How many GPs will philosophical trait add?

[Heroes]

Philosophical trait increases great people points by 100%. So how many more GP would you expect to gain from being philosophical?

I think the answer comes like this. The first GP needs 100 GPP, the second 200, and so on. The nth GP needs n*100 GPP, and the sum from 1 to n is n*(n+1)/2. Let's call the total GPP/50 as x, then the number of GP n is gotten from solving n*(n+1)=x. A little more math: (n+1/2)^2=x+1/4, n=sqrt(x+1/4)-1/2. ("^2" means square.)

Without considering wonders, philosophical trait doubles x. Let's say x'=2x, n'=sqrt(2x+1/4)-1/2. The relation between n' and n is:

(n'+1/2)^2=2x+1/4=2*[(n+1/2)^2-1/4]+1/4=2*(n+1/2)^2-1/4.

n'=sqrt(2*(n+1/2)^2-1/4)-1/2.

This may look a bit messy. But when you gather many GPP and n becomes relatively large (say 10), it gets close to n'=sqrt(2)*n=1.414*n. For example, when a non-philsophical civ gets 4500 GPP and 9 GPs, a philosophical civ will get 9000 GPP and very close to 13 GPs (needing 9100 GPP). When a non-philosophical civ gets 10500 GPP and 14 GPs, a philosophical one will gain 21000 GPP and exactly 20 GPs.

The national wonder "national epic" increases GPP by 100% for any civ, which makes the effect of philosophical trait less dramatic. It will be then a GPP ratio of 3:2, and n'=sqrt(3/2)*n=1.225*n. The same is true for the great wonder Pantharon (adding 50% GPP). Of course, wonders are not there from the beginning, and an earlier GP makes larger difference.

Conclusion: Philosophical trait is expected to give you 40-50% more GPs before considering wonders, but this effect will be smaller (20-30%) after having relevant wonders. Nevertheless, philsophical trait is still handy for poping more earlier GPs.

 

[ritterpa]

I was just wondering about this today. Seriously. I'm not going to check your math, but it intuitively sounds about right. Good info to know...the trait is probably good for 5-8 more GPP per game max.

 

[MrThing]

Too bad none of the leaders have both philosophy and industry.
Since many of the wonders help a lot with creating great people, combine that with philosphy and the caste system and you have tons of great people.

 

[JavalTigar]

I think this is why there is no Ind/Phil leader. This combo would be devastating.

My 1st game, I had 3 cities just cranking out the GP. I played Mao Phil/Org & I was playing on settler level and did manage to get all the right wonders as well. If I had Ind instead of Org, I could have had those wonders faster => more GPP.

Edit: MrThing beat me to the punch.

 

[AdonisFigure]

Great analysis.

I would say that having played games as the Arabs, and then as other non-philo civs, that I find I can get Mecca to be such a factory for Great People that I find a %50 percent increase.

That's purely anecdotal, but I think if you use the GP early to a single city's advantage, i.e. Mecca or another capital, that you can make the factory stronger and earlier. Great prophet and Great scientist are my favorite combos, which combined with a wonder can give a lovely boost.

By the way I've played on Prince and Monarch levels thus far.