[Vote] (6-62) Remove Dependence on Monument for Border Growth Rate

[ma_kuh]

The Problem:
Border growth rate scaling is added on the monument. The monument, being a culture source in the early turns of the game, already has enough making it a go-to building. Having the increased growth scaling on the monument suppresses alternative starting buildings, because growing tiles becomes contingent on building the monument. If you can generate equal border growth, from the smokehouse for example, your border scaling will still require a monument.

Additionally, culture from passive, per-turn sources is given greater weight for border expansion than instant yields. This causes inconsistencies, either with how instant yields are handled (by letting them trigger with increased border growth, unlike other instant yields), or by having some types of culture count for "extra" for border growth.

The Proposal:

• Monument:
  • +2 Culture
  • +34% Border Growth Rate Increase
• Stele (Unique Monument):
  • The rest unchanged
  • +34% Border Growth Rate Increase
• Ger (Unique Smokehouse):
  • The rest unchanged
  • +50% +40% Border Growth Rate Increase
• God of the Expanse:
  • The rest unchanged
  • +34% +25% Border Growth Rate Increase
• Angkor Wat (Classical Wonder):
  
  • The rest unchanged
  • +50% +40% Border Growth Rate Increase
• Fiefdoms (Fealty Policy):
  • The rest unchanged
  • +100% +75% Border Growth Rate Increase during "We Love the King Day"
• UPDATE Defines SET Value = 15 12 WHERE Name = 'CULTURE_COST_LATER_PLOT_MULTIPLIER';
  • The scaling border growth costs have two main components: the fixed base value, 20, plus a scaling value.
  • This is the scaling value's base multiplier used in an exponential function for augmenting the cost of tiles.
  • For the first tile, this value is multiplied by 0, so the first tile cost is always 20 (scaled by speed). There will be no change to the cost of the first tile with this proposal.
  • Each additional tile costs 20+(C * 15)^1.35. I'm proposing changing it to 20+(C * 12)^1.35, and removing the "free" +34% growth rate that every city gets from the monument.

The Reasoning:
We should separate the mandatory border growth scaling modifier from this building to allow space for emergent strategies, and giving more consistent border growth while going for shrine-first, smokehouse, or unit-focused play. The Border Growth Rate Increase from other sources becomes magnified with this change, so a slight reduction is in order to match current power levels. Sovereignty is negatively affected slightly, but will still fulfill its function of being the single most impactful modifier to border growth costs in the game.

Spoiler How the formula works :

The threshold for gaining a new tile follows this formula:

[Base threshold] = [First plot culture base] + [Additional cost]
[Additional cost] = ([Culture level] * [Later plot culture multiplier]) ^ [Later plot culture exponent]
[Total threshold] = [Base threshold] + [Additional cost]
[Total border growth] = [Border points per turn] * (1 + [Border Growth Rate Increases...])

These values are currently:
[First plot culture base] = 20
[Culture level] = The number of the tile you're trying to acquire, e.g. 0, 1, 2, 3...
[Later plot culture multiplier] = 15
* This is where Russia's -33% cost applies (I think?)
[Later plot culture exponent] = 1.35
* This is where Sovereignty is applied, becoming 1.35*0.80, or 1.08.
[Border Growth Rate Increases] = 34% for God of the Expanse, Monument (stacking)

You get a new tile when:
[Total border growth] > [Total threshold]
which can be arranged as:
[Border points per turn] > ([Total threshold] / (1 + [Border Growth Rate Increases...]))

