Policy Cost Calculations

[Omelet]

Due to the current Hall of Fame contest being a cultural victory, I have decided to take a more mathmatical look all the policy costs to try to formulate the best possible timeframe to produce a cultural victory.

Assumptions

The policy cost for a second city is 30%... i.e. Original Cost x 1.30. The policy cost for a third city is the cost for two cities + Original Cost x 1.30. This means there is a static cost for each addition city added, it is not (thankfully) multiplicative.

CIV5 seems to like number divisble by 5, so the exact values you see in game may not match the chart exactly. However, they should be off by less than 5.

Next Steps

Enhance interface

 

[Ozbenno]

Interesting work! Will be good to get my head around this for my eventual attempt at the gauntlet.

 

[Neuro]

For informational purposes, here's a list of Policy costs for a single city, first one is Base with no bonues, the second is with both Cristo and Free Speech. The second list starts at policy #10 cause that's where I was when I got Cristo (11 actually, but that's including the Oracle).

No Bonuses
-----------
25
45
90
160
245
345
465
595
745
905 <-- 10th paid policy
1075
1260
1460
1670
1890
2120
2365
2620
2885
3160
3445
3745
4050
4365
4690
5025
5370 <-- 27th policy

Price w/ Free Speech + Cristo
-----------------------------
450 <-- 10th Policy
535
630
730
835
945
1060
1180
1310
1440
1580
1720
1870
2025
2180
2345
2510
2685


Hope this info helps!

 

[Omelet]

Thanks for the post Neuro! I will incorporate this into my data.

I have noticed after playing the game of the month that the policy cost is also dependant on the difficulty level.

At warlord level, the policies were at 20 and 35 for the first two with one city... Lots more work to be done!

 

[Neuro]

From what I can tell, it's a straight multiplier. For example, the 10th policy is 905. I know that before I got Cristo but after I got Free Speech, it was listed at 675. 905 * .75 = 678 and change, which is rounded down to the nearest five I guess. With both Free Speech and Cristo, it went down to 450. 950 * .75 * .66 = 447.975, rounded up to 450.

 

[Omelet]

The calculation of Original Cost * 0.75 (Free Speech) * 0.66 (Cristo) starts to fail at the higher culture cost levels...

i.e. Policy 27

5370 (Original Cost) * 0.75 * 0.66 = 2658 vs. 2685 (Displayed value)

Either they are using a different formula, or the actual original culture values are not as displayed on screen.

 

[sanabas]

The calculation of Original Cost * 0.75 (Free Speech) * 0.66 (Cristo) starts to fail at the higher culture cost levels...

i.e. Policy 27

5370 (Original Cost) * 0.75 * 0.66 = 2658 vs. 2685 (Displayed value)

Either they are using a different formula, or the actual original culture values are not as displayed on screen.

Use 2/3 instead of 0.66, and it is 2685.

 

[Omelet]

Thanks... I should have caught that myself

 

[KrikkitTwo]

Its probable that 25, 45, 90, 160, etc. Aren't the original values, its more likely that those are the original values AFTER rounding off to the nearest 5.
(since the values don't make sense for multiple cities otherwise)

 

[Omelet]

I have modified the spreadsheet to allow some interaction to allow the calculation of the best possible approaches.

You can now enter the number of cities you expect to have at each policy number (One, Two or Three) the applicable abilities that allow a reduction in policy cost (N = None, Free Speech = FS, Cristo Redeemer = C, Both = B).

You can also input the number of turns to win and see the required culture per turn output over all turns.

Any questions or suggestions are welcome.

 

[pagh80]

Nice spreadsheat. '

I tried to check what it meant to get a second city after 4 policies(+1 free) as that is needed to get the CSs bonuses + constitution
Basically you have to get a extra ~8000 SP with 2 cities which seems pretty steep.
That means the extra city have to give 40 SP per turn assuming you get the second city at turn 40 and end at turn 240.
By comparison my capitol in my last game gave 22 SPT at turn 100.

 

[erajah]

Cool spreadsheet! Maybe you should also add a last column to include Sydney Opera House so you only need 26 policies to finish.

 

[DrakenKin]

I am loving this spreadsheet, thanks a lot.

Btw have you considered making it into a Google documents? everybody can subscribe to the document (if you make it public) and we get automatic updates.

Cool spreadsheet! Maybe you should also add a last column to include Sydney Opera House so you only need 26 policies to finish.

You will typically always finish a cultural win before you get to the opera house. My first Civ5 game ever was on a huge map isolated start, I made many big mistakes including no conquest/puppets and making 3 cities. Yet I finished utopia way before getting access to the opera house.

 

[DrakenKin]

In your calculations, when exactly did you apply the free policies from oracle and free religion?

The sheet says Oracle saves 3232.5 culture... but we are forced to get oracle very early so it will only save about 25 to 90 culture max.

Free religion on the other hand sounds right, since you will be using it to pop the last 2 policies for a total of 6277.5 culture.

 

[Lexad]

The sheet says Oracle saves 3232.5 culture... but we are forced to get oracle very early so it will only save about 25 to 90 culture max.

It doesn't matter when you use it, it means you have to unlock one less policy by culture - so you unlock 29 instead of 30 and save the costs of the 30th.

 

[DrakenKin]

It doesn't matter when you use it,

You are saying it doesn't matter when you take your free policies, meaning you can pop them at any time. But I don't see how it could be true...

Lets take a practical example with free religion : for this let's say I have an empire that is producing 100 culture per turn, and I just got my 27th policy this turn.

If I pop my 2 free policies right now I get the 28th and 29th policies for free, for a total of 5907.5 culture, and i need 3232.5 / 100 = 32 turns to reach utopia.

But if I wait until i have 28 policies (2862.5 / 100 = 28turns), and use free religion to get my final 29th and 30th policies, I get 6277.5 culture for free and reach utopia 4 turns earlier.

 

[pagh80]

In your calculations, when exactly did you apply the free policies from oracle and free religion?

The sheet says Oracle saves 3232.5 culture... but we are forced to get oracle very early so it will only save about 25 to 90 culture max.

Example:
lets say you pay the following for 5 policies:
50 - 75 - 125 - 175 -225
In total that will cost you 650.
Now if you get a free policy lets say the first one for 50. the subsequent policy costs is the following:
free - 50 - 75 - 125 - 175
In total that is 425 and you save 225
So you actually save the price for the last policy you dont have to pick.(as Lexad said)

You are saying it doesn't matter when you take your free policies, meaning you can pop them at any time. But I don't see how it could be true...

Its true though:
50 - free - 75 - 125 - 175 = 425
50 - 75 - 125 - free - 175 = 425

 

[sanabas]

If I pop my 2 free policies right now I get the 28th and 29th policies for free, for a total of 5907.5 culture, and i need 3232.5 / 100 = 32 turns to reach utopia.

You will still only need 2862.5, because the cost only increases when you pay for policies. Taking a free policy does not increase the cost of the next one.

 

[DrakenKin]

You will still only need 2862.5, because the cost only increases when you pay for policies. Taking a free policy does not increase the cost of the next one.

Oh I didn't know that... awesome, thanks.

 

[Omelet]

Thanks everyone for the feedback. I hope the spreadsheet is getting a bit of use.

I will look into adding it to google and adding the Sydney Opera House calculations... it is possible to beeline to globalization if you have enough science in a game where you are significantly ahead on technology / military strength.