Too early for golden ages

[yanner39]

I'v been playing a couple of games on the last few days and my focus has always been to get my happy cap as high as possible. Say my cap is 7. If I don't plan on expanding horizontally for the time being, is it a good idea to trade one of my luxury resources for 30 turns for a limp sum of gold even if I only have one of them?

Has the math ever been done has to whether it's better to keep the as high as possible to trigger a golden age sooner and reap the rewards or is it better to get gold sooner?

My initial feeling is that it would be better to get the gold earlier and later on when the cities are better developed with more tile improvements, then you trigger the first golden age.

 

[Randall_Flagg]

I want my GA asap. I can barb hunt for early gold. I do know quite a few people do the Trade fast. I just will not do the AI gold trades, I limit myslef to lux for lux only.

 

[alpaca]

A detailed analysis of what's advantageous here would be relatively complicated as the problem depends on a multitude of variables:

- number of gold-working tiles in your empire
- growth rate of the same when analyzing whether it's better to save up the cheaper early GA to pop it later
- number of cities in your empire
- growth rate of the same for the same reason as above
- the gold you can get for trading
- whether you have any modifiers to golden age length
- weighing of the production and cultural bonus accrued during GA

I can give you a very simple rule of thumb:

The number of turns the four happiness would take to trigger a golden age is

t = H/h

where H is the happiness required for the next golden age and h=4 the happiness of the luxury. This assumes selling the luxury puts you at 0 happiness, or, equivalently, that you weigh the golden age yield by the fraction of h/hE where hE is your total excess happiness.

If n is the number of gold-yielding tiles in your empire and m your average gold multiplier (1 if you have nothing in the way of markets and the like), the total gold yield during a golden age of length l is

G = n*l*m

The total amount of money you can make by selling the luxury during that time is

G' = t*s/30 (= 8 usually)

where s is the amount of money you sell the luxury for and the 30 is from the 30 turns, assuming you don't cheese out by declaring war or somesuch.

Saving for the golden age will be better if G > G' so we can check

G = G'

n*l*m = H/h * s/30
n = H/h * s/30 *1/(l*m)

If H is, for example, 500 (first GA and only one city), s/30 = 8 (240 gold) and l=10 (no modifiers), h=4

n = 100

So your one city would have to provide a hundred gold-working tiles for this to be better from a purely financial point of view, discounting culture and hammer benefits.

If H = 1000 (larger empire and maybe second GA), and assuming m=1.1, you'll need 180 tiles that work gold to yield the same amount of cash during a golden age.

Judging from this, it's typically advantageous to always sell your luxuries as long as you stay happy. Once you get unhappy, lack of growth has to be taken into account. The problem for GA is that 8 gpt is a lot and a golden age takes a ton of happiness to trigger.