# Bad math in strategy forum when talking the philosophic trait

#### emills

##### Warlord
In many places in the strategy forum, people will pull some bad math regarding the philosophical trait and the various modifiers in the game, i.e. parthenon, pacifism and national epic. Actual it is not bad math but a misinterpretation of the math that has lead many to understate the value and mistate the effects of the modifier.

A common statement may be: "The parthenon gives 50% bonus for a standard civ but only 25% for a philisophical civ."

This statement is incorrect.

say you have the parthenon which gives 2 GPP

Bad math that reinforces the statement:
Standard civ
2 + 1 = 3, 3/2 = 1.50
Philisophical civ
2 + 2 + 1 = 5, 5/4 = 1.25

There are various versions of the above math using percentage totals and such.

The misinterpretation is that many people add the 100% philisophical bonus to the base, not mathmatically prior to the bonus, but in the results.

the good math for the philsophical trait is
2 + 1 = 3, 3/2 + 2/2 = 1.5 + 1 = 2.5

You see, in this example, the parthenon gives one extra GPP for both parties. As far as I know, 1 = 1. there is not a "1" that is more powerful than another "1"

+1 over 10 turns is still 10 for either the philosophical civ just as it is for the nonphilosophical civ.

For the time to effect spread sheet junkies, numbers game abound:
Say your target is a 100 gpp with the above parthenon example.
2 gpp without parthenon takes 100/2 = 50 turns
2 GPP with parthenon takes 100/3 = 34 turns
2 gpp with philisophical takes 100/4 = 25 turns
2 gpp with philosophical and parthenon takes 100/5 = 20 turns.

The parthenon only guy saved 16 turns compared to the 5 turns of the philisophical+parthenon guy!

Again this is an incomplete comparison since people do not state that the philisophical + parthenon guy actually has more gpp at comparitive milestone points.

@ 50 turns
straight = 100 gpp, 100/100 = 1.0
parthenon only = 150 gpp, 150/100 = 1.5
philisophical only = 200 gpp. 200/100 = 2.0
parthenon + philisophical = 250, 250/100 = 2.5

Both the parthenon and parthenon+philosophical are getting 50%, no more no less.

So is the parthenon worth more or less to a philisophical civ when compared a non philisophical civ? The answer is that it worth the same.

#### malekithe

##### King
While I do agree that it's a bit misleading when people say "the parthenon is only a 25% bonus for philosphical civs", I still think the the parthenon can benefit non-philosphical civs more.

In my opinion, what really matters in all of this is the number of great people you're going to generate over the course of a game or any arbitrary period of time. The parthenon has the effect of increasing your total GPP generated by some number; that number is the same whether you're philosphical or not. Now, if the cost of each great person were the same then the parthenon would grant the same number of extra great people to either civ. However, since the cost of each successive great person increases, the extra great GPP mean less to the philosphical civ, as they will buy him fewer extra great people. (An extra 2500 on top of 5000 means a whole lot more in terms of number of great people than 2500 on top of 10000)

This problem is only exacerbated if you follow the traditional approach of creating a single Great person farm with the national epic. In that scenario, the non-philosophical civ is looking at 2500 added to 10000 GPP, whereas the philosphical civ is looking at 2500 added to 15000 GPP. After you've collected 15000 GPP, an additional 2500 barely buys you one more great person.

The real reason why the parthenon is still of great benefit to philosphical leaders is because you're likely to be running more specialists, regardless, and getting greater effect from them. But, if you look at the problem solely from the perspective of "how many extra great people is this buying me", it's actually of greater benefit to the non-philosphical civ.

#### Wreck

##### Prince
There's nothing bad about the math you posted. Yes, the Parthenon does not benefit a Philosophical leader as much as a non... but only if you assume all other things equal. Like, they both run the exact same number of specialists, use the same civics, etc.

As Malekithe said, a Philosophical leader is very likely to run lots of specialists, and to work on that early. This, regardless of whether he builds the Parthenon (I never build it myself). So, he is likely to benefit from it much more.

