Maximizing your PFF: Production Possibilities Frontier

Hsinchu

Prince
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If you've recently taken economics, note that this lesson isn't intended to be quite as soporific as the lectures you are used to. This is a lesson for players looking to be more competitive in the difficulty they are playing in, or that want to move up a difficulty and need a new tool. This is ONE tool and is not a guarantee of victory, but it does shed some light on how micromanaging is more useful than governorship.

I recently started a new game that I'm planning to take slow so I can learn from it and win and have fun at the same time. You can read all about it on my new Civ IV blog.

Spoiler :
http://civlegend.blogspot.com/2009/10/sally-sells-seashells-by-seashore.html

I'll be repeating some of what is there, here.




This is our starting position. Our given is that we are going to be building an obelisk, we have 22 food to next pop, and 30 hammers to an obelisk, and we are trying to win buddhism, which means teching meditation as fast as possible (commerce!).

We have a couple of great resource tiles in our reach, and a border pop due in 5 turns.

What are our possibilities? The first thing we need to rationally come to grips with is that we are NOT going to be working any tile that is less than any other tile, just common sense. Basically, we have three tiles we can work with: 3:food:1:commerce:, 2:food:1:hammers:1:commerce:, and 1:food:2:hammers:

We need to produce 30 hammers, 22 food, and 119 beakers in as few turns as possible.

If we rely on the governor, we will grow to city size 2 in 8 turns by working our sugar tile.

3:food: x 7 turns = 21
The last turn will give us a surplus of 2 food.
Over these 8 turns we will receive 8 hammers from the city tile.

If we instead choose to work the silk tile, and only the silk tile:
22:food: / 2:food: = 11 turns growth
(1:hammers:worked+1:hammers:city) x 11 turns = 22:hammers:

In both cases, we see that commerce remains relatively constant.

For simplicity, we are going to use 11 turns as our equalizing turn limit.

By turning off the governor, we will attempt to grow at turn 8 AND produce 22 hammers after 11 turns, as opposed to one or the other.

If we work the silk tile for two turns and sugar tile for six turns:
Food: 2x2turns + 3x6turns= 22
Hammers: 1x6turns + 2x2turns = 10
and then we consider the three turns at pop 2, working silk and fur to "catch up"
Food: 1x3turns = 3
Hammers: 4x3turns= 12
totalling:
Pop2 + 3:food: + 22:hammers:

If we had let the governor pick for us, just the total (assuming sugar->silk):
Pop2 + 10:food: + 14:hammers:

At face value only, we are paying 7 food for 8 hammers. Note, once we incorporate Pop3, that 7 food may have been worth more than 8 hammers, but for now, let's focus on the Obelisk and the culture we are creating.


Another situation, silk for 8 turns, sugar for 2 turns, then silk+fur to catch up.
Pop2 + 1:food: + 22:hammers:

Now, strictly on point, this situation is definitely not worth it. For those of you who have also been keeping track of commerce, you'll note that the sooner you reach pop 2, the sooner you start getting that extra 1:commerce: irregardless of whether you are working sugar, silk, or fur.

Working your PPF means taking these sorts of costs into account. Playing with the governor can be hazardous to your civilization's health such as in the latter case or if you accidentally end up working the "citizen" specialist. At least with the governor, you're sure to be going in some direction. The governor typically favors food and hammers, so you'll be okay, but if you are trying to squeeze out units or improvements with cold efficiency, you'll need to take a hand manually.

Also, if you use spies or worldbuilder, you're going to notice that in order to crank out units, the AI typically forces itself into starvation. In order to compete, you'll need to do the same on occasion. The only way to do this effectively and not eat through your population like sliced cheese is to measure what you're buying and what you're paying for it.

Learning what tiles are the best for the situation takes practice and more than a little math, but the master of this art is the one that can confidently say they did everything possible with what they were given. Combining this skill with proper city placement and good decisions in what to build will go a long way.
 

vicawoo

Chieftain
Joined
Feb 12, 2007
Messages
3,226
For simplicity, we are going to use 11 turns as our equalizing turn limit.
This is a little confusing, if you had explained that working the silk for 11 turns satisfied all conditions and therefore served as a benchmark which we would call an equalizing turn limit. Also in none of the situations does it reach 30 hammers, nor does it reach 119 beakers. Also there are bonuses to teching, as 10 commerce x 10 turns does not equal the 119 beakers, but buddhism finishes in 10 turns.

