5/5/2021 Founder Beliefs

CrazyG

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Work in progress:

Let's do the math on these guys and make a tier list. I'm going to do an analysis based on these ideas, which should represent a fairly typical game:
  • You get a religion on turn 85.
  • Let's see what you get in the first
  • I'm estimating that you buy a missionary to spread to your own cities every 8 turns (a 25:c5faith: per turn estimate, it's a decent start), so you'll use 4 in this window.
  • I'll give each a 'score' mostly equal to their total yields
  • I'm counting :c5gold: as 0.5 a yield
  • Not counting :c5goldenage: or :tourism: as part of total yield counts
You could add more, such as discounting :c5food:, however it isn't really needed. These numbers don't end up close together, the gaps are very large and small changes won't affect it.

Spoiler Apostolic Tradition, S Tier :

Whenever a missionary spreads, you get 25:c5food:. You get 25 more per :c5citizen: he converts, and it applies to great prophets too (probably inquisitors too but I cannot confirm).
You can repeat cities.
You get 100:c5faith: for discovering a tech, scaling with era.

If each missionary can convert 4:c5citizen: each spread (this estimate is low) you'll have collected 1,000:c5food:. You probably discover 7 or 8 techs in this window, so 800:c5faith:.

A rough score of 1,800, and these assumptions were on the low end. That averages to 20:c5faith: and 25:c5food: per turn, with a lot of room to increase.

Granted :c5food: isn't always useful, but on the other hand :c5faith: always is. This is a good choice to fast enhance since it provides :c5faith: without requiring you to spend :c5faith:, and you can wait to collect the food.


Spoiler Council of Elders D Tier :

You'll get 30:c5production::c5science: for your capital and per each new city you spread to. Bonus caps at 15 Cities.
This increases slowly per city already following (math is 30+x/3+(x^2)/3).
You cannot repeat cities, thus it becomes weak in the late game.

You'll earn 385:c5production::c5science: by turn 125, averaging 9.8:c5production::c5science: per turn.


Spoiler Ceremonial Burial, B Tier :

15:c5culture::c5faith: for using a great person, scaling with number of cities, max 25 cities.

If you have tradition, it's possible to have a few great people in this era. I'll try these estimates, which are possible but generous.
  • Engineer born with 3 cities following
  • Scientists born with 5
  • Writer born with 7
  • Merchant born with 9.
You'll get 360:c5culture::c5faith:, a score of 720, or 9:c5culture::c5faith: per turn on average. In the short term it's weak, but eventually it becomes very strong, potentially 375:c5culture::c5faith: per great person, but :c5faith: also drops off in value in the late game.

In conclusion it's hard to evaluate. It gets a B because while it's not bad there are stronger options.


Spoiler Divine Inheritance C Tier :

+20% to all yields in holy city during golden ages.
One perk is you don't need to spread at all!

This is hard to compare to beliefs that give bonus yields, but I'll start. The natural comparison is Way of Transcendence since both give all types of yields.

From below, WoT is giving around 9:c5food::c5production::c5gold::c5science::c5culture::c5faith: per turn if you average it out (with 4 missionaries by turn 125 when you reach medieval era).
If you had permanent golden age, you would need 45:c5food::c5production::c5gold::c5science::c5culture::c5faith: to match, which partially be done (a tradition cap can reach 45:c5culture:/:c5science: by this point).
However with a more realistic 10 turns of golden age, you need 180:c5food::c5production::c5gold::c5science::c5culture::c5faith: which is totally unreasonable.

What about later eras?
Well from below, to match a very poor WoT bonus for medieval era, your holy city needs 60 of every yield and infinite golden age. You just won't get close.

I really like playing with this belief, but truthfully it's a C.


Spoiler Holy Law, B Tier :

When you unlock a Policy, gain 5 :c5faith:,:c5science:,:c5gold: for every Follower of your Religion (max 250 Followers).

There are probably 3 social policies in the 40 turn window? This requires guessing followers, not just cities, which is harder.

I'll try these numbers:
  • New policy with 3 cities following, so 10 followers
  • New policy at 7 cities following, maybe 25 followers
  • New policy at 9 cities, so 40 followers
That will get you to 375 of each, or a score of 938, or about 23 yields per turn on average.


Spoiler Hero Worship Unranked :

Receive :c5faith: and :c5goldenage: when you conquer a City, as well as Great General Points (if City is landlocked) or Great Admiral Points (if City is coastal). Bonus scales with City population and Era.