As for the "true" mathematical benefit... well, nobody wants GPP per se. They do nothing for you by themselves. What you want are GPs; as many and as early as possible. If you really want to account for the value of something like the Parthenon mathematically, you've got to show that spending a certain amount of shields at time X is worth it, to buy an accelerated schedule of GPs that contains ~two more than you'd otherwise buy.

Why just two more? Because you should stop making GPs when the returns from using specialists drop below tile usage. Given the ability to make the National Epic, the Parthenon is thus an increase in your net GPP multiplier from 2, to 2.5 (or 3 to 3.5 if Philosophical). Possibly one higher, if you run Pacifism to get the last few. In any case, somewhere out there, perhaps at the 11th GP, or the 21st, where prices go up extra-fast, you should stop making them. But with the higher multiplier, you'll typically want to make 2 more, perhaps 1 or 3 (I'd have to do the math to know for certain).

In any case, it's not that few extra GPs way down towards the end of the game that are most important for computing the value of the Parthenon (or any other GPP multiplier). (They are so far in the future that their value is small when accounted for at the time of building the Parthenon.) It's getting the early GPs earlier than you'd otherwise.

#### Dueck

##### Walrold
The integer value of GPP gained from having the Parthenon is identical with both philosophical and non-philosophical civs, since the % bonuses are added up and then applied once.

Say, a city has 10 base GPP. If the civ has the Parthenon and Philosophical, that city gets +50% +100 = +150% GPP, which is 1.5*10 = 15 extra GPP.

The parthenon will add 50% of the original, which is 5. Philosophical will add 100% of the original, which is 10.

#### Beamup

##### Higgs boson
Neither approach is "bad math." They're just measuring different things - or maybe it's better to say they measure the same thing in different ways.

emills' approach measures the absolute gain in GPP. This is perfectly legitimate and meaningful - and, yes, the absolute gain in GPP is the same in both cases.

The statement that the Parthenon provides only a 25% bonus to a Philosophical civ measures the gain in GPP relative to what was already being earned. This is an equally legitimate, meaningful, and correct measure.

So the question becomes one of which measure is more practically useful. Due to the escalating costs of generating additional GPP, the relative increase tends to be more relevant. It's not ideal, as it doesn't convert directly into a measure of additional GP (which is, in the end, all that matters). But it tracks the number of additional GP more closely than the absolute method.

#### Zombie69

##### Emperor
emills said:
You see, in this example, the parthenon gives one extra GPP for both parties. As far as I know, 1 = 1. there is not a "1" that is more powerful than another "1"

This is where you're wrong. Because GP cost more as you get more of them, if you're philosophical, there is less chance that this added 1 GPP will give you an extra GP.

In the end, it's not GPP that matter, it's actual GP generated by those GPP.

This is why talking in percentages makes a lot more sense than talking in absolutes.

#### narmox

##### Emperor
Zombie69 said:
This is where you're wrong. Because GP cost more as you get more of them, if you're philosophical, there is less chance that this added 1 GPP will give you an extra GP.

It's not less "chance" that you'll get an extra GP, since you've already had the extra GP by that time, that someone else is still working at getting (say for example, you're trying to get your 10th GP by the time your non-PHI opponents are close to getting their 6th).

So yeah even in that case it's an advantage.

And of coursre the other advantage is - with PHI you don't need to adopt Pacifism or build Parthenon or whatever to get the bonuses these civic/wonder give. So you can if you chose get GP as slow as anybody else, and not get as many in your game as everyone else

#### KrikkitTwo

##### Immortal
The fact is a '50% bonus' is stated as a relative bonus (and indeed it is) so for it to be a properly understood relative bonus it needs to be translated properly.

The 50% of your BASE is unchanged
The 50/25/16/12% of what you have Without it (if you have Philosophical, Pacifism, National Epic) depends on what else you have... the actual amount

Of course for GPP, the math has to be changed even farther because of the decreasing returns.

The fact is what time you reach point X in the game is often more important than how much you have at some time X. And the ratio of X before to after is also important

So for example for an army is it worth sacrificing a building to get one more Maceman.... well it depends on how big your army is already, and how big the opponents army is.

