Rough payoff times and exchange rates

[SevenSpirits]

Well on a micro level you're correct- a corn farm is obviously better than working 3 unimproved grassland tiles, even if they both produce the same total crop yield. But I think it's safe to assume that no one is going to do that- or, if they do, they're going to grow very slowly.

It seems like a safe assumption to make, but that's because your example is extreme. The fact is that if your economy involves lots of farms (and thus higher pop) you will do much better in this metric for the same real output, compared to someone preferring cottages.

[luddite]

Here's a comparison of the values from pbem19. From the map tuner I calculated 3.91% for RL7, 3.65% for GES, and 3.45% for Commodore. The actual values were 3.87%, 3.61%, and 3.25%.


I don't actually think this relationship should be quite that exact, but at least it's reasonably close.

[luddite]

It seems like a safe assumption to make, but that's because your example is extreme. The fact is that if your economy involves lots of farms (and thus higher pop) you will do much better in this metric for the same real output, compared to someone preferring cottages.

Is that a problem? Someone who goes all-out on farms is definitely going to have higher growth and production in the short term than someone who works cottages. But in the long term their growth will stagnate, from maintenance and lack of tech (like mathematics).

Mostly I just don't think we have any way to compare beakers to food, yet.

[Thoth]

Is that a problem? Someone who goes all-out on farms is definitely going to have higher growth and production in the short term than someone who works cottages. But in the long term their growth will stagnate, from maintenance and lack of tech (like mathematics).

Mostly I just don't think we have any way to compare beakers to food, yet.

That depends on the happy/health caps plus future ways to turn food into beakers and hammers.

Food now = hammers/commerce later. (excepting Slavery which allows the conversion of future hammers/commerce into NOW hammers).

The conversion rate of foods is dependent on game speed and the max food surplus you can run (Slavery tends to be better at faster game speeds than slower game speeds. It's a lot easier to get 1t growth on Quick speed than on Marathon)

The value of surplus food is connected to current city size vs max city size, assuming you are growing into some form of improved tile (happy cap is the most important variable here, although health also factors if you're running Specialists).

The lower your pop vs max city size, the more valuable additional surplus food is as it accelerates the growth curve towards maximum pop (and hence maximum productivity).




As far as beakers:food.....it depends.

What will the food get you?

vs:

What will those beakers get you?

If the food lets you whip out a settler to grab a contested city site first....food wins.

If the beakers let you grab a first past the post tech or a game winning military tech...beakers win.

Play the map.

[luddite]

Play the map.

No way! Everyone knows that the true way to play is with spreadsheets and graphs!

On that note... Here's NS7's growth from PBEM23. I stopped at turn 85 since that's when they started fighting with mackoti and it messed up their growth. This, again, is with "FpH" counted as 1.5*food + hammers, and then with the total beakers researched on top. I separated the different game phases into different colors to make the trend clear.



I noticed a few interesting things. First of all, the FpH basically followed the trend I expected- superfast growth in the early game of 7.36%, then a more reasonable (but still fast) growth of 4.55% afterwards. The trend here is very clear.

The beaker growth actually slowed down at the same time that the FpH did, which surprised me. Partly that's because this was an emperor map with high maintenance...but mostly it's because I think they were sandbagging research potential for their monstrous golden age (shown here in red) which massively pumped up their beakers by bulbing philosophy, machinery, optics, and astronomy. They increased their beakers by a factor of 5 during that golden age! But after the golden age, their beaker growth slowed down greatly. The end result was roughly the same as if their initial research speed had continued steadily.

[pindicator]

No way! Everyone knows that the true way to play is with spreadsheets and graphs!

Preach it, brother!

[Ichabod]

So, if I take this course, I can be sure to play like Novice and Seven after I graduate?

[luddite]

So I know I've been spamming this thread with a lot of esoteric math and graphs. Some of it has been pretty flaky. After all that random number crunching, here's the list of ideas for this that I'm fairly confident are true (for experienced players under reasonable game conditions):

• Players have already figured out all the best strategies through regular play. This kind of theory-crafting isn't going to discover anything new. At best, this might help someone decide between two hard-to-predict long-term strategies or figure out some tile micro. Mostly I just think it's interesting to try to translate intuition into hard numbers.
  
• The best decision is that which maximizes long term growth.
  
• Roughly speaking, a decision is "good" when it gives more value than the otherwise expected rate of growth, and "bad" if it gives less.
  
• Long-term growth in food, production, and research is roughly exponential.
  
• Until something big happens to change the state of the game(usually war, a golden age, or running out of room to expand), total yields grow at a very constant rate. That rate depends on the map, player skill, and game conditions.
  
• Food and hammers are usually closely related. The relationship with commerce is "fuzzier" (meaning, I don't know how to model it). GPP, culture, and military value is extremely fuzzy.
  
• As long as you're in slavery, food and hammers are basically interchangeable at the rate of 1 food = 1.5 hammers. I've been calling it "FpH" to describe 1.5*crop yield plus Mfg.
  
• A good player on a resource-rich map, developing peacefully, can probably double their FpH every 13 turns (6% growth) during the first part of the game when they're working only special tiles. As they start to build cottages and other regular improvements, that slows to doubling about every 20 turns (3.5% growth).
  
• Because of that, 1 hammer (or food) per turn is worth about 13 hammers (or food) up front in the early game, and 20 later. Teching mathematics is a good marker for the transition point.
  
• Overall, research speed increases faster, but less consistently. It really depends on what techs you research, since some techs speed it up dramatically while others do nothing.
  
• Switching to caste system weakens the food-production link, and ties food to research instead (especially when you're doing a full-on specialist economy of course).
  

Questions, objections, comments? If you have any more ideas for how to model long-term research growth, I'd love to hear them. Otherwise I think I've taken this about as far as I can.

So, if I take this course, I can be sure to play like Novice and Seven after I graduate?

No but you can play like a crazy AI! :P Or, I guess, nitpick them in lurker threads for not living up to their "potential optimum growth rate"

[luddite]

Random research question- how many great people do you think a full-on specialist economy with representation would get by turn 100? Does 13 sound reasonable (with 3 of them going to golden ages)?

[Krill]

Between 4 and 15.