What's a Great Person Point worth?

[Steamwerks]

Originally Posted by Mylene

On normal speed, mounted units are better than on Epic or Mara..yeps.
Also, Deity (i know it's annoying to repeat that, but it's important for many strategic points..) often requires fast wars.

You have big AIs around, they usually will have solid research and techs for bribing others in on you, and peace vassal also dangerous.
If you take too much time getting steel and maybe grennies too, then can only move 1 tile per turn thru enemy culture..can lead to very unpleasant situations
With Curis you have a fast moving unit, very strong on open field and can react better.
You can also blitz or fork some cities, before they have time to bring reinforcements.

...aaand it's a better bulbing tech path. If you go steel, that's what AIs like doing also, and you get no good trade bait (for bribing in others, i.e.).

I guess it was kind of hidden in my post, but yes, I am referring to deity strategy as well , and at this difficulty I prefer cannons/grens. As I mentioned before, steel and mil.science are great trade bait if you get there first (as the AI will avoid researching them), and secondly, the overall beaker investment is on par with mil.tradition, since you get to skip techs like music and nationalism. Lib->chem, self research steel is still a very fast tech path, and remember that you're still going to be bulbing towards lib, the main difference being that you will pick chem if you make it.

As for the the effectiveness of the units themselves, I like the fact that a gren/cannon invasion works off very high atk percentages, and tends to lose very few (sometimes zero) units overall. This usually means highly vetted inf and arty are ready to go for the next campaign, and you aren't continually reinvesting hammers to replace losses. (Cuirs can really evaporate due to unfavorable dice rolls!) While you definitely lose the raw speed and forking opportunities of the cuirs, cannons aren't slow by any means; with a decently sized stack you can bombard and attack on the same turn.

I'll have to give cuirs another shot next time I play, but my overall impression is that while it is certainly a viable strat, the cannons/grens play is usually more efficient and robust.

[karadoc]

I think it's too hard make a rock-solid formula which accurate determines the value of GPP. The value of great people is very situation dependent.

It's far more complex than just calculating how many beakers you'd get from bulbing, and how many GPP points will be left wasted at the end of the game - there are often powerful synergies which also need to be factored in. For example, sometimes bulbing Philosophy is very powerful, because it can get you a religion, and deprive someone else of the religion, and it can give you a boost towards getting liberalism. Maybe sometimes the bulbing of Philosophy will only be worth the of the tech and nothing more, and so it isn't very valuable – but on the other hand, sometimes it is the critical boost you need to also win the liberalism race, and so its effectively worth a lot more than just the Philosophy - because you also get all the value of the from whatever tech you get with liberalism, and you deprive someone else from getting it, and maybe the boost from liberalism gives you the tech edge you need to win an important war, and so on...

Sometimes a single great person at the right time can mean the difference between winning or losing the entire game; whereas other times it might be of very little value. If someone pips you at the post when trying to found Mining Inc, your great engineer might go from being a huge boost the productivity of your entire civilization, to just being a small boost the productivity of just one city.

...

All I'm trying to say is that the true value of the great people very much depends on the in-game situation. It depends on what your strategy is, and it depends on what your rivals are doing.

In the K-Mod AI, I decided not to attempt to evaluate GPP points accurately, mostly because I think it would be too computationally expensive to do it really well. So, I've made some pretty good (but still simple) calculations for what the AI should do with the great people once they have them; and some decent calculations to work out which type of great person points the AI should aim for in any given situation, and how much emphasis it should place on getting the right kind of GP points; but for the value of the GPP points themselves relative to the value of raw commerce the calculation is very rough and arbitrary. (Although, the GPP evaluation does take into account the fact that GPP points are worth less in cities other than the best GPP city because of the growing threshold value.)

--

You said that 'this is very much a work in progress...'. I'm curious about what 'the work progress' is. Are you intending to do some AI work? Or are you considering writing a guide or something? Or maybe you're just curious about how other people think about these things?