Putting in some numbers:
CURRENT:
(20 + (L * 15)^1.35) @ L=3 = your 4th tile to claim costs 190 border points with no monument
(20 + (L * 15)^1.35) / 1.34 @ L=3 = " " costs 142 border points with a monument, or with God of the Expanse (the Pantheon belief)
(20 + (L * 15)^1.35) / 1.68 @ L=3 = " " costs 113 border points with a monument AND God of the Expanse
(20 + (L * 15)^(1.35*0.8) / 1.34 @ L=3 = " " costs 61 border points with a monument and Sovereignty (the Tradition Policy)

PROPOSED:
(20 + (L * 12)^1.35) @ L=3 = your 4th tile to claim costs 146 border points with the proposed new scaling, with or without a monument
(20 + (L * 12)^1.35) / 1.25 @ L=3 = " " costs 117 border points with the proposed new scaling and with God of the Expanse
* Without the reduction to God of the Expanse, later tiles start costing less than the current balance. The goal here is to be balance-neutral.
(20 + (L * 12)^(1.35*0.8) @ L=3 = " " costs 68 border points with the proposed new scaling and Sovereignty
* This one's actually somewhat impactful, but to match the original curve better you'd need to use 21% on the reduction. I'm assuming people would prefer to keep the number round at 20%, and Sovereignty is already a huge contribution to border-expansion, being almost a linear scale compared the the exponential scale of other policy trees.

This chart shows the change in strength of various border growth sources.

Spoiler Chart comparing the existing Tile Costs with the Proposal :

The transparent lines are the current costs, the dotted lines are with the proposed changes.
Note that God of the Expanse, despite reducing its multiplier, follows nearly identically with current overall costs.

Statement of impact:
These are the situations where this will change things:

• In your capital, if you build something other than a monument before your first border tile is claimed (usually ~20 turns), then you will claim your second tile faster by a few turns.
• Cities with access to culture or border growth before the monument is built, after the first tile is claimed, will see their second tile sooner.
  • This maybe be from terrain (Natural Wonders, Smokehouse, etc.).
  • This could be from instant yields (Authority kills/city founding, Progress building completion).
• Slight buff to later tiles from Angkor Wat or Ger.
• Minor nerf to all tiles from Sovereignty (average of about 7% more expensive overall).
• Culture/border growth per turn that is less than 3 with still benefit from the reduced cost of second+ tiles; currently 2 border growth points per turn receives no benefit from the 34% increase.

Notable strategies that will be buffed by this: unit-focused no-monument (or delayed monument) Authority play; shrine-first play; fast early culture, such as from luxuries or civ-specific triggers, coupled with delayed monuments.


Database Changes

 

[rkkn]

sovereignty needs a nerf anyway
or rather, I might propose that some of sovereignty's power is made baseline. like 5%, and then cut sovereignty from 20 to 10 or 15

 

[adan_eslavo]

Axis should be named for clarification of what the numbers mean.
How will this proposal affect UBs based on Monument?

 

[ma_kuh]

Thanks for the reminder, I'll update details later today when I can check. The intent will be to match existing impact, so if they're 34% then they'll be removed as well. If they're more than that, I'll approximate a fair value like I did for God of the Expanse.

 

[ma_kuh]

So fun fact, to acquire all 30 workable tiles around your city costs you effectively need around 38270 border growth points (with just a monument scaling your growth).
Adding God of the Expanse reduces this to an effective number of about 30525.
Sovereignty reduces this to about 8630 (no God of the Expanse).

For all of the tiles in the 2nd and 3rd rings. (This is using the current scales.)

38.3k, 30.5k, 8.6k

Sovereignty is a huge bonus.


Reducing the exponent from 1.35 to 1.30 and pulling out the Monument's +34% would have a similar effect to reducing the scaler.

(Seen here in the orange, red (practically identical), and black dotted lines)


I think "fixing" Sovereignty is an independent conversation all together, and it could easily be lowered to 15% and play about the same way, with just a little more delay on reaching capped cities. But it's also key to making border-blob strategies work at all, and Tradition isn't exactly killing it in the stats, so I don't know that a nerf is needed at this time. It's "broken", but the benefit of that brokenness doesn't really seem to be impacting win rates.

 

[adan_eslavo]

Sovereignty is a policy or ideology tenet, right?
I think we could fix this as well in the proposal. It's a consistent approach we want to achieve.