Depends on how much you conquer and I don't know the details for the numbers, so I can't do an analysis like the others. I really like the design and concept but I suspect it's trash compared to what the others can give.



Spoiler Theocratic Rule Unranked :

+15% :c5gold::c5culture::c5faith: during WLTKD in all cities.

This is hard to evaluate compared to the bonus yields because how much early WLTKD you get changes a lot game to game.

Early on it's weak because its a % bonus and because :c5faith:/:c5culture: always round down (if you have 6:c5faith:, an extra 15% is 0.9, but it rounds down to 0).

My gut says C because I think it's close in quality to divine inheritance but I won't rank it until I can think of a decent math estimation.


Spoiler Way of The Pilgrim, S Tier :

8:c5food:8:c5gold: in every city. Let's say you have 6 cities and you spread to them on turns 96, 97, 106, 107, and 116 (this assumes you can buy a missionary every 8 turns, so 25:c5faith: a turn).

Those numbers would give you 1144:c5food::c5gold:, for a total score of 1716. This ignores the :tourism:.


Spoiler Way of Transcendence: S+ Tier, The Overall Strongest :

When you enter a new Era, Holy City gains 20 of every Yield for each City following your [ICON_RELIGION] Religion (max 25 Cities), scaling with Era.

If you can get 4 missionaries out before medieval era, you'll have 9 cities following (including your holy city.) That'll be 9x20x2 = 360 of each yield:c5food::c5production::c5gold::c5science::c5culture::c5faith:), a total of 2,160 yields (I'm not including :c5goldenage: here), or a score of 1980.

It gets even better for later eras. If you enter Renaissance after another 50 turns, and spread to just 10 cities (and you can easily spread to more), you'd earn 600 of each, or 12 per turn. From there it just scales with era and keeps getting better.

A turn 85 religion into turn 125 medieval era means you effectively earned 9:c5food::c5production::c5gold::c5science::c5culture::c5faith: per turn on average (this is the most-backloaded, but it's still ridiculous). Also it's providing :c5goldenage: and :tourism:


Note that generally if you can spread more, it makes the good choices even better and the weak choices even worse.
 
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DeAnno

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Depends on how much you conquer and I don't know the details for the numbers, so I can't do an analysis like the others. I really like the design and concept but I suspect it's trash compared to what the others can give.

IIRC the last time I tried it was right before I conquered a size 4 city, and it gave 100 of each of its yields, suggesting the base scalar is 25. I reset and chose something else instead because I found it quite weak. Considering all these yields but Faith suffer pretty steep diminishing returns, and that conquering cities is hard at higher difficulties, I think it could afford to have much higher numbers and not be broken.

I do feel WoT deserves to be better by the numbers than the rest, maybe not as much as it is but definitely better, because it's very awkward to use it and you often have to wait a long time for the first yields.

You forgot the WLTKD belief here, though maybe you just hadn't wanted to try working it out yet. In my experience on more recent patches WLTKD is overall pretty easy to keep up if you want though, especially if you are swimming in gold from trading strategics away.

Council of Elders has been trash since the "bug" in it was found and the yields dramatically reduced. They are just too small now to justify how bad it becomes later on. You have a lot of control to land wonders with but its too weak now just not worth it anymore.

Pilgrim and Apostolic both have new elements which don't fit the old Founder beliefs and they've been a little divisive. I appreciate the new mechanic on Apostolic even if it needs toning down, but I do think Pilgrim feels a bit too much like a follower belief on steroids right now.
 

Stalker0

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So I've been using Apostolic in the last several games, and those food numbers are much higher than what I see. The highest food I see per conversion is like 300, so 900 if your doing a borodur missionary. I would also say from Immortal turn 100 is the standard for a religion, 85 is much earlier and definitely seems more like a deity bias to me.
 

CrazyG

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So I've been using Apostolic in the last several games, and those food numbers are much higher than what I see. The highest food I see per conversion is like 300, so 900 if your doing a borodur missionary..
Oops I had an error. It should be 1,000 total (125:c5food: x2 spreads, x4 missionaries). I was coutnign the 2 spreads twice in my spreadsheet, fixed.

To be clear though, even with the error my numbers were lower than yours, right? 300:c5food: per spread means your missionary converted 11:c5citizen:, I'm guessing that each spread converts only 4:c5citizen:.