[damerell]

Originally Posted by karadoc

All I'm trying to say is that the true value of the great people very much depends on the in-game situation. It depends on what your strategy is, and it depends on what your rivals are doing.

Of course. But then, so does the value of a .

But that doesn't mean we can't make a stab at it. There is a mass of situational factors - but for the really significant ones, you don't need a rule of thumb to know about them. But if you don't have some very definite need, some very definite plan, any time you decided whether to work a tile or appoint a specialist... you decided, unconsciously, what a GPP was worth. It wouldn't hurt to try and quantify that.

You said that 'this is very much a work in progress...'. I'm curious about what 'the work progress' is. Are you intending to do some AI work? Or are you considering writing a guide or something? Or maybe you're just curious about how other people think about these things?

I think what I might do next is consider other means of assessing their worth. What's a GPP worth if it goes to settling a GP as early as possible? In the middle game? If we're playing on a Standard map and it eventually turns into 1/something of a shrine?

[karadoc]

Originally Posted by damerell

...any time you decided whether to work a tile or appoint a specialist... you decided, unconsciously, what a GPP was worth. It wouldn't hurt to try and quantify that.

I've thought about this a fair bit (because it goes the core of writing AI), and my conclusion is that I don't actually do any kind of meaningful evaluation for most of the decisions I make when I'm playing the game, but rather most of my decisions are based on my memories and experiences of what worked well in previous games. And so when I choose to appoint a specialist, I might actually have no algorithm for determining the value of the specialist, unconscious or otherwise, but rather the evaluation is just based on an arbitrary collection of memories from previous games and decisions with other players and so on -- not much different from just programming arbitrary values into the AI (except that human players can learn and refine their values whereas the AI cannot - at least not in the current system!).

(* When I 'arbitrary values' in this post, I don't mean that the specific values are unimportant or chosen randomly. I just mean that the values are not calculated based on game mechanics or anything like that. Perhaps they are chosen using a process of trial-and-error or something like that.)

[Tlalynet]

Originally Posted by damerell

Of course. But then, so does the value of a .

But that doesn't mean we can't make a stab at it. There is a mass of situational factors - but for the really significant ones, you don't need a rule of thumb to know about them. But if you don't have some very definite need, some very definite plan, any time you decided whether to work a tile or appoint a specialist... you decided, unconsciously, what a GPP was worth. It wouldn't hurt to try and quantify that.



I think what I might do next is consider other means of assessing their worth. What's a GPP worth if it goes to settling a GP as early as possible? In the middle game? If we're playing on a Standard map and it eventually turns into 1/something of a shrine?

The value of and their conversion options stays consistent throughout the game.

Every GP you get has a different GPP cost, so even if you had a base value for 'the first GP' the GPP would be 1\2 as valuable for the second, 1\3 for the third etc... That in and of itself isn't too terribly hard to put a value too.

Next you have to deal with the fact that which GP you get is random and the precise values of each GP fluxuates, sometimes wildly, so you not only have to place a value-to-GPP value which divides as the game goes on, but you need a value-range for each possible GP.

Next, you have different ways of using them, some are bursts, some are multipliers, some are points per turn, and some are global effects. Most GP's have at least 3 of these options available to them...

If you could put a value on each of those things, you'd have a 3-step equation giving you a range of 'what the GPP was worth'.

But, you cannot get general values for many of those things, multiplier buildings and shrines fluctuate in value depending on in-game circumstances. Golden ages fluctuate wildly depending on how you built your civs tiles, and the cost of golden ages fluxates even more wildly and somewhat unpredictably (will you get 2 of the same GP?). It's very difficult to compare the value of bulbing with the value of settling due to opportunity cost concerns.


Of course you CAN make these calculations (or generalizations) quickly in your head in a game to decide weather you need more GPP or not, but you cannot realistically make these calculations for 'every game' to give a solid conversion rate. Step 1 alone would stop you from making a consistent conversion rate.

Henpecking situations and saying 'say I used my third specialist to bulb education' won't give you anything remotely like a valid conversion of GPP->beakers in most situations.

