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Do not be afraid of decadence making buildings. Regional decadence degrades by 10% each turn. So a building doesn't give you infinitely upscaling decadence until it overcomes you. Take the monument you have probably seen. When its decadence is fully spun up it is giving you 10 culture but only 2.5 decadence. So you are winning the ratio.
Note that any given category of building has tiers. You can access tier 2 when you have 3 buildings of its type made, and tier 3 with 6 buildings. Note that these are separated by type even if they share the same line in the UI. So infrastructure (yellow) do not advance the tier of military (red) buildings. If you really want to boost your culture you want those tier 2 and tier 3 buildings.
Final note here. Don't panic if you dip in the rankings because of some early conquests. The rankings tend to be very close early on so a little bit of change can swing you pretty wildly. Plus you get a shot of extra decadence when conquering a new territory but the 10% per turn degradation still applies. As long as you don't let yourself stay in the bottom third for so long you regress it'll be fine. Get the territory you need, stabilize your culture, expand a bit more and so on. As you get bigger new conquests will hit your ratio less and less so you'll see smaller and smaller swings.
As for your religion. Its all tied up into your pop's ethnicity. As egypt you likely have a mix of egyptian, hellenic and desert nomads. The non-egyptians will convert gradually and you'll get decisions and events to help push that along.
PS I got status age penalty +139. I regressed in government rank and get some nasty modifiers. What game does? Add twice more decadence so I can crumble at much higher rate...
BTW I got status age penalty at +200 without getting any new provinces. I had most of my population working on culture but my CDR is still tanking.
PS If this is beating TW so easily tell me where I can find my conversion rate details, how many pops converted from egyptian to hellenic, etc.
http://www.slitherine.com/forum/viewtopic.php?f=563&t=98992
Here are 4 save game files from my Aegypt campaign:
https://we.tl/t-92OLKXfTr3
Just DL them into your save game folder and open them up in game. You can check out what I did in detail.
One strategy is to use diplomacy to add Nubia, Aethiopia and Cyrene as Client States. This seals your borders with buffer states and doesn't give you decadence from conquest. Then concentrate on culture. Also, plenty of buildings don't add any decadence. Build those. If you do conquer a region, deconstruct any buildings that cause decadence.
P.S. This is from the manual (chapter 6.3.4) on ethnic conversion:
You can slowly change the ethnicity of your population by enacting
certain decisions. The chance of a given population point converting
to your ethnicity is related to their underlying unrest value (6.4.2,
derived from their own ethnicity). Basically a Germanic population
point is less likely to change ethnicity than a Hellenic one.
I don't know how this works exactly because I win anyway. Good luck!
Here's a link to a lot of general tips I made:
http://www.slitherine.com/forum/viewtopic.php?f=563&t=98599