 2 happy, which is still worse than a luxury. Of course you don't actually rush buy everything in your cities so it comes down to how you evaluate hammers vs. gold. The possibility of building the Circus Maximus also helps improve the value of Coliseums. How much would it cost to ally and keep a mercantile CS for those 150 turns? Assuming 1 influence lost per turn, so that you'd need to buy 210 influence in total, that could amount to something like 3500 gold (assuming you can buy 60-70 influence for 1000 gold every now and then), or 23.3 gpt for 11 happy; even that is just about on par with a basic luxury, so it comes down to situational stuff like luck with quests. All in all I've played with a base assumption that Circuses are great, while Coliseums, luxuries and merc CS's are about equal until something tips the balance towards one thing or the other.
But basically I agree... pop costs happy which costs gold. And while pop is great cause it creates beakers, hammers and sometimes gold too, it can be economically straining to run a large and growing empire. And gold is uniquely valuable as the currency for diplomacy, where it can often help you to control the game, undermining the stronger AI's chance of winning and eventually leading to your own (by diplo or whatever).
Yeah, the Hammers need to be taken into account when building Happy. Because rush-buying a Colosseum to stay happy is going to carry a different set of costs.
But the thing is, when you're staying small to avoid excess unhappy, your opening build order looks a lot different. When I am expanding Liberty-style for space, size or military, then my BO is usually Monument > Granary/Archer, then possibly Water Mills on top, mixed in with Forge/Stable/Stone Works. Obviously in this style, it makes no sense to trade Happiness away, because this approach is using Happy/Gold to get Hammers/Growth in the first place. So, I will either have enough Happy to avoid building Colosseums until 5th or 6th build, or I will not have expanded.
Under an Economic/Religious style though, I am looking for things I can build that do not charge too much maintenance. It can even become a struggle to avoid this. I don't want Units or Growth. Granaries themselves are a good building at 2F for 1G, but it is the less-productive population itself that you don't want to pay the Gold for. Small cities where I want to work 2-3 low Food tiles build Granaries, but otherwise no. What a more typical opening build looks like is Shrine (if Religious) > Monument > Circus/Colosseum > Temple/Market, then everything else, buying Workers/Trade Units. The Happy buildings are so high in the build-order because at the rate I can trade luxuries to the AI (~2G/1H), they actually represent the most immediately productive building that a size 2 city with one Gold tile can build. It basically nets 3 Gold (4, less 1 maintenance) right away, without having to rely on modifiers, etc. Temples under Theocracy are good once you have some base tile yield, but are neutral or negative otherwise. I'm certainly building Markets instead if I've unlocked Currency, but second build usually dictates a Happy building.
So, you're right when you say that it comes down to how you value Gold v Hammers. But the principle here is changing your play and BO depending on which, and not to just follow one BO for all games that presumes size > all.
On Mercantile CS's as well, I find those always represent Gold savings if you are not competing with an AI. They provide 2 luxuries at 4 Happy each, then 6 for allied status. That's 28 GPT at 2g/1h. Your Influence degrades at 1/turn, .75/turn if shared Religion(?), and the worst deal you are getting on Influence is 250g/15, or ~17. Doing the math straight across, the worst you can do is 28 to 17 surplus, with shared Religion putting it up to 28/.75 or ~37 to 17. Even an oddball double-luxury CS that is not Mercantile gives 16 to ~17, and then whatever it gives you goes straight to net.
To get the Influence up in the first place, you should consider the initial investment a sunk cost. In economic terms then, you don't count it at the margin like this. You buy a Merc CS because it is a profitable asset. Or coming at the other end, you buy CS's because the alternatives of rush buys in cities is such a bad deal (except Workers and Trade Units). Even if you do allocate the overhead over the life of the game, the net ~10gpt worst case Mercantile recoups even a 1000g outlay within 100 turns. About Turn 90-100 where the second round of 30 turn luxury trades expire is where you should be looking to buy them, and that's more than enough time to get positive. The astute thing to do is keep an eye on CS personality types, look at which quests they're offering, and plan accordingly. They often ask you to hook up the Merc luxury of the type they don't give, and you should be able to trade straight across for a normal lux they're asking for too.
Bottom line, it is a good deal at this Turn 90-100 point in the game to trade your own Luxuries to Friends until you're unhappy, then use that Gold same turn to buy up a Mercantile CS to put yourself back into positive. It's something that I've often done to good effect. The only thing you have to watch out for are the CS hungry AI's on the map, and who is competing for those CS's at that point.
@multiplayer, that is always good for a laugh. This game works only slightly better in MP than an FFA map of Starcraft. There's no check on human player's ability to exploit one another for the very reason that there's no diplo. It's brinkmanship at its worst. Never trade lump sum, or you'll get DoW'd within a turn every time. A human player will DoW you Turn 40 just to capture your Settler, then justifiably expect you to come to the trading table 10 turns later if it's in your best interest. Talking about Multi, you might as well be talking about the "always war" setting.
That's not to mention the double-blind, rock-paper-scissors nature of Multi to begin with. Two players go war, one peace, and the slowest one to go war wins. Two go peace and one war, whichever peaceful player doesn't get attacked wins. It's just completely about perverse incentives and collusion, not about game mechanics at all. Which is why "this would never work in multi" is such an absurd refutation.
I'd say around 30% of the time actually. (on the other hand EVERYONE loves aesthetics... and piety... can't remember a game where these trees were not picked)
