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Krill Wrote:I just want to see it applied to an actual game. I do have reservations about some of the assumptions, but they aren't major. As Seven has already admitted, this only applies to a small subset of games, and that's after the start has been played out.
I agree. I think the oracle situation is way too complex for this kind of analysis. The Oracle also comes too early - the opportunity cost is therefore going to be something like a specific other city with certain resources, as well as delaying key worker techs.
A better application would be thinking about how much is it worth to get math 10 turns sooner, or something like that. Even that is freaking hard.
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Krill, you're expecting an awful lot from such a vaguely developed theory. Think of it as a work-in-progress. I know I ignored a lot of factors, and it's obviously better just to rely on intuition rather than such a simplistic model. I just wanted to check if it's possible to quantize the relationship between short-term hammers, and long-term hammers-per-turn, in a way that roughly makes sense.
I doubt anyone will ever be able to make exact decisions based on a formula like this, at least not without doing a ton of AI work. But maybe we could develop it into something that would be roughly useful for the tough decisions that otherwise seem totally blind.
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SevenSpirits Wrote:A better application would be thinking about how much is it worth to get math 10 turns sooner, or something like that. Even that is freaking hard. That seems like something that you can just figure out exactly. I mean, just count up how many forests you're going to chop in those 10 turns, then you can decide whether you'd rather have those extra hammers or the benefits of whatever other tech you decided to research.
For the Oracle, could we just pretend like it gives no other benefits other than early forges? Seems like this model is having trouble walking the line between things that are too trivial (not worth estimating) or way too complicated.
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Krill Wrote:As a rather specific counter point: SANCTA in the MTDG went Oracle>MC, and it worked out quite well. Was that on normal speed or quick speed? Normal speed would definitely help, since it makes chopping easier.
In fact the relative value hammers/beakers might be adjustable based on the map terrain. If you have a map with tons of forests, then chopping out the oracle is quite cheap. But if it has few forests, and lots of riverside grassland, then just growing onto more cottages looks more attractive. I'm wondering if it might be possible to use Novice's map analyzer tool to adjust the relative value of hammers and beakers.
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luddite Wrote:That seems like something that you can just figure out exactly. I mean, just count up how many forests you're going to chop in those 10 turns, then you can decide whether you'd rather have those extra hammers or the benefits of whatever other tech you decided to research.
Wow, I totally disagree. In fact I think I gave a bad example and it's too complicated too, because there are too many variables.
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SevenSpirits Wrote:Wow, I totally disagree. In fact I think I gave a bad example and it's too complicated too, because there are too many variables.
Alright, let me rephrase that. Figuring out whether those hammers are better than something vague like a religion is quite tough. But at least the nominal value of earlier math is easier to figure out. If you chop 5 forests in that time, that's an extra 35 hammers. Figuring how to value those 35 hammers might be hard, but at least you know what exactly what you're getting. The benefits from teching towards, say, monotheism are a lot harder to quantify.
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I'm morbidly curious to see how I rated there in the 19 graph. My general impression is that I managed to be in the top of the pack most of the time in GNP/tech, at the expense of expansion. In my defense, first game. 
I thought a big reason for the Oracle -> MC was that it usually locks down the Colossus for the Oracler, as it's a darned cheap wonder hammer-wise, the big expense for Colossus is the tech. I do think on a land map, a toroid if Org, or anytime with Spi CoL as an Oracle target makes a lot of sense too. Of course, the leets Oracle Feudalism, Civil Service, Theology, or Machinery.
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luddite Wrote:Alright, let me rephrase that. Figuring out whether those hammers are better than something vague like a religion is quite tough. But at least the nominal value of earlier math is easier to figure out. If you chop 5 forests in that time, that's an extra 35 hammers. Figuring how to value those 35 hammers might be hard, but at least you know what exactly what you're getting. The benefits from teching towards, say, monotheism are a lot harder to quantify.
Well I'll agree with that. I don't think this thread can help you figure out how good Monotheism is very well. But it can help you value those math hammers!
Interest rate says that 20h 10t from now are worth about 14h right now, which is barely more than the actual hammers you get from chopping now. So all other things being average, 10t before math is about when you'd want to start avoiding chops in favor of non-time-sensitive worker tasks. (You already wanted to do time-sensitive worker tasks before pre-math chops in most cases.)
Without knowing the specifics of the situation I can also say that at most you will lose X hammers from delaying math 10t, as you can do better by microing your workers to chop later. But just by continuing your chopping as if nothing was happening, if you are e.g. doing 1 chop every other turn on average, then you are losing 3.5h/t for 10t which is about 21h now.
(3.5h/t -> 70h. 70h 10t from now -> 49h. 3.5h/t for 10t = 3.5h/t now - 3.5h/t 10t from now = 70h - 49h = 21h. Or more generally I guess x/t for the next 10t -> 6x)
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Alright, smart guy, now calculate whether those math hammers are worth running extra cottages to get math earlier, or whether working mines is better. 
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Thanks to all for posting your thoughts here. I think this discussion is actually why it's fun to play Civ4...trying to get a sense of the payoffs of investments which are variable and difficult to value.
I can't help but think that some of the evaluations are actually suited to quantum computation. Winning vs not winning a religion/wonder race--or a war--is like entanglement: Everything is probabilistic until the wave function collapses, ie the wonder is built or the war is won.
To do more comparisons, maybe run a map with symmetric start positions--maybe rotationally symmetric?--and compare players' approaches. Depending on how detailed you get, you could either qualitatively compare or keep track of things like food/hammers/beakers to see which pays off.
If some kind of running score were kept in raw food/hammer/beakers in addition to a weighted score of 8F+5H+3B, you could see how players' in-game position correlates with this very rough estimate.
Anyway, I'm enjoying your discussion. Thanks for it.
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