#### Dueck

##### Walrold
You can't just math out the great person benefits. It's also a massive advantage to have a ton of great people much earlier in the game. The way this interacts with game mechanics can't be easily calculated.

#### Zombie69

##### Emperor
narmox said:
It's not less "chance" that you'll get an extra GP, since you've already had the extra GP by that time, that someone else is still working at getting (say for example, you're trying to get your 10th GP by the time your non-PHI opponents are close to getting their 6th).

It's less chance that it will give you another GP over what you already have, which is the only thing that should matter to you.

#### emills

##### Warlord
I guess I was trying to make a point in how the game adds all of the precentage increases prior to applying it to a base, whether it be production, culture, or in this case great people points.

The other point I was trying to make is that statistics is an evil math, with many interpretations of the same number set.

I think the parthenon is a valuable wonder if for only the fact that the AI is a golden age ho. The great artists it helps produce are great for the obvious culture bombs, but the real value is that the great artist is often a not wanted GP and lends itself to the gaolden age intitiation.

Good replies and discussion.

#### Zombie69

##### Emperor
This is actually a good argument for NOT building the Parthenon. Golden Ages are worthless in Civ 4. If the AI wants to produce them, i say let him. Let him have the Parthenon too if it lets it shoot itself in the foot some more.

IMO, Great Artists are by far the worst GP in the game, unless going for a cultural victory.

#### emills

##### Warlord
While golden ages are not the all powerful per civ III, I would not say they are worthless. An industrial to modern era golden age can be the deciding factor in a space race.

I agree that the great artist is not the most useful GP, that why I think they are good for golden age initiation.

#### Zombie69

##### Emperor
The only time you would ever want to use Great People on golden ages is when you're building the spaceship. At any other time during the game, a single Great Person will always be more useful doing something else, let alone two of them. Building the Parthenon in the Ancient Age, so that you can get more Artists to use for golden ages 5000 years later, isn't exactly a winning strategy!

#### Archbob

##### Ancient CFC Guardian
I actually think the Philo trait is quite weak unless your trying for cultral victory maybe since the bonuses are additive and not multiplicative.

#### Dueck

##### Walrold
A few early great scientists, engineers, prophets and merchants can really give you an edge over the course of the entire game. I find philosophical to be one of the strongest traits...

#### Archbob

##### Ancient CFC Guardian
I find Financial and Industrious to be much stronger. And early on, you still need food production from regular citizens.

#### jar2574

##### Prince
Zombie69 said:
Building the Parthenon in the Ancient Age, so that you can get more Artists to use for golden ages 5000 years later, isn't exactly a winning strategy!

Yes, that's why the Parthenon shouldn't be built in the GP farm. Unless you're going for a cultural victory.

#### Breunor

##### Deity
Well I guess I'm going to buck the trend, but I'm more likely to go for the Parthenon when I'm philosophical.

Basically, I tend to build wonders in three -- five cases: When I'm philosophical, when I'm industrious, when I have a resource that lets me build it cheap and other players' don't. (I can add a fourth -- sometimes the quirks of the tech chart, I can get a good wonder and others can't, I might pull one out. Fifth, I'm going for spaceship, I build the elevator).

So, when I'm philosophical, I'm building wonders to get more great people. Yes, there are diminishing returns, but those early great people are pretty amazing. At my level, I can often get some of them. The wonders go obsolete later, but at that point the diminishing returns are already manifesting.

Indeed, I try not to use too may specialists except engineers since I need the production for the wonders. Since I'm gunning for those GPP, I grab the parthenon.

I suspect this doesn't work on high levels but I try this on mine, Prince, ready for Monarch).

Best wishes,

Breunor

#### DaveMcW

##### Deity
Zombie69 said:
The only time you would ever want to use Great People on golden ages is when you're building the spaceship. At any other time during the game, a single Great Person will always be more useful doing something else, let alone two of them.

More generally, a golden age is most useful in the last 10 production turns before you win. This applies to spaceship, conquest, and domination.

Diplomatic uses artists to rush Radio & Mass Media, and culture uses them for great works.

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