SevenSpirits Wrote: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?So I was thinking about what this meant and how to evaluate it in a real game sense. Does this mean that, according to your calculation, getting 67 instant gpp is equivalent to getting four tenths of a free great person? That roughly makes sense I guess- 67 gpp gets you a merchant that can be used to bulb about 4/10 of economics for the free merchant there. Or you can do the same thing with a great scientist and physics.
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!
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Rough payoff times and exchange rates
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I think he meant something like even though you get 67 GPP which gets you one great person, it delays your next great person so it's worth less than one whole great person. I have absolutely no idea what the table afterwards means though.
Civilization IV: 21 (Bismarck of Mali), 29 (Mao Zedong of Babylon), 38 (Isabella of China), 45 (Victoria of Sumeria), PB12 (Darius of Sumeria), 56 (Hammurabi of Sumeria), PB16 (Bismarck of Mali), 78 (Augustus of Byzantium), PB56 (Willem of China)
Hearthstone: ArenaDrafts Profile No longer playing Hearthstone. 
luddite Wrote:Does this mean that, according to your calculation, getting 67 instant gpp is equivalent to getting four tenths of a great person? That is specifically if you are making 13gpp/turn starting now and for the rest of the game. What is the actual effect of that 67 gpp? It probably doesn't increase the number of great people you produce throughout the game. But it does make all your GPs for the rest of the game come out about 6t sooner. According the the 1:20 interest rate getting them ALL 6t sooner is worth approximately 0.4 GPs right now. Breaking it down: the first GP comes now and is therefore worth 1 GP, instead of coming 6t from now and being worth about 0.81 present GPs. (Future things are less valuable than present things.) The second GP comes 10t from now instead fo 16 turns from now and is therefore worth 0.7 present GPs instead of 0.57 present GPs. As you get farther and farther out, the 6t difference is less valuable for each subsequent GP, and the total difference in value for getting all of them 6t sooner ends up summing to 0.4 GPs. (According to the way I calculated it. Which, since it assumes that your gpp will be 13/t all game long, is pretty simplistic.) (Obviously in a real game things are not so clear-cut. A GP doesn't necessarily degrade by 3.53%/turn. Maybe you don't need it until later anyway. Or, maybe you really really need it before your golden age ends so you can bulb Civil Service and swap into Bureaucracy. This is just trying to estimate the average value.) The second entry in the table says: You're making 26gpp/t for the rest of the game, and you've already produced one GP. How much value would you get from an instant 134 gpp, enough to produce the next GP? And specifically, at that rate, how many gpp would be required to produce one full GP worth of value? Etc.
I wonder if it's possible to use this kind of analysis to calculate a real decision?
Like, say you're debating whether or not to go for the Oracle. To keep things simple, I'll assume that no one else is competing for it, and that you're going to use it to pick up Metal Casting. My intuition is that, for industrious leaders, that's usually a strong play, but for leaders who aren't industrious it's usually not worth it. But I'll check if the math agrees. Getting the Oracle requires meditation (79 beakers), priesthood (59 beakers), and 100 hammers. I won't count mysticism since you'll probably need that anyway and you might have started with it. The reward is metal casting- 450 beakers for free. This is with standard/monarch/quick speed settings. I suppose we should also discount the 1.2 prerequisite bonus, so you only need to research (79+59)/1.2=115 beakers. Those aren't totally wasted, since you would have needed meditation and priesthood eventually anyway, but probably not for a very long time. Total (nominal) cost: 115 beakers, 100 hammers. The 115 beakers would be devalued by inflation over the time you spend researching them. However, the same is true for anything else you research also, so it's the same cost as anything else (bronze working, for example, is almost the same). Same goes for the 100 hammers. However, chances are you wouldn't have researched metal casting so early, so you have to discount those 450 beakers. You'd need to estimate what turn you would have normally researched it on. If you assume that 20h = 1 hpt (I think that underestimates early game hammers, but nevermind), then an 80h forge is worth 4 