Since you finish buddhism in 10 turns working a 1 commerce tile, you don't have to worry about the commerce requirement. So you only need to grow to size 2 and generate 30 hammers. Once you reach size 2, you can exchange hammers for food 1 to 1 and you can stall your growth. So the best method would be to grow to size 2 and stall your growth for maximum hammers:
7 turns sugar 7x(3/1/10)
1 turn plains forest 1/3/9
4 turns fur and plains forest 4x(0/5/10)
result: 12 turns 22 food, 30 hammers, 119 beakers
 

Hsinchu

Prince
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This is a little confusing, if you had explained that working the silk for 11 turns satisfied all conditions and therefore served as a benchmark which we would call an equalizing turn limit. Also in none of the situations does it reach 30 hammers, nor does it reach 119 beakers. Also there are bonuses to teching, as 10 commerce x 10 turns does not equal the 119 beakers, but buddhism finishes in 10 turns.

Since you finish buddhism in 10 turns working a 1 commerce tile, you don't have to worry about the commerce requirement. So you only need to grow to size 2 and generate 30 hammers. Once you reach size 2, you can exchange hammers for food 1 to 1 and you can stall your growth. So the best method would be to grow to size 2 and stall your growth for maximum hammers:
7 turns sugar 7x(3/1/10)
1 turn plains forest 1/3/9
4 turns fur and plains forest 4x(0/5/10)
result: 12 turns 22 food, 30 hammers, 119 beakers

Lol. I guess so.

But now I'm getting confused to. At turn 8, we are both at pop 2, no food. And we can feasibly substitute fur for the plains forest in order to get that commerce back.
Any of the 4 "stuff" tiles is effective for the rotation resulting in max PPF, which was the point I was making.

With 4 turns left to get 20 hammers, stunting growth is one option. I would kill to get a second plains forest fur to ensure max limit.

However, I took the free commerce in exchange for the turn for obelisk and some food.

I didn't extrapolate to the end point, but maybe I should have.

As for the research, there is a 3 beaker per turn freebie that I can't account for. Incidentally, in the game, the AI beat me to Buddhism. The commerce has been "re-invested" into longer term goals. XD
 

vicawoo

Chieftain
Joined
Feb 12, 2007
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But why do you care about the free commerce when the goal was to get 22 food, 30 hammers, and 119 beakers as soon as possible?

Basically my approach was recognizing that all these tiles produce at most 3 food/hammers combined, so the way to maximize total food/hammers is to grow as soon as possible. And then I simply redistributed my tiles into 1 food/2hammer tiles so I could meet the goal as quickly as possible.
You start with 4 food+hammers per turn, and by growing you boost yourself to 5 food+hammers per turn. Likewise, the fastest way to get commerce (aside from working the 2 food/2 commerce tile), is to grow as fast as possible. Without having unequal tile yields (like 3 food vs a mine), the way to maximize your PFF as I understand it is to grow as soon as possible.
 

Hsinchu

Prince
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Messages
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But why do you care about the free commerce when the goal was to get 22 food, 30 hammers, and 119 beakers as soon as possible?

Basically my approach was recognizing that all these tiles produce at most 3 food/hammers combined, so the way to maximize total food/hammers is to grow as soon as possible. And then I simply redistributed my tiles into 1 food/2hammer tiles so I could meet the goal as quickly as possible.
You start with 4 food+hammers per turn, and by growing you boost yourself to 5 food+hammers per turn. Likewise, the fastest way to get commerce (aside from working the 2 food/2 commerce tile), is to grow as fast as possible. Without having unequal tile yields (like 3 food vs a mine), the way to maximize your PFF as I understand it is to grow as soon as possible.

You'd be right. To increase your maximum PPF, you do want to grow as soon as possible (under cap). 8 turns is the minimum amount of turns to grow from size 1 to size 2. Hammers don't influence growth directly.

What this thread was intended to do (and in hindsight, has done poorly) is to show the necessary balance between short-term and long-term goals and how they are interrelated. I added the race for Buddhism as a restricting element. Often there are other restricting elements, such as maintenance, and this is meant to simulate that at small scale.

