Questions on Representation (Liberty policy)

[Browd]

Although the discussion in this thread is directionally correct, in my view, it is hampered a bit by reliance on the numbers in the Mathematics of Civ wiki, which were correct for the Dec. 2010 vanilla game but are no longer correct. In Delmar's formula above, replace the 1.7 exponent with 2.01 and the 21.03 multiplier with 9.1. And in vanilla, Pm in his formula (the per city policy cost penalty) was 30%, as compared to 10% in BNW today.

Also, the modifier for Representation uses an additional RoundDown function that effectively increases the Representation discount from 33% to 40%. See http://forums.civfanatics.com/showpost.php?p=13126363&postcount=11 and subsequent posts.

 

[wayneb64]

So does this latest information indicate Representation is a better or worse deal?

 

[Delnar_Ersike]

Also, the modifier for Representation uses an additional RoundDown function that effectively increases the Representation discount from 33% to 40%. See http://forums.civfanatics.com/showpost.php?p=13126363&postcount=11 and subsequent posts.

The rounding functions are actually just the result of integer division in C++ and are in slightly different places. In Excel language, the culture cost function would be:
FLOOR((25 + FLOOR((3 * [non-free policies unlocked])^2.01, 1))) * (1 + FLOOR(FLOOR(10*(100-33)/100, 1) * ([num cities] - 1) / 100, 1)))*[policy cost mod]*[game speed mod]*[handicap mod], 5).

The equation is therefore the following, though the constant round-downs do introduce some inaccuracies:

Replacing sums with finite integrals is not accurate at the small amount of sum terms I would be replacing, I've opted to run my calculations using the actual sum with the help of some scripting.

Actual stats are as follows, once again assuming n(x) is constant: k = 2 is 17 cities, k = 4 is 27 cities, and k = 5 is 44 cities. If we assume 2 extra policies before Rationalism and Liberty are completed (almost always the case by Atomic), k = 2 is 12 cities, k = 4 is 15 cities, and k = 5 is 18 cities. If we assume 4 extra policies before those two policy trees are completed (usually the case for Liberty by Information Era), k = 2 is 9 cities, k = 4 is 10 cities, and k = 5 is 12 cities, with these values decreasing by about 1 for each extra policy afterwards (5 extra policies in addition to full Liberty and full Rationalism is 8, 9, and 10, and 6 extra is 7, 8, 9). Remember, this is also all assuming you're always siting on this many cities from the turn that Representation is unlocked: gaining or losing cities at various points in the game can push your free policy's worth of culture saved back or forward quite a bit. Basically, you'll always need to wait for Information Era before getting your free policy's worth of saved up culture.

 

[InFlux5]

Great discussion, and thank you to the people willing and able to work out the math on this.

I have to say though, whether or not you get a free policy doesn't seem like it should be the only consideration. You're still getting subsequent policies sooner than you would otherwise, right? Obviously this is harder to quantify than a full, discrete policy.

I have to say, too, that this discussion has resulted in me valuing the Liberty tree less overall, which is sad, because I hate how Tradition is so strong as to be unbalanced vs the other trees. At the same time, however, the discussion has strengthened my feeling that Liberty is more suited to partial filling - i.e. only taking some policies in Liberty and spreading out into other trees.

Maybe this is the not-so-obvious "benefit" of Liberty, that it allows more diversity in your policies overall, whereas Tradition locks you into one tree. Still, that seems like an iffy benefit, since you are "locked into" the Tradition tree simply because it's so good.

 

[beetle]

You're still getting subsequent policies sooner than you would otherwise, right? Obviously this is harder to quantify than a full, discrete policy.

Yes, but I actually think that benefit is easier to quantify.

I have to say, too, that this discussion has resulted in me valuing the Liberty tree less overall

I have come away with the opposite conclusion! The main culture source in Tradition, the opener. But Representation does pay for itself! This is actually an example of Liberty > Tradition.

since you are "locked into" the Tradition tree simply because it's so good.

But you are locked into the Tradition tree only because the finisher is so good, and any delay to that finisher significantly weakens the value of the tree overall. Liberty, by contrast, each policy is of closer relative weight. (Well, except for the half price setter, which you want to unlock asap for the strongest effect.)

 

[Delnar_Ersike]

Representation is basically Liberty's Oligarchy: I wouldn't devalue Liberty solely based on Representation for the same reason I wouldn't devalue Tradition solely based on Oligarchy. Oligarchy gives an early benefit in a tree that is based around bonuses that have their biggest payoff later on, while Representation gives a lategame benefit in a tree that is based around bonuses that have their biggest impact earlygame.

Don't forget about the free Golden Age, either (especially for Persia): the +1 gold on tiles is usually fairly negligible earlygame for low population Liberty who cannot afford to work gold-earning tiles as much, but the +20% production and +20% culture for 16 turns is still a great boost earlygame. Hmm, they really didn't think of Golden Ages when they removed gold from tile yields in favor of gold from trade routes...

 

[Redaxe]

Then there is also the issue of social policy costs in regards to map size.

If you are on a standard size map each new city you found increases culture cost of the next social policy by 10%.
On a large map this reduces to 7% if I recall correctly.
Not sure about huge.

So the 33% is less effective the larger the map size is because the penalty is smaller.