Culture Mechanics Disassembled

[Perugia]

Cabert, thanks for the response.

Academy also scales with many of the commerce factors that affect the culture bomb such as free speech and printing press.

Note also that the Culture bomb and Academy both also scale with Bureaucracy which will matter on a crowded map where you can move your settler and settle within 3 tiles of your opponents capital.

I see now that sequencing is important. For example if lightbulbing leaves a shortfall of beakers then it is better to save the GP until later as population will have grown giving potentially more beakers from the GS reducing the total number of turns needed to get the tech. Likewise with GE: grow city pop while and acummulating the shortfall hammers then hurry production with GE then whip if required.

I agree it would be better if culture bomb was to scale with something non-instantaneous. I suggest it uses the average cpt not for the last 1 turn but for the last 20 turns. Alternatively why not restrict the instantaneous effect to a fixed amount based on the 4000 figure and follow this by a mini-golden age for that city where culture plots will be 2x there normal values for the next 20 turns.

 

[uberfish]

I have to agree with Mutineer, the max-culture trick merely brings late game culture bombs up to the power level where they should have been in the first place.

 

[cabert]

I have to agree with Mutineer, the max-culture trick merely brings late game culture bombs up to the power level where they should have been in the first place.

yes, and that's OK.
But it's still undocumented and unfair (the AI won't use it right, or will it?).
+ needing such MM isn't usual in the game.

 

[JackOfClubs]

So it's not totally absurd that culture in tiles after a great work scale with cpt. It's still not right IMHO, but at least it's somehow logical.
Thanks .

I think the expoitive aspect is not so much that the GA Bomb scales with available culture in the city but that you can temporarilly raise the available culture then shut it back down after the bomb with no effect on the end of turn cost of culture that you would normally incur. It should work more like whipping or chopping where the overflow is calculated at the end of the turn, thus forcing you to leave the modifiers (ie Culture Slider and Artist Specialists) in place until the next turn. That would still maximize culture but you would pay a penalty in commerce, production and growth, which seems a reasonable tradeoff.

I realize that it would be difficult to program such a result, but it could have some cool side-effects. For instance, if you banked the GA culture in this way, it might be neat if changing the culture slider and artists could visibly affect the culture borders of the city. That would allow you to further optimize the effect you were trying to achieve. For instance if you were trying to flip a city 3 tiles away and the maximizing effect would pop the border to 5 tiles, you could dial it back down to avoid wasting that extra culture in the outer ring.

To answer your question, lightbulbing scales with population empire wide.
If you have a really huge population, you can lightbulb electricity in 1 turn.

Really? I had thought the lightbulb was for a fixed number of . That seems to be the assumption in analyses such as this:

For this argument, Great People (other than the Great Artist) will be valued based on the beaker-strength of their lightbulb -- which is 1500 for a Great Scientist and 1000 for all others.

I have seen recent games where the lightbulb is less than 1500 and I assume that is due to the population of my civ. Can you point to a discussion of the scaling effect? I would really like to know more.

 

[KMadCandy]

Really? I had thought the lightbulb was for a fixed number of . That seems to be the assumption in analyses such as "For this argument, Great People (other than the Great Artist) will be valued based on the beaker-strength of their lightbulb -- which is 1500 for a Great Scientist and 1000 for all others."

I have seen recent games where the lightbulb is less than 1500 and I assume that is due to the population of my civ. Can you point to a discussion of the scaling effect? I would really like to know more.

Yes really. this thread shows the formula for different game speed. it doesn't lift it from the code (i didn't bother searching that long). according to that thread, on normal speed a GS contributes [1500 + 3 * pop] in beakers from a lightbulb. so i'd read "beaker-strength of their lightbulb which is 1500" in that analyses you quoted as "base beakerstrength before scaling" (or as a misunderstanding of what happens, i didn't read it).

i hope this helps. if not, there are plenty of people that know more about it than i do!

 

[JackOfClubs]

Thanks. Yes that helps. So the general formula would be

SF * (1 +0.5 * GS) * (1000 + 2 * TP)

Where:
SF is the game speed factor
GS is 1 for Great Scientist and 0 for other great people
TP is the total population of all cities

Since the cost of technologies is going to scale with game speed, SF is irrelevant. That means that in order to lightbulb Electricity with a GS, as mentioned above, you would need

1500 + 3P = 2800
3P = 1300
P = 434 (rounding up)

That means you would need 21 cities at size 20 plus one at size 14. Or more than 40 cities at an average size of 10. I suppose that is possible, but it doesn't strike me as very likely.

 

[Phoenix1595]

Good article/thread. I enjoyed learning more about the math behind the culture mechanics in the game, as a culture hound myself.