I would also say from Immortal turn 100 is the standard for a religion, 85 is much earlier and definitely seems more like a deity bias to me.
Which belief does this change the numbers for? I think I've been really generous to the weaker beliefs while low-balling the stronger ones (my Way of Transcendence numbers assume you never spread to more than 10 cities).

You can test a range of turn 100 to 140 if you wish, the goal is just to look at the first 4 missionaries in detail, most of the numbers are about the same the beliefs are so far apart that changing the details doesn't change the results.

You try, throw some wild assumptions in (I did) and you'll never get CoE even close to what WoT gives.
 
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CrazyG

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IIRC the last time I tried it was right before I conquered a size 4 city, and it gave 100 of each of its yields, suggesting the base scalar is 25. I reset and chose something else instead because I found it quite weak. Considering all these yields but Faith suffer pretty steep diminishing returns, and that conquering cities is hard at higher difficulties, I think it could afford to have much higher numbers and not be broken.
If it's 25:c5gold::c5faith: per pop you conquer (are the GG/GA points the same? That's a lot!). So if you conquer 20 population before medieval era (like 4 cities, so hard to do) you would get like 500:c5gold::c5faith:. That's low compared to what WoT or Holy Law can give, but you also get some free generals and admirals. For reference, here are some other values:
  • 10 pop in medieval earns 500 :c5gold::c5faith:
  • 15 pop city in renaissance earns 1125:c5faith::c5gold:
  • 20 pop in industrial earns 2500:c5gold::c5faith:
It's not bad but it's slow. I'd give it a B? To be honest I really like Hero Worship and I'd rather see more founder beliefs had it's level of strength. There's just a lot that I love about it:
  • It's focused on the late game, so no cheesing snowballing
  • The design is on point
  • It just feels good to collect all those yields for conquest
  • It requires support (such as zealotry) to really get value from it's yields.
  • When you support it it's strong but it still won't win the game by itself
You forgot the WLTKD belief here, though maybe you just hadn't wanted to try working it out yet. In my experience on more recent patches WLTKD is overall pretty easy to keep up if you want though, especially if you are swimming in gold from trading strategics away.
Yeah I'm missing 2 beliefs, I'll add them.
 

stii

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Spoiler Way of Transcendence: S+ Tier, The Overall Strongest :

When you enter a new Era, Holy City gains 20 of every Yield for each City following your [ICON_RELIGION] Religion (max 25 Cities), scaling with Era.

If you can get 4 missionaries out before medieval era, you'll have 11 cities following (including your holy city.) That'll be 9x20x2 = 360 of each yield:)c5food::c5production::c5gold::c5science::c5culture::c5faith:), a total of 2,160 yields (I'm not including :c5goldenage: here), or a score of 1980.

It gets even better for later eras. If you enter Renaissance after another 50 turns, and spread to just 10 cities (and you can easily spread to more), you'd earn 600 of each, or 12 per turn. From there it just scales with era and keeps getting better.

A turn 85 religion into turn 125 medieval era means you effectively earned 9:c5food::c5production::c5gold::c5science::c5culture::c5faith: per turn on average (this is the most-backloaded, but it's still ridiculous). Also it's providing :c5goldenage: and :tourism:

I think the number on this one are a bit off. You say 11 cities but it should be 9, although I think you do the calculation for 9 anyway. I think you are a bit generous on spreads as sometimes it will take more than one to flip a city. You are also spreading outside your own cities which depends on how strong the AI pressure is. If you can't get a reformation you might end up spending a lot of faith to get a few cities which then flip back.

That said it is still one of the best, I would just put WoP ahead on these numbers, it is much more front loaded. It does depend what food is worth. I think it is worse than science/culture but it is hard to work out to what degree. It is better to spread out yields and static ones do reduce unhappy as well. Food and gold aren't the best but they do have synergy together.
 

Stalker0

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If you can't get a reformation you might end up spending a lot of faith to get a few cities which then flip back.

This is a really important point, so the strength depends a bit on your neighbors. If your neighbors don't found then spread away, and they will be happy you came. If your neighbors are holy city owners, good luck holding on to those conversions in the early game. AIs now a day literally create an inquisitor per city, so you'll need a GP to break in, and then probably at least 2 spreads a city to sink the faith in..... then it depends on the mood of the AI. Some AI I see will finally accept your religion, others will fight till the end of time and just keep on converting it back.