hpt, and is therefore a good investment for cities making more than 16 base hpt. Even counting slavery, there aren't many cities like that early in the game. (since this is getting really complicated, I'm going to ignore all the other benefits like the Colossus, triremes, happiness, Prophet points, etc. and just focus only on the hammer benefits of early forges). Let's say that, when we first finish the Oracle, there aren't any cities where it's worth building a forge. But 20 turns later you build 2- one in the capital making 24hpt, and 1 in another city making 20 hpt. So that's a total of 3hpt "profit" from the forges, which we'd say is worth 60 regular hammers. But that came 20 turns after the Oracle was finished, so it gets discounted by half, to be worth only 30 hammers at the time the Oracle was built. So, in hammers, you've traded 100 hammers for 30 hammers. Not a good trade. Let's say that you would have normally researched Metal Casting 20 turns after the date you got the oracle. So that would make it worth, equivalently, 225 beakers. Minus the 115 you invested in priesthood and meditation, gives 110 beakers profit. So in this situation, building the Oracle gives a very rough equivalent of +110 beakers, -70 hammers. Using Seven's points system that comes to -20 points, for a net loss. So roughly speaking the math agrees with my intuition that it's not a great deal for non-industrious leaders, especially compared to the benefits of getting earlier math and an extra settler. On the other hand, for an industrious leader, things change quite a bit. Now the Oracle is 67 hammers, and forges cost only 40 base hammers. So the profit from the early forges is 70 hammers, and metal casting would probably be worth more as well since you'd want to research it earlier. But even without that, you're getting +3 hammers, +110 beakers, or +345 points.
This thread is just so much hand waving until you actually use it in a specific situation.
So...case study time. Krill Wrote:This thread is just so much hand waving until you actually use it in a specific situation. How about PBEM11 as an example? Plako (non-industrious, but he settled on marble) built the Oracle turn 31. GES (Huayna Capac) teched Metal Casting turn 54. Overall I'd say Plako fell behind there from building the Oracle, and the land was identical for everyone. I think he got his first forge around turn 55.
I like that writeup, luddite (Krill's crankiness aside.) Yeah, Oracle to MC does often intuitively feel like a wash or small gain at best. Of course one thing you leave out is denying the Oracle to your rival industrious civ, but that's virtually impossible to quantify.
But the Oracle's GPP can be quantified. How does that turn out? Does it push the Oracle ahead, or too small to make a difference, or even actively bad when you want scientists or merchants instead? T-hawk Wrote:I like that writeup, luddite (Krill's crankiness aside.) Yeah, Oracle to MC does often intuitively feel like a wash or small gain at best. Of course one thing you leave out is denying the Oracle to your rival industrious civ, but that's virtually impossible to quantify.heh thanks... glad someone read through all that mess. I'm not sure how much I agree with the end point values, though. One thing to bear in mind is that, if you use the 67 industrious hammers to build a settler instead, that will instantly get you an extra +2 food and +2 hammers, which is worth 520 points in this scoring method and grows quickly. I doubt that a settler is that much better than the oracle. The 2GPP is really, really hard to quantify. There's just so many variables to consider- like, if you want to get a shrine, how many cities will the religion spread to, and how much is that gold worth on a given map? Seven's formulas give a simple handwaving formula to use. 2GPP/turn = 40 GPP = 0.2 great people. So if it gets you a prophet for bulbing theology, that would be worth 500*0.2= 100 beakers, or 300 points. But it seems weird that the prophet points should be worth so much more than the early forges. Maybe discount that to 150 points since you wouldn't normally tech Theology so early. Overall it really depends on what you'll be able to do with that Prophet. T-hawk Wrote:I like that writeup, luddite (Krill's crankiness aside.) Yeah, Oracle to MC does often intuitively feel like a wash or small gain at best. Of course one thing you leave out is denying the Oracle to your rival industrious civ, but that's virtually impossible to quantify. 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. Some of the qualms I have with Luddites post are:
As a rather specific counter point: SANCTA in the MTDG went Oracle>MC, and it worked out quite well. |