 

[cabert]

Thanks. Yes that helps. So the general formula would be

SF * (1 +0.5 * GS) * (1000 + 2 * TP)

Where:
SF is the game speed factor
GS is 1 for Great Scientist and 0 for other great people
TP is the total population of all cities

Since the cost of technologies is going to scale with game speed, SF is irrelevant. That means that in order to lightbulb Electricity with a GS, as mentioned above, you would need

1500 + 3P = 2800
3P = 1300
P = 434 (rounding up)

That means you would need 21 cities at size 20 plus one at size 14. Or more than 40 cities at an average size of 10. I suppose that is possible, but it doesn't strike me as very likely.

well I had a lot more than that
I tried my skill at milking score in WotM9 (after submitting my game).
I had something like (domination limit -5%) land and 90% of the world's population. Not very useful for winning the game, but it happens.

 

[VoiceOfUnreason]

Thanks. Yes that helps. So the general formula would be

SF * (1 +0.5 * GS) * (1000 + 2 * TP)

Not quite... This formula gives the correct answer until people start modding the great people. The lightbulbing yields for each flavor of great people is configured separately. The fact that Prophets, Artists, Engineers, and Merchants lightbulb the same number of beakers is coincidence.

 

[Vynd]

Thanks for the post, Deranged Duck! Great work!

 

[KMadCandy]

edit: post now spoilered to save space, since klarius answered my question, thank you . the question was:
can a revolt occur while a different type of revolt is already happening? my city meets all of those rules for "If a revolt can occur" unless there is an exemption for the period of time that city is in initial revolt after capture during a war (when you just moved in and they say "Viva la Resistance!"). is there an exemption like that?

the answer is "yes, you can't revolt while you're in revolt" so i didn't need to panic.

Spoiler :

i have an odd case going on, it probably doesn't come up that often. i do wonder whether anybody knows the answer about whether the worst case scenario i envision here is possible.

A revolt in a city can occur if the owner of the city and the person who would own the underlying square if there were no city are different. In other words, a city might revolt if a neighboring city belonging to a different civilization has it within its cultural radius and that civilization's plot culture under the city is greater than the city's owner and that of all other civilizations with a city in range. You don't have to have a majority, you just have to have more of your nationality than the other guy. If a revolt can occur, there is a flat 10% chance each turn of making a revolt check.
....
During a revolt check, a random number between 0 and the city's revolt power is compared with the garrison strength. .... Also, there is a possibility that the city may change sides (called a flip) .... A non barbarian city won't flip if this is the first revolt (there is always one warning revolt)

here is how the possibility came up in my current game:

i captured a city from the russians last turn, it is still in the initial revolt. so the brats are still thinking "we don't yet like KMad, we wish we were still russian, we're going to hold a grudge for 6 more turns." but the russians are DEAD now, that was their last city.



usually, during this initial "You're not our leader, we hate you for the war" grudge time the nationality bar would show my culture and the russian culture, maybe a neighbor such as america if they were close enough. in my case, russia doesn't show up on the nationality bar. they're not around. that's not a bug. the city is showing a chance to revolt to the americans, who have a city nearby. it certainly could revolt to the US, so that's not a bug either.

but ... if it is possible for america to roll a "revolt check" during that initial revolt period of a city i captured from not-america, and america succeeds at the roll, will i get a message about it? i am not at all sure, since the city is already in revolt, for a reason that america had nothing to do with. i can imagine a scenario where next turn, roosevelt sneakily wins a revolt roll, and fails to mention this to me. the event log might not mention it either if the city is already in revolt due to some other reason? and then suddenly 70 turns down the line, roosevelt wins his second culture-revolt roll for this city, and i watch it flip to the americans instantly because this odd circumstance hypothetically blocked me from seeing that "(there is always one warning revolt)" if it happened during the period the city was in revolt for an entirely different reason. that would make me sad.

does anybody know if that's hypothetically possible? i noticed the chance the turn after russia's demise, and have started moving troops back in to eliminate that chance to revolt. i'd rather not find out the hard way that you can be unpleasantly surprised like this.

 

[klarius]

There's no revolt check during a revolt.
But you can have back-to-back revolts (going from 1 turn left directly to a new revolt).

 

[Excedrin]

Thanks for the post, Deranged Duck!

It is greatly appreciated and helps me understand more of the complicated strategies going on in game that I can employ and counter.

Great Job! Give yourself a raise

 

[Remy_B]

Also thanks from me for this post, it's really helped me out to understand things. Really excellent info.

In trying to explain this to other people (during complex peace negotiations regarding my borders with a Spiritual culture bomb crazy neighbour ) I drew out these diagrams and found them helpful in explaining it, so I thought I would post them here in case others found them handy.

This is WIP and if anyone can confirm if these are correct or point out any mistakes, that would be marvellous.