I would also rank Food as half a yield, as that is our common discount. It doesn't look like your discounting Transcendence's yields at all when you give it a score. I know that its "such a gap it doesn't matter"....but if the case is being made that we should make changes, we need to know the scope.

I will finish with.... historically you often use to praise CoE due to its ability to help snag an early wonder, do you think that is no longer a factor worthy of inclusion?
 

pineappledan

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Irrespective of balance, I just really hope Apostolic and Pilgrim are changed.

Apostolic's yields on tech should scale with followers.
Flat yields in every city is just so terribly boring; all the other Founders require some condition. It's also a Founder that can be co-opted by a civ you are spreading to, rather than funneling yields back to the holy city/religion founder. Follower beliefs are the ones that should have local bonuses that everyone can benefit from.\

They just aint Founders.
 
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CrazyG

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I will finish with.... historically you often use to praise CoE due to its ability to help snag an early wonder, do you think that is no longer a factor worthy of inclusion?
Well I realized something. Rather than rush Oracle, you just take WoT, and it gives you the Oracle every era. Way of Transcendence will give more :c5production::c5science: while also providing everything else. Note that as time goes on WoT gets better every era but CoE runs out.


It's still good compared to not getting a religion though, that's why I gave it a D not an F.


This is a really important point, so the strength depends a bit on your neighbors. If your neighbors don't found then spread away, and they will be happy you came. If your neighbors are holy city owners, good luck holding on to those conversions in the early game. AIs now a day literally create an inquisitor per city, so you'll need a GP to break in, and then probably at least 2 spreads a city to sink the faith in..... then it depends on the mood of the AI. Some AI I see will finally accept your religion, others will fight till the end of time and just keep on converting it back.
Let's say you only spread to 6 cities that you control. Way of the Pilgrim is relatively better in that situation (but I gave it an S anyways). Other than that, which belief do you think gets ahead of WoT as a result of this?
 

Stalker0

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So I was intrigued by the discussion and I'm doing a comparison run to see how they fare. I have completed the AP and Coe runs, now going into WoT.

I've give the full details once I have everything collected, but as a quick jist.

I ran the scenario from the first GP until Physics (aka the start of the medieval era).

AP: 1455:c5food:, 800 :c5faith: (Physics on Turn 153)

CoE: 411:c5production:, 411:c5science: (Physics on Turn 148)

A few quick observations:
  • The medieval rush is a big deal, as this is when the AIs often love to pounce on a player. Having your medieval military unit available to you 5 turns early is a big deal.
  • You do feel the extra faith from AP. For example I had 2 CS that I was able to flip because there pop hadn't yet gotten too high, whereas with CoE, the slower spread meant they were just a bit too high to convert with 1 spread. This is a double penalty for Coe, for while AP gets yields with every spread, CoE gets nothing until the flip occurs.
  • CoE does not scale linerally (30, 31, 32, etc). Its steeper than that, again I'll have the full numbers when I'm done.
 

CrazyG

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Here's a spreadsheet for CoE vs WoT. Here are the numbers comparing raw total yields:
  • CoE gives less :c5production::c5science: if spread to less than 24 cities.
  • At 24 it's dead even (960:c5production::c5science: each).
  • At 25 CoE pulls ahead, because WoT is at it's cap.
This comparison is as strong as CoE will ever be. Moving to later eras, matching in :c5production::c5science: because practically impossible (you would have to spread to 36 new cities before renaissance to get a raw match).

I'm really into abusing early yields to snowball but WoT is just clearly better here. I would prefer WoT even if it only gave :c5production::c5science:.

I would also rank Food as half a yield, as that is our common discount. It doesn't look like your discounting Transcendence's yields at all when you give it a score. I know that its "such a gap it doesn't matter"....but if the case is being made that we should make changes, we need to know the scope.
I halved the :c5gold: and ignored the :c5goldenage::tourism:. Counting :c5food: as only a half hurts WoT, but it lowers the score on the two closest competitors even more.

When I praised CoE it scaled by 30:c5production::c5science: per city, not 1:c5production::c5science:! Furthermore, I realized rather than take it to rush Oracle (or another equally useful wonder), you can just take WoT and get a free Oracle every era.

To be clear, I really like the design of CoE, as well as Hero Worship and Divine Inheritance. I also think they are strong enough to be worth taking and lead to enjoyable games where they play a big part in winning. However, none of that changes that they are weak compared to the better choices.
 

