Faith cost of great prophets, chance to spawn great prophet and general culture costs do not match lekmod

[O-spin]

The great prophet formula in lekmod is: 300 + 100 * (prophets spawned) * (prophets spawned +1)/2
Great prophets are spawned with 100% chance once enough faith has been generated
The formula used for culture costs is probably the one mentioned in this reddit thread:
https://www.reddit.com/r/civ/comments/3hx572/just_how_much_do_cultural_policies_increase_each
From in-game tests I've empirically sampled these values (On a small map with 1 city):
25,30,60,105,170,255,355,475,615,775,955,1150,1365,1600,1855,2125,2415,2730,3055,3405,3775,4160,4565,4990,5435

These are currently not moddable, however I have a pull request up in the unciv repo that makes them moddable. Once it is accepted I propose we change them for rekmod.

As an aside I was told in the discord that the culture formula used by normal unciv is wrong on-purpose, the discrepancy is not unique to lekmod but I think it's more important that it's fixed here for balance reasons.

[SeventhM]

300 + 100 * (prophets spawned) * (prophets spawned +1)/2

That's... huh. Wasn't aware that was even different. Once that is possible to be changed, I could be willing to change it........

That said, that isn't the formula. At least... Idk if it is. It's actually
100 * (prophetsSpawned - 1) + costOfProphets(prophetsSpawned - 1)
where the cost of the very first prophet is instead 300

As an aside I was told in the discord that the culture formula used by normal unciv is wrong on-purpose, the discrepancy is not unique to lekmod but I think it's more important that it's fixed here for balance reasons.

Wait... Wrong... "on purpose"? How? What do you mean? Comments within Lekmod's codebase suggests that the only thing wrong in Unciv is that it increases by 6 per policy in Unciv when it should increase by 7 in Civ 5 (I have not checked if that comment is BNW specific or also present in base/GnK). It's Lekmod that seems to have changed it to increasing by 3 per policy, to the exponent of 2.01 instead of 1.70

[O-spin]

300 + 100 * (prophets spawned) * (prophets spawned +1)/2

That's... huh. Wasn't aware that was even different. Once that is possible to be changed, I could be willing to change it........

That said, that isn't the formula. At least... Idk if it is. It's actually 100 * (prophetsSpawned - 1) + costOfProphets(prophetsSpawned - 1) where the cost of the very first prophet is instead 300

They changed it at the same time as changing prophet spawn chance to 100%.

As an aside I was told in the discord that the culture formula used by normal unciv is wrong on-purpose, the discrepancy is not unique to lekmod but I think it's more important that it's fixed here for balance reasons.

Wait... Wrong... "on purpose"? How? What do you mean? Comments within Lekmod's codebase suggests that the only thing wrong in Unciv is that it increases by 6 per policy in Unciv when it should increase by 7 in Civ 5 (I have not checked if that comment is BNW specific or also present in base/GnK). It's Lekmod that seems to have changed it to increasing by 3 per policy, to the exponent of 2.01 instead of 1.70

When I was checking in civ 5 without lekmod I was getting the 2.01 numbers. I'll try a full reinstall, maybe there's something weird going on with the lekmod install.

[O-spin]

Ok, on a clean reinstall (Without lekmod there to do anything funky) I get the 2.01 numbers irrespective of DLC choice.

All DLC enabled
25, 30, 60, 105, 170, 255, 355...

BNW DLC Disabled
25, 30, 60, 105, 170, 255, 355...

All DLC Disabled
25, 30, 60, 105, 170, 255, 355...

Surely the 1.7 numbers have been a part of civ 5 at some point (why would they be in the mathematics of civ 5 wiki page otherwise). I belive they were changed for the base game in some patch...
https://civilization.fandom.com/wiki/June_2011_patch_(Civ5)#Mechanics
Look at that, I've found the patch.
"Tweaked Policy cost formula (cheaper earlier, more expensive later)."

So this was a change done before g&k was released in 2012.

[SeventhM]

They changed it at the same time as changing prophet spawn chance to 100%.

Apparently no, it's always been something like that. Not at my computer so I can't double check the base cost or what the increasing cost is, but the calculation has always been recursive

https://github.com/Gedemon/Civ5-DLL/blob/aa29e80751f541ae04858b6d2a2c7dcca454201e/CvGameCoreDLL_Expansion1/CvReligionClasses.cpp#L1557

Note that that's for expansion 1 (GnK), not expansion 2

[O-spin]

They changed it at the same time as changing prophet spawn chance to 100%.

Apparently no, it's always been something like that. Not at my computer so I can't double check the base cost or what the increasing cost is, but the calculation has always been recursive

I meant to say that I think nqmod changed from 200 to 300 at the same time as changing from 5%+excessfaith to 100% prophet spawn chance.

The recursion is trivially the same formula as the one I wrote. (With prophetsSpawned being n-1)

[SeventhM]

The recursion is trivially the same formula as the one I wrote. (With prophetsSpawned being n-1)

Fair enough, didn't know if the math resolved to that (though if we're throwing it into Wolfram Alpha, we could probably use ”a" and "b” instead of 300 and 100)

I meant to say that I think nqmod changed from 200 to 300 at the same time as changing from 5%+excessfaith to 100% prophet spawn chance.

Ah ok. I wouldn't know tbh (would need to check BNW's xml files, but if it's different, it's different. Either way, still waiting on your PR (or yairm210/Unciv#14938) to get merged