What's weird about it is the way it draws in the diagonals between the fat cross cultural expansions, which are easy to work out. It’s not a simple tile radius from the city at all, even at level 2, because if it was, culture would expand in a perfect square around the city. This means cities have more cultural influence on their N/S/E/W spokes than on the splits between these directions.

This is also where I am kind of guessing how it draws in the culture bonuses, based on what I've seen in the game. I'm definitely not 100% sure of this though, especially on the bigger culture sizes.


# = city site
c = tile receiving base CPT
2 = tile receiving base CPT + 20
4 = tile receiving base CPT + 40
6 = tile receiving base CPT + 60
8 = tile receiving base CPT + 80
0 = tile receiving base CPT + 100


A basic city starts like this.

Level 1 Culture: 1-9 points

ccc
c#c
ccc

Level 2 Culture: 10-99 points

 ccc
c222c
c2#2c
c222c
 ccc

Level 3 Culture: 100-499 points

  ccc
 c222c
c24442c
c24#42c
c24442c
 c222c
  ccc

Level 4 Culture: 500-4999 points
(Note the diagonal looks especially odd & 'jagged' at this level and higher)

   ccc
 cc222cc
 c24442c
c2466642c
c246#642c
c2466642c
 c24442c
 cc222cc
   ccc

Level 5 Culture: 5000-49,999 points

    ccc
  cc222cc
 c2244422c
 c2466642c
c246888642c
c2468#8642c
c246888642c
 c2466642c
 c2244422c
  cc222cc
    ccc

Level 6 'Legendary' Culture: 50,000+ points

     ccc
   cc222cc
  c2244422c
 c244666442c
 c246888642c
c24680008642c
c24680#08642c
c24680008642c
 c246888642c
 c244666442c
  c2244422c
   cc222cc
     ccc

 

[DaviddesJ]

What's weird about it is the way it draws in the diagonals between the fat cross cultural expansions, which are easy to work out. It’s not a simple tile radius from the city at all, even at level 2, because if it was, culture would expand in a perfect square around the city.

It's a normal tile radius for Civ. Distance to (x,y) is floor(max(x,y) + min(x,y)/2), a well-known formula.

 

[VoiceOfUnreason]

It's a normal tile radius for Civ. Distance to (x,y) is floor(max(x,y) + min(x,y)/2), a well-known formula.

Just so.

The game actually has two different measures of distance: stepDistance (which gives you squares) and plotDistance (which you see here).

 

[Remy_B]

Have to admit I don't understand that formula at all (max and min of what?) Sorry about that.

But does this mean those diagrams look like they are right or wrong?

It's clear to me that plotDistance will often give 'fractional' results, but it's how the game deals with these. I suspect is it normal (=> .5 rounds up) rounding though just from instincts.

 

[DaviddesJ]

Have to admit I don't understand that formula at all (max and min of what?) Sorry about that.

If you're measuring from the city center to a square that's 4 up and 3 left (in your example format), then the plotDistance is floor(max(4,3) + 1/2 min(4,3)) = floor (4 + 3/2) = 5.

 

[Remy_B]

Ok, starting to make sense, max is the higher of the two x,y values, min take the lower...
So does "floor" means round 5.5 down to 5 then?

Sorry, this just isn't notated like anything I've seen before! (At a risk of appearing even more stupid, could I ask is if this a form of programming or mathematical notation. I'll be shocked if you tell me it is mathematical notation and I've never come across it, but that's the way it goes! Darn crummy education At least I'm learning here )

 

[PieceOfMind]

It's a normal tile radius for Civ. Distance to (x,y) is floor(max(x,y) + min(x,y)/2), a well-known formula.

It's more like a norm really, which in this case is much the same as "distance from origin". Though I knew how to calculate the plotDistance in my head, I hadn't realised the formula was so simple. Thanks for pointing it out in any case!

To make it a distance formula, or metric, you'd have:
d(x,y) = floor( max(|x1-y1|,|x2-y2|) + 1/2 * min(|x1-y1|,|x2-y2|) )
where x = (x1,x2) and y = (y1,y2)

Ok, starting to make sense, max is the higher of the two x,y values, min take the lower...
So does "floor" means round 5.5 down to 5 then?

Sorry, this just isn't notated like anything I've seen before! (At a risk of appearing even more stupid, could I ask is if this a form of programming or mathematical notation. I'll be shocked if you tell me it is mathematical notation and I've never come across it, but that's the way it goes! Darn crummy education At least I'm learning here )

Floor and Ceiling Function
Floor and Ceiling are common function in maths but they're usually written with the shorthand notation (which is not possible in the forums so we use "floor()" and "ceiling()").
Mind you, they are most frequently seen in computational maths problems or computer science rather than the classical pure maths fields.

Max and min are even more common!