 

[ma_kuh]

It's the Tradition policy, yes. It's very strong for an Ancient era policy, but that power is spread over the whole game (or at least into the mid-game). I do think that it being so strong is somewhat necessary for low-city counts to be able to stand up to wider play. Yes, it's nearly 5x as many effective border points to claim all working tiles for a non-Sovereignty city, but getting those tiles is somewhat easy if you plan on putting down an extra city every once in awhile anyway.

I'm going to underscore again, I don't want to influence overall Tradition power with this proposal. I don't want to muddy the goal here, which is to separate core border growth rate from the Monument. To put it another way, I would rather pass this change with out touching Sovereignty than have voters who don't want to nerf Tradition vote against it.

I think a separate proposal could be made to reduce Sovereignty to a 15% reduction, and that could pass/fail on its own merits.

 

[axatin]

Here's a chart comparing the existing Tile Costs with how they would be with the Proposal.

The transparent green line would be the new baseline then?

Another problem with Sovereignty is that it's effects are so obscure. Understanding them requires knowledge of the internal formula and that shouldn't be the case. Also, the description "costs to claim a new tile are reduced by 20% (exponentially)" doesn't make it clear at all how strong that policy actually is, and that's not newcomer-friendly. But I agree that changes to sovereignty should be a separate proposal.

 

[ma_kuh]

The dotted green line would be the new baseline. Maybe I should have used black for that one... The new baseline is with AND without monument, and yes it basically overlaps the transparent green line.

 

[Diomedes_]

Wow I had no idea how good sovereignty was. But besides that, I feel like this change to the monument makes sense and would help to clarify and simply things, so long as all of the other border-growth related bonuses were properly adjusted. It does also open up cool opportunities to start with a shrine or even a warrior/pathfinder as the monument wouldn't be quite as strong.

 

[ma_kuh]

Okay, so I'm finally getting around to double-checking some of the other forms of +% Border Growth Points.

I think this amounts to:

• Stele (unique Monument): 34% (same as monument) => This should be removed with the change to Monument
• Ger (unique Smokehouse): 50% => Magnified by these changes, mathematically this should be reduced to ~40% to match current benefit
• Angkor Wat (world wonder): 50% => 40% according to the math (see above)
• Fiefdoms (Fealty policy): +100% border growth during WLTKD => 75% to match current benefit

If I missed any, let me know. Also, I'm not super clear on where in the formula the Russia reduction applies, I think it's on the scale as a multiplier, so these changes would stack multiplicatively, and don't change the trajectory for Russia according to my models.

For now I'll amend with reductions, but one thing I wanted to informally poll the community on was whether Ger and Angkor Wat should be reduced to 40%, or stay at 50%. Specifically in the case of the Ger, if you build Ger first with no other culture (so not in your capital, but in early expansions), you will be gaining +2 BGP/turn and +40% BGRate = 2.8 BGP/turn which floors to +2 BGP/turn (no benefit unless you have +1 culture from something else). With +50%, you would immediately see the +1 BGP/turn. Angkor Wat is deeper into the early game, and you would be more likely to have enough culture that the 10% shift down wouldn't matter much, but the same general question applies.

So what do you think, should we give Angkor Wat/Ger a small buff to keep the numbers cleaner, or follow the math? (I could also see changing Ger from +% BGRate to just a flat +2 bonus BGP/turn (so they get +4), giving them an early game buff and a later game nerf, but providing the BGPs during the time they're most likely to mean something.)

---

Amended:
Added other sources of +% Border Growth to the proposal, with reductions as appropriate for maintaining current power levels.

 

[axatin]

Also, I'm not super clear on where in the formula the Russia reduction applies, I think it's on the scale as a multiplier, so these changes would stack multiplicatively, and don't change the trajectory for Russia according to my models.

