Rough payoff times and exchange rates

[luddite]

Well I was ignoring stuff like that on purpose, trying to think of how to model "bulbing vs. bpt" in rough general terms, so that we can come up with an accurate "inflation" value for beakers. If bulbing philosophy directly leads to getting Liberalism and Taj then I guess you could say that the value of that bulb is 3000 beakers, and make the comparison on that basis. But if you're behind on tech and have no chance of getting Lib or Taj, then the value is just 1000 beakers (assuming you're not going to immediately switch to pacifism). You'd also have to account for the likely growth in value of the academy, as the city grows.

[luddite]

So, because I am a crazy person, I decided to make a graph of both of our demos from PBEM19, which was a very fast teching game (both of us got into the modern age around turn 120). This is graphed with a logarithmic y-axes and an exponential trend line (meaning that a perfectly straight line represents exponential growth).



All of the demos increased roughly exponentially, from 4 to 4.5% each turn on average. Both of us had our food yield and MFG increase faster than average in the mid game, and slower than average towards the end (although your Mfg spiked up at the very end when you went into total war mode). Your GNP growth was almost constant throughout the whole game, whereas ours was slow in the midgame and very fast towards the end.

Of course this doesn't account for bulbing, golden ages, or culture. I just thought it was interesting data. It's much closer to being perfectly exponential than I had expected, maybe because this was such a fast-teching game.

[Nicolae Carpathia]

I've always observed a very distinct exponential growth phase, with an always painful hump just before it.

The trick is how the hell you can replicate it.

[luddite]

I took a stab at estimating the value of GPP as well. Basically I assumed that you're running only scientists, without representation, and that you're using them all to bulb for 1000 beakers each time. If anything, that underestimates the value of a bulb, because of the "first to X" bonuses, but mainly I wanted to compare running specialists vs. working cottages. "No bonus + 3" means the number of beakers/turn each scientist is worth without any kind of GPP bonus, 2x+3 means a 2x bonus, and so on. I also assumed that printing press comes in right when the cottages turn into towns, so villages are worth 3 while towns are 5.


Going by this it kinda seems like scientists are always better than cottages. At least outside of a bureaucracy capital and up to the 20th great person. I figure a scientist basically costs 2 cottages (because you need to run two grass farms to make up the food cost, and those farms could be cottages instead). The two cottages can never be worth more than 10 bpt (assuming no bureaucracy or free speech) , and that's not even counting the time value of developing the cottages.

Even in the extreme case with: No representation, No GPP bonus, and 20 (!) great people, it still takes 31 turns for the cottages to match the scientists. 31 turns is really a long time. Of course, this ignores the time value that comes from having the scientists deliver most of their research all at the end (from the bulb), whereas with the cottages you get more along the way. I haven't tried to figure out the time-discounted value yet though.

[SevenSpirits]

Here's what I have for estimating the value of gpp. The basic problem is that producing a GP makes future gpp less valuable. How much less valuable?

Say my empire is producing 13gpp/turn. This will result in GPs appearing at certain turns in the future, spaced farther and farther apart, until the game ends. My question is, if I get an influx of 67 gpp on turn 0 of our counting, how much is that worth? If we assume that the value of a GP degrades with time like everything else, then even if we end up producing the same number of GPs, we get them sooner and that's worth something.

According to the program I wrote and the 3.53% interest rate, the value we get from those 67 instant gpp is 0.39 GPs. Quite a good deal!

A perhaps more useful way to look at is to divide the 67 gpp by the 0.39 to normalize it to the effective cost of a single GP.