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Stalker0

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Hehe so this scenario clearly wanted me to know the power of "yields now vs yields later". So the WoT I'm trying to do has run into a little snag.....War! With the CoE and AP runs, everyone was peaceful, not an issue. Now with the WoT run, I've been declared on by both Spain and Russia.

At first I thought it was a fluke, and started over to see if I just failed to make units or something. The second time it was delayed but the war still came. What is the difference? Is the fact that WoT is losing out on these little leads mean I'm just a little behind in culture and science, just a little behind in my unit production.....just enough to show enough weakness for them to go to war with me?

Spoiler :

upload_2021-5-16_22-6-46.png



I will note that with the both the other runs i was at physics by this point, and I'm desperately trying to get there, and yet on this run I've got a long way to go, as Spain and Russia both have medieval armies crushing down on me.

I'm going to rerun the WoT one more time, as obviously a big war is a MASSIVE variance between teh other two results, but it is a solid reminder..... even if WoT does give better yields later....sometimes you just have to have yields right this moment.
 

DeAnno

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This is an interesting point when thinking about the yield interest rate. If you have a very solid defensive position you can more afford to wait for yields, but in a rather exposed setup like the America here the diplomatic factor is an additional hidden cost of waiting.
 

tothePAIN

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@CrazyG with the hot take - Way of Transcendence as the strongest? Crazy in my opinion. The yields are delayed. Your analysis takes into account the first 40 turns, in part, I assume, because this is a snowballing game. But Way of Transcendence yields don't arrive for a while. Also, for any of the spreader beliefs, you're going to have to maintain the spread, which isn't that easy.

Let's compare Apostolic to Way of Transcendence for comparison. Apostolic is great for tradition, decent for progress, and not that great for authority because of authority's slower science and also, that much food is bad. Tradition Apostolic uses the food for extra followers, which is more culture and more yields. But calculating these yields isn't very easy, so it elides an easy comparison to Way of Transcendence. But there are more yields there. Same with the other beliefs - Council of Elders hammers are used to build something. If those hammers build wonders and the wonders are strong enough, it's worth it. If not, meh.


One last point - you suggest using the extra faith from Apostolic to enhance quickly. IMO, the right play is to use the faith to reform quickly. Spreading religion is easiest before other religions take place in a city. The food yields from apostolic are strongest then too. The extra faith means extra missionaries and food early and fast. I've even managed to reform on deity with 3 neighbors who founded as well (and one non founder) because Apostolic's faith engine is that good.
 

Stalker0

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Ok, my rerun of WoT went well this time. I focused a little more on science over culture, and a bit more on units over infrastructure. The thinking of course is that I'll get a "big payday" once Medieval Hits, and so I can skimp on a little infrastructure and culture to get to the finish line. Once WoT gives me the payout, then I can return to the regular schedule.

Alright so I have attached the following:

  • The Excel. Nothing super fancy, just shows when I get what yields when. For WoT I didn't track much, just the payout when I hit Physics.
  • The start point and the mods I use. Feel free to play at home if you want, choose which belief and go to work.
  • Saved games for each religion at phyiscs, so you can see how things look.
So the grand total is:

AP: 1455:c5food:, 800 :c5faith: (Physics on Turn 153)

CoE: 411:c5production:, 411:c5science: (Physics on Turn 148)

WoT: 400:c5food:, 400:c5production:, 400:c5science:, 400:c5culture:, 400:c5faith:, 400:c5gold:, 400:c5goldenage:, 400:tourism: (Physics on Turn 154....intentionally delayed 1 turn to convert 1 more city).

A quick look with some of our new time discounting!
Spoiler :

Now the discount formulas are still very much a work in progress, but just to get a feel, lets see how CoE and WoT's science yield compares due to the science discount formula.

Coe: 35.7 :c5science:
WoT: 18.5 :c5science:

So based on our current WIP formula, you can see that WoT science yield is about half as good as CoE....even though their original total was roughly the same, due to the time discounting. Still, that is but one yield, and WoT has plenty more.


Now a note about WoT. I actually don't think we should discount the gold at least on the first era hit. The reason is....in a competitive game most of the time you are going to have an army in need of a big upgrade. Whether its horses -> knights, skirmishers -> heavy skimishers or spears -> pikes....you generally have a lot of upgrading to do as you go into medieval, and you'll need those forces against the AI who likes to get aggressive at this point. so having 400 gold that I can immediately use to modernize my army is a really big deal. This is doubly true since with the science bonus you can often get steel right after physics....so you can then upgrade all of your forces.[/Spoiler]
 

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stii

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Its not 1 per city. Not sure what the exact formula is, but here are the actual amounts.

