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:
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.
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.
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:
Database Changes
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
- +2
- 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 =
1512 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.
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.
Database Changes
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