Rough payoff times and exchange rates

[darrelljs]

YI will usually work all of this out in advance to make decisions.

Which is why IMHO the end game to this analysis would be improved AI, not improved player performance. Formulae are very helpful in programming an AI, but good players at least will either sandbox it out or play by feel.

Darrell

[SevenSpirits]

For interest rate... I dunno. I've thought about that as well, and I'm not sure it's possible to calculate a fixed "interest rate" like that. If the interest is constant, that would imply (by math) that your total yields should all follow a simple exponential curve. In the beginning that might be true, but in the late game the growth seems more linear than exponential. At any rate, the rate of growth is going to depend a lot on how resource-rich the map is, how good your micro is, and how much military you have to build. It's definitely worth thinking about long-term profit vs. short-term profit, but I don't think you can use a single number like 20 turns for all game situations.

4 Factors here.

1) If the game is going to end soon then of course long-term investments become worse. And the game becomes more and more like this every turn.
2) Several things in the game are not linearly costed; prices of GPs, population points in a city, and maintenance for additional cities all ramp up. Note however that the costs ramp up linearly or quadratically and this does not make growth non-exponential.
3) Tile yields become better in the late game which actually increases the interest rate.
4) Military becomes increasingly efficient compared to other options and therefore lots of economic surplus is channeled into a black hole where it does not accrue interest.

It's 1) and 4) that could make the effective growth rate of empires stagnate into non-exponential growth (while 2) and 3) just affect the steepness of the curve). However the individual investments you still DO make can still be judged in the same way, based on their rate of return.

Certainly it's more complex than 1 per turn = 20. I think it's useful to have a baseline though.

[SevenSpirits]

From PBEM4V:

That's a fair bit faster that 3.5% growth, even excluding the effect of civics and the Academy.

I'd expect it to be faster than 3.5% growth because you are working tons of cottages! Cottages sacrifice value now for value later. So the earlier numbers are artificially suppressed because you own a lot of capital which has a rate of return that, while equivalent to $3/turn, is heavily skewed towards providing its actual output later.

[Krill]

True, but it does give you at least one small sample to consider for calibration of that number.

[luddite]

4 Factors here.

1) If the game is going to end soon then of course long-term investments become worse. And the game becomes more and more like this every turn.
2) Several things in the game are not linearly costed; prices of GPs, population points in a city, and maintenance for additional cities all ramp up. Note however that the costs ramp up linearly or quadratically and this does not make growth non-exponential.
3) Tile yields become better in the late game which actually increases the interest rate.
4) Military becomes increasingly efficient compared to other options and therefore lots of economic surplus is channeled into a black hole where it does not accrue interest.

It's 1) and 4) that could make the effective growth rate of empires stagnate into non-exponential growth (while 2) and 3) just affect the steepness of the curve). However the individual investments you still DO make can still be judged in the same way, based on their rate of return.

Certainly it's more complex than 1 per turn = 20. I think it's useful to have a baseline though.

Hmm well what do you consider "late game"? I would define it roughly like:

Early game: land grab. Cities will mostly be growing onto resource tiles, and workers can chop forests, so the growth rate is extremely high.
Middle game: All the decent land has been claimed, and the early game happiness cap has been lifted, so cities begin growing onto a lot of regular tiles. This is where your analysis seems to be focused.
Late game: Everyone is focused on military and the game is going to end before any long-term investments can be profitable. Usually there's a clear leader by this point so micro decisions aren't as important.

If we're just talking about the middle game then most likely the advanced tile yields like railroad mines and bio farms won't be available yet. Military might or might not be an issue, just depends on the game.

The biggest factor IMO is still the map. If you have a map like the one in PBEM11, with tons of riverside grassland, the growth rate is going to be insane even after all the food specials are hooked up. In that case farms and specialists are probably the way to go, especially if they can win you a lot of "first to X" bonuses like liberalism. On the other hand, with a map like PB4 with lots of hills and coasts, there's more time for cottages to grow. Even regular coast tiles might have time to out-produce specialists (assuming you've already got a fair number of specialists in a NE city).

I wonder if you could calibrate the interest rate based on the "greenness" of the map?

edit: actually 23 and 29 might be the best comparison. It seems like, in both those games, you and novice ran a specialist economy with the mids while mackoti used a lot more cottages with the GLH. Your specialists worked better in 23, but his cottages seem to have worked better in 29.

[SevenSpirits]

I pretty much agree with your characterization of game stages.

Early game when you are growing onto resources I consider a special case. It pretty much requires individual calculation to see which order to make your amazing investments in. I think the growth rate I suggested is reflected in a lot of things - growth, slavery, chops, and quite a few buildings, and it's a useful comparison all game long even though it is most prevalent in the midgame.

Greenness/riverness of the map can be a factor, as can difficulty level and world wrap for maintenance.

We probably shouldn't discuss pbem29 here as it's still ongoing.

[luddite]

Sorry, hope that wasn't a spoiler for anyone. Are there any other completed games here where people have made heavy use of specialists? And yeah, difficulty/world wrap definitely makes a big difference too.
edit: I just checked PBEM9 where mackoti build the pyramids as a philosophical leader and cleaned up. Admittedly that probably had more to do with his micro skills than anything else, but it was also an extremely green map.

[Krill]

PBEM2, but that was also a wonder clearance job whilst on the back lines...

[luddite]

One thing that might make this discussion more scientific is data on how many turns it takes for a game to reach the modern era. Roughly 130-180 in most quick speed PBEM games here? At that point, offense becomes much easier and even a brief military advantage can be enough to do a lot of damage. Also, once you've reached the modern era, you've pretty much reached the end of all the really good economic techs. Roughly speaking, I think "get to the modern era as fast as possible" is a reasonable overall tech goal, and that could help you quantify bulbing vs. per-turn research at least.

For example, I'm pretty sure that, say, bulbing electricity for 1000 beakers is better than settling an academy for 40 extra bpt, whereas for philosophy I'd rather have the academy (even if you assume that the academy will produce just 40 bpt forever and the city can never grow).

[SevenSpirits]

I think you're ignoring that getting to intermediate techs faster can be incredibly potent too. If you only do long-term stuff and I only do short-term stuff I guarantee I will crush you sometime before the modern era, or possibly even reach it first because I got Music, Liberalism, The Taj Mahal, etc and these propelled me much farther than your investments could.

In the case of philosophy, 40bpt is insane for that early but say I'm not just bulbing for kicks, I actually want philosophy because it's useful to me. Now I win Liberalism from you, build Taj, and get 2000+ beakers for free, so now I'm up 3000 beakers. 50 turns later you've caught up by 1000 beakers but I've surely reached Electricity by now; we both get another scientist and I build an academy while you bulb into it. And the end result is that now we both have that 40btp academy and I am still 1000 beakers ahead of you.

And that is just counting Philosophy for its prerequisite value! In reality I am going to use Pacifism and earn another scientist in short order.

You are right of course about bulbing being better the later it gets. I'd be better off bulbing electricity when I finally got there instead of building a wimpy 40bpt academy.