30
31
32
34
37
40
44
49
54
60

Is these one of those find the pattern games? Or maybe I need to break out my maths text book to work it out? :)
 

CrazyG

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@CrazyG with the hot take - Way of Transcendence as the strongest? Crazy in my opinion. The yields are delayed. Your analysis takes into account the first 40 turns, in part, I assume, because this is a snowballing game. But Way of Transcendence yields don't arrive for a while. Also, for any of the spreader beliefs, you're going to have to maintain the spread, which isn't that easy.
I analyzed those 40 turns because they are the easiest ones to analyze. If you include the rest of the game it generally favors WoT because it scales with era while most others don't. By industrial era you aren't spreading anymore so Apostolic probably gives 0:c5food: and CoE does nothing.

All spreader beliefs suffer if you don't spread, true. But really Divine Inheritance suffers no matter what you do, WoT pretty easily gives more even if you don't spread beyond 5 cities. Also I stand by 9 cities being achievable and it's not capped until 25. I think 9 cities all game is a low-ball guess, you can easily have 6 yourself then like 3 city-states get you to 9. I'm confused by how pessimistic y'all are about spreading religion.

Let's compare Apostolic to Way of Transcendence for comparison. Apostolic is great for tradition, decent for progress, and not that great for authority because of authority's slower science and also, that much food is bad. Tradition Apostolic uses the food for extra followers, which is more culture and more yields. But calculating these yields isn't very easy, so it elides an easy comparison to Way of Transcendence. But there are more yields there. Same with the other beliefs - Council of Elders hammers are used to build something. If those hammers build wonders and the wonders are strong enough, it's worth it. If not, meh.
I don't dispute that Apostolic is the top pick for tradition who needs food (I gave the belief an S). I think it's a major reason that tradition is so strong currently.

However for progress/authority, no way. It only works as tradition because you have powerful specialists and 1:c5culture: per 2:c5citizen: to collect, so the :c5food: converts into strong yields quickly and easily. Furthermore, as tradition you can try just using other :c5food: sources to grow, and then go greedy with Way of Transcendence. That's why I said generally best, it's just consistently strong in almost any situation.

For CoE I just don't think there's anything to build strong enough to give up WoT. Oracle is a good use of :c5production:, right? Well WoT is much stronger than Oracle is. Also if you reach medieval era with a wonder available you build it in one turn + enough :c5production: for another building.
One last point - you suggest using the extra faith from Apostolic to enhance quickly. IMO, the right play is to use the faith to reform quickly. Spreading religion is easiest before other religions take place in a city. The food yields from apostolic are strongest then too. The extra faith means extra missionaries and food early and fast. I've even managed to reform on deity with 3 neighbors who founded as well (and one non founder) because Apostolic's faith engine is that good.
I intended the suggestion as "If you want to enhance quickly, take this". I agree spreading first is generally the better move.
 
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CrazyG

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Beijing
Now a note about WoT. I actually don't think we should discount the gold at least on the first era hit. The reason is....in a competitive game most of the time you are going to have an army in need of a big upgrade. Whether its horses -> knights, skirmishers -> heavy skimishers or spears -> pikes....you generally have a lot of upgrading to do as you go into medieval, and you'll need those forces against the AI who likes to get aggressive at this point. so having 400 gold that I can immediately use to modernize my army is a really big deal. This is doubly true since with the science bonus you can often get steel right after physics....so you can then upgrade all of your forces.
You can also get a rush of :c5science::c5gold::c5production: when you discover gunpowder :D.
400:c5production: is enough to build Colossus in 1 turn and still have overflow for a trebuchet.

Its not 1 per city. Not sure what the exact formula is, but here are the actual amounts.
Okay I'll update my OP. I can't tell the pattern though. These numbers help but I still think it's weak.
 

DeAnno

King
Joined
Feb 22, 2011
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30 31 32 34 37 40 44 49 54 60

Differences are 1 1 2 3 3 4 5 5 6, classic quadratic because they're linearly increasing. Seeing the rate is 2/3 you can tell the Ax^2 term is 1/3x^2 from calculus.

A little tinkering gives f(x)=round[30+x/3+(x^2)/3] as the formula, if you count the first 30 spread as x=0. (Ie the formula takes how many cities had the religion before this spread.)
 
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