Russia has reduced total tile costs, so in your formula it would be (20 + (L * 15)^1.35) * 0.67 / (1 + Border Growth Increase)

 

[adan_eslavo]

Can you post the updated chart in the op?

 

[Stalker0]

I think "fixing" Sovereignty is an independent conversation all together, and it could easily be lowered to 15% and play about the same way, with just a little more delay on reaching capped cities. But it's also key to making border-blob strategies work at all, and Tradition isn't exactly killing it in the stats, so I don't know that a nerf is needed at this time. It's "broken", but the benefit of that brokenness doesn't really seem to be impacting win rates.

Fast Tradition borders is part of the play to me. Tradition has fewer cities with large borders, progress has lots of cities whose borders don't grow for anything.

I commonly have to buy tiles as progress, almost never as tradition....and that works to me.

 

[pineappledan]

I disagree with the premise.

the border growth on monument is fine. Yes it’s early, but you still have to build it, the the border speed it gives is a factor in early build orders.

If the monument only gives 2 then the rate or border growth between it and the smokehouse is even (smokehouse gives 2BGP). Except the smokehouse does like 3 other things. If all you’re concerned about is order growth rate then this makes monuments far inferior

 

[ma_kuh]

"You have to build it" is the problem though. It chokes out other options for build-first buildings. It beats out pantheon buildings most of the time, even.

Shrine doesn't do anything more than provide 2 rare yields, I feel like Monument is going to be fine to exist in the same space. And the Smokehouse requires tech, so if it's stronger than the Monument I'm not sure that's wrong.

 

[Stalker0]

"You have to build it" is the problem though. It chokes out other options for build-first buildings. It beats out pantheon buildings most of the time, even.

That's a fair concern, but this change doesn't address that. The monument will STILL be the first building built after this change. That culture is too important, and as your own chart shows, I will still ultimately have the same border growth when I build my monument.

This proposal ultimately does not change the monument itself at all....it only changes border growth adjusters that follow it.

 

[ma_kuh]

The baseline adjusts down to the monument's scaling. If you can get culture or border growth points from other sources, like your pantheon or your UA, then you can delay the Monument itself because you don't need the +34% scaling to be "on track" with expected border growth points.

You might build the Monument because you want culture, but you don't NEED the Monument if you're trying to expand borders. That's the difference. The fact that the Smokehouse might eclipse the Monument for border-expansion purposes is a good thing.

Here's an updated graph with more situations. I'll add it to the OP.
Dotted lines are with proposed values, solid lines are current values.

 

[Stalker0]

The baseline adjusts down to the monument's scaling. If you can get culture or border growth points from other sources, like your pantheon or your UA, then you can delay the Monument itself because you don't need the +34% scaling to be "on track" with expected border growth points.

You might build the Monument because you want culture, but you don't NEED the Monument if you're trying to expand borders. That's the difference. The fact that the Smokehouse might eclipse the Monument for border-expansion purposes is a good thing.

Here's an updated graph with more situations. I'll add it to the OP.
Dotted lines are with proposed values, solid lines are current values.
View attachment 675717

I get what your saying, but the +2 culture from the monument is still a major factor in border growth, AND it gives culture.

Sure the smokehouse might give equal border growth now....but it still doesn't give me culture.

If you want to do this to smooth out border growth in other areas, fair enough. But if your goal here is to make the monument less "build first"....than this proposal is a failure.

 

[ma_kuh]

I think it's objectively less build-first for two reasons:

1. It's losing something. Even if it didn't "move the needle enough", it's still a step in that direction.
2. In this conversation we've already had competing views on whether the Smokehouse or Monument is superior.
   • I think this is important because it highlights a legitimate build decision: do you pump out another 2 culture/turn for policies, or do you turn on your population growth??

I don't want to remove Monument as the default build-first building. That's just a factor of culture being necessary to activate more culture from policies. I just want the choice to be a little more meaningful. Otherwise you might as well have Settlers cost 65 more production and start the city with a Monument.