How lux slider and happy faces are calculated?

Say I'm in Monarchy with 30% lux, with MP it keeps people happy.

Now if I revolt to Republic, will I have to keep the lux rate higher? (40%?) Since I will lose the MP. Or it will actually be lower, since Republic gives more commerce thus more gold goes into lux with the same lux rate?

Anyone knows how the lux rate / happy face formula is? Does the "percentage" count, or the "absolute gold"?

Your city produces base commerce. This base commerce is then divided into luxuries, science, and taxes. Then building bonuses take over.

Each citizen produces a certain amount of commerce. An unroaded square not by a river produces 0. Roaded squares not by a river or squares by a river but unroaded produce one (as do sea squares, I think). Roaded squares by rivers or coast squares produce two. Various resources can increase this.

Now, the answer to your question is that it greatly depends on the commerce of the city.

City 1: Size 6 with all 6 citizens working producing 10 base commerce. This gives 3 happy faces from lux tax. One born content and 2 MP and it's good to go in Monarchy. Change to Republic and the citizens produce 17 base commerce, none of which is lost to corruption (in this example). 30% luxes gives 5 happy faces from lux tax and one borne happy and it's fine.

City 2: Size 6, not as developed. All 6 citizens working but 3 are on undeveloped squares, so you have only 4 base commerce. That's one happy from lux tax, say 3 from MP, one born happy, and a temple. Change to Republic and base commerce is only 8 (only the three citizens getting commerce initially plus the central square gain the bonus). Lux tax gives 2 happy at 30%, which isn't enough in Republic, with the loss of MP.

City 3: Size 12. All citizens working developed squares gives 20 commerce in Monarchy. That's 6 happy from lux tax at 30%. One born happy means 5 happiness is coming from other sources (say 2 MP, a temple, and two luxes). Changing to Republic gives 33 base commerce, so 30% lux tax gives 10 happy faces. That's 14 with a temple, two luxes, and one born happy. You can almost get almost away with 20% luxuries (7 happy + 1 for temple + 1 born + 2 lux = 11 is CLOSE) in this city.

The key is the base income from worked squares, for happiness. Lux tax is a straight percentage of that and has no multipliers.

HTH,
Arathorn

Thanks Arathorn, very intuitive post. Let me summarize:

1. Each city sponsors its own happy faces from its own lux spendings.
2. 1 base gold == 1 happy face (which brings one unhappy face to content, or one content face to happy). So if the city produces a lot of gold, even just 10% can sponsor a lot of happy faces.

microbe said:

Thanks Arathorn, very intuitive post. Let me summarize:

2. 1 base gold == 1 happy face (which brings one unhappy face to content, or one content face to happy). So if the city produces a lot of gold, even just 10% can sponsor a lot of happy faces.

Click to expand...

Remember that in Arathorn's excellent post his examples did not suffer any corruption. In highly corrupt cities the luxury slider will be far less effective since corruption is first applied to the base commerce, and then the luxry slider percentage is applied to the net available commerce. So, a city might produce 40 commerce, but if 35 are lost to corruption, then a 10% luxury slider works against the net available 5 gold, yielding 1 gold for entertainment.

Also, entertainment (like luxuries) is first applied to content citizens (moving them to happy) before any entertainment is applied to unhappy citizens (moving them to content).

Corruption is indeed a big issue and is applied to calculate the net gold income. That is, a city producing 40 commerce but losing 34 to corruption will only get one happy face from 10% or 20% lux tax (6*.1 and 6*.2 both round to 1). I don't recall the exact rules for roundings of .5, so I gracefully avoided them. It can be an issue, occasionally. Typically, however, cities suffering from very high corruption can be handled with specialists, because the loss in production from "working the fields" is minimal.

Whether content are made happy or unhappy made content only mattes if you're looking for WLTxD. Otherwise, you just need to sum to zero or greater (where happy citizens count as +1, content/specialists count as 0, and unhappy as -1). 4 happy, 2 content, and 4 unhappy is just as riot-free as 10 content. In my mind, they're essentially equivalent.

But, yeah, looks like you've got it pretty well under control. The key fact I kind of skipped over but that you got anyway is that 1 gold = 1 happy face.

Arathorn