We basically have the same strategy getting to pop2. You don't want any surplus at pop 2 if you want to capitalize on hammers. You, likewise, don't want to capitalize on hammers only if you want to maximize growth (hence, turn 8 requirement). Then, to top it all off, if you want to maintain a maximum rate of science, you don't want to throw away any potentially useful commerce elements.

You've been very helpful in allowing me to enumerate vilcawoo. Thanks.

However, I found a wrench in my plans that I'm going to blog about...

But summarizing, the "free beaker" phenomenon makes it so that if you are focusing on min/maxing tech, it doesn't necessarily correspond to tile min/maxing. The number of bonus bpt seems to be tech dependent, and "carry over" beakers don't appear to have any bonus attached to them. Two bad tech choices later, I am rethinking my entire strategy and I think I'll be taking my save to the "strategy hospital" threads later.
 

Silu

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I found it kind of funny that the thread title has "production possibilities" in it and features a capital with zero hills.

Didn't quite understand the "Obelisk first" move though ;)
 
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As for the research, there is a 3 beaker per turn freebie that I can't account for. Incidentally, in the game, the AI beat me to Buddhism.

You probably had between 9 and 13 commerce the entire time, with the slider at 100% throughout?

(a) There is a one beaker "having any cities at all" bonus. In other words, you can never turn off research completely. This takes you up to 10-14 research.

(b) Your test was researching Meditation, which means that you had Mysticism (a prerequisite), so you were getting a 20% boost to your research each turn. 10-14 * 20% = 2 in in integer math.

So your observed research rate (which is to say, the progress that you were making each turn) should have been between 12 and 16 beakers per turn.
 

Hsinchu

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Nice math.

Unfortunately, you'll still lose to someone who built a worker first.

I found it kind of funny that the thread title has "production possibilities" in it and features a capital with zero hills.

Didn't quite understand the "Obelisk first" move though ;)


Lol. I agree completely. Worker mucks up the mathematics, though. I am probably going to abandon the game in about 90 more turns for bad decisions, but in the meantime, gathering information.
 

Hsinchu

Prince
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Messages
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Location
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You probably had between 9 and 13 commerce the entire time, with the slider at 100% throughout?

(a) There is a one beaker "having any cities at all" bonus. In other words, you can never turn off research completely. This takes you up to 10-14 research.

(b) Your test was researching Meditation, which means that you had Mysticism (a prerequisite), so you were getting a 20% boost to your research each turn. 10-14 * 20% = 2 in in integer math.

So your observed research rate (which is to say, the progress that you were making each turn) should have been between 12 and 16 beakers per turn.

I didn't know this. Thanks! I actually have observed this phenomenon. There is a 1 beaker bonus for fishing (The having any cities at all bonus), and a 14 bpt rate for pottery (Which has prerequisites fulfilled, 11 commerce + 1 free beaker + 2 from the 20% boost).

What I also learned is that when a technology is completed, Only nonbonus beakers carry over to the next tech. Hence, I had 11 commerce at the end of meditation with 1 beaker to go, I only received 10 beakers poured into fishing. I did not receive my cities beaker. I've got one more test at the end of pottery (switching to no prereq hunting) and then I'll rethink forfeiting my current game.
 
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What I also learned is that when a technology is completed, Only nonbonus beakers carry over to the next tech. Hence, I had 11 commerce at the end of meditation with 1 beaker to go, I only received 10 beakers poured into fishing. I did not receive my cities beaker. I've got one more test at the end of pottery (switching to no prereq hunting) and then I'll rethink forfeiting my current game.

That's probably a rounding bug. Back when we were researching techs uphill both directions in the snow, there was an exploit by which you could over research the final turn, and get bonus beakers as a consequence.

I don't know that anyone ever verified that they got the fence post case right.
 

Hsinchu

Prince
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That's probably a rounding bug. Back when we were researching techs uphill both directions in the snow, there was an exploit by which you could over research the final turn, and get bonus beakers as a consequence.

I don't know that anyone ever verified that they got the fence post case right.

Fence post case?

I do know that I sharply completed fishing for a 0 beaker surplus by pushing one extra beaker from my dye tile. The subsequent turns, pottery has been receiving 14 beakers like clockwork.

Another player mentioned on another thread that bonuses are given for techs that have already been researched? I have not yet experienced any such bonus. If it is incremental (5%) then it could be a rounding problem at present.
 
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