Here are the numbers for the first 20 GPs. They are like the example except that we have produced N-1 GPs already and our empire is outputting enough gpp per turn to make a GP in about 5 turns in each case:

Gpps cost / normalized GP value for GP # 1 while producing 13gpp/t: 171.7253735899068
Gpps cost / normalized GP value for GP # 2 while producing 26gpp/t: 267.41788113559164
Gpps cost / normalized GP value for GP # 3 while producing 40gpp/t: 359.91971206262264
Gpps cost / normalized GP value for GP # 4 while producing 53gpp/t: 444.35416607629946
Gpps cost / normalized GP value for GP # 5 while producing 67gpp/t: 544.3222978213304
Gpps cost / normalized GP value for GP # 6 while producing 80gpp/t: 610.8147435263924
Gpps cost / normalized GP value for GP # 7 while producing 93gpp/t: 701.1267918680009
Gpps cost / normalized GP value for GP # 8 while producing 107gpp/t: 786.0493877035542
Gpps cost / normalized GP value for GP # 9 while producing 120gpp/t: 865.5855800264285
Gpps cost / normalized GP value for GP # 10 while producing 134gpp/t: 1037.1745900507403
Gpps cost / normalized GP value for GP # 11 while producing 147gpp/t: 1117.0831324840087
Gpps cost / normalized GP value for GP # 12 while producing 174gpp/t: 1269.9557492593874
Gpps cost / normalized GP value for GP # 13 while producing 201gpp/t: 1475.3800003505614
Gpps cost / normalized GP value for GP # 14 while producing 227gpp/t: 1574.1974245458466
Gpps cost / normalized GP value for GP # 15 while producing 254gpp/t: 1736.2765978338794
Gpps cost / normalized GP value for GP # 16 while producing 281gpp/t: 1887.8176495914374
Gpps cost / normalized GP value for GP # 17 while producing 308gpp/t: 2046.7976596803144
Gpps cost / normalized GP value for GP # 18 while producing 335gpp/t: 2311.5975779934806
Gpps cost / normalized GP value for GP # 19 while producing 361gpp/t: 2381.659013001224
Gpps cost / normalized GP value for GP # 20 while producing 388gpp/t: 2564.376145455695

I don't know how much of that made sense, but what I'm saying is that if you weigh the benefit of a GP that you are considering producing vs the normalized costs listed there instead of vs their actual cost, you might make better decisions.

However note that the numbers vary quite a bit based on how much gpp you assume your empire to be producing per turn. The more gpp you are producing, the less useful pumping out an additional GP is, because it will have a smaller effect on the speed and number of your game-long GP production.

[novice]

I couldn't follow either of these attempts at quantifying the value of GPPs.

I like Luddite's graphs though. Interesting that his empirical approach and Seven's trial and error / intuitive approach give pretty similar growth rates - 4.2% vs. 3.5%.

[darrelljs]

Bulbing is non-directed research. Try building that into a formula :neenernee.

Darrell

[Krill]

PP applies to villages Luddite...

[luddite]

PP applies to villages Luddite...

Yeah I know... well I wanted to account for the earlier part of the game where you wouldn't have PP yet. But of course if you add the PP bonus to the village then they look a lot better. Also I didn't account for the extra maintenance of the farms/scientists, so that might make a big difference too.

[luddite]

I couldn't follow either of these attempts at quantifying the value of GPPs.

I like Luddite's graphs though. Interesting that his empirical approach and Seven's trial and error / intuitive approach give pretty similar growth rates - 4.2% vs. 3.5%.

Yeah, that shows that this approach isn't totally misguided at least.

I do think it's better to separate out the early game and midgame phases, though. It's especially noticeable on GES's graphs from 19, since he was totally peaceful there and filled up his land pretty quickly. In the early game his Food and Mfg grew at like 6% and his GNP was almost flat, but then after about turn 40 the Food and Mfg growth slowed down and the GNP started growing much faster (about 6% also).

Maybe the conversion rate of food/hammers: beakers should be adjusted depending on the game phase? Or try to make decisions in a way that doesn't depend on that conversion rate.

edit: this picture shows the difference. He actually had over 8.3% Mfg growth in the first 40 turns! (Not counting the first 10 turns where he wasn't growing at all of course) and then almost 6.2% GNP growth after that. Doing it this way also creates a much better fit.