[damerell]

Originally Posted by Tlalynet

The value of and their conversion options stays consistent throughout the game.

Absolutely not, in the sort of context karadoc was talking about - in-game situation. The that build the unit that saves your capital have far higher utility than the ones that build a work boat that accidentally gets eaten by barbs.

Of course you CAN make these calculations (or generalizations) quickly in your head in a game to decide weather you need more GPP or not, but you cannot realistically make these calculations for 'every game' to give a solid conversion rate. Step 1 alone would stop you from making a consistent conversion rate.

Frankly, it really ought to be obvious from everything I've written in this thread that I am well aware of that fact.

No, you'll never be able to say "a GPP is worth .23 ". But I never suggested you could. That doesn't stop one looking at some situations and trying to have a stab at the worth of a GPP - because that may aid the calculations in the head.

[Tlalynet]

Absolutely not, in the sort of context karadoc was talking about - in-game situation. The that build the unit that saves your capital have far higher utility than the ones that build a work boat that accidentally gets eaten by barbs.

Just plain no. You seem to be confusing concepts here. One concept is what something is worth in terms of conversion to other units, the other concept is what you need at any given time. Hammers, food, and commerce are all directly or semi-directly interchangeable, and you normally have options to choose between one or the other at set values at any given time. You can work a 4 hammer plains hill or a 3 hammer grassland farm for example. You can whip food into hammers, and while the precise exchange rate varies it is still only a one-step calculation to figure out what that food was actually worth. You can also build hammers directly into commerce for a set exchange rate.

This is where we get our food>production>commerce axioms when comparing them point by point. 4 food is generally worth more than 4 production which in turn is worth more than 4 commerce. 4 commerce may be the better situation option if that 4 commerce turns the tide in your liberalism race, but that's not the point of the comparison.

The post railroad\bio comparison still makes Food>Prod>Comm true, even though the ratios change slightly.

The hammers that saved your captial have the same value as the hammers that lost you your workboat... 1000$ is worth 1000$ weather its blown on junk food or invested wisely...

How much you need something doesn't directly change its value in comparison with other resources.

For an In-game example, I've worked pigs over plains-hills while at war to whip units out of a small city faster. I needed production, but food had a better conversion, so the food was the way to go, In that case even a 4 food tile would be better than the 4 hammer tile. The conversion and relative worth is a constant.

No, you'll never be able to say "a GPP is worth .23 ". But I never suggested you could. That doesn't stop one looking at some situations and trying to have a stab at the worth of a GPP - because that may aid the calculations in the head.

Henpecking situations and saying 'say I used my third specialist to bulb education' won't give you anything remotely like a valid conversion of GPP->beakers in most situations.

Mind, that doesn't stop you from trying. But learning the principles of how to evaluate them is more profitable then looking at some situations here and there.

[karadoc]

Tlalynet, you're right that 1 is always worth exactly 1. But damerell's original post doesn't seem to be talking about converting the value of GPPs into units of . I think he's talking about something more general than that; and the value of does indeed change depending on the current situation.

[Tlalynet]

What I'm trying to get at is that while your immediate needs change, the value of a relative to other tile yields does not. A hammer still costs roughly .75 food early game or .8 food late-game. You may need to sacrifice a 3 food tile to get 4 hammers in many situations, you even need to overpay the conversion and sacrifice a good food tile for a mediocre production tile to get those units out or that wonder up, but the basic conversion remains the same.

I'm working of of this quote to see what damerell is trying to do:

Now, the hard part. We're really trying to deduce the value of a GPP per turn - because we are comparing with tile yields,

He wants a value of GPP per turn by comparing it to tile yields. I'm trying to express how futile that is. A GPP is after all not even always worth 1GPP, but its value diminishes directly over time. Furthermore the value of GPP relative to other tile yields and yeild types does change radically, and would even if the price of a great person didn't scale.

Mind I'm working with value as meaning "the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange."

Civ isn't a free market where values fluxuate directly based on needs, it's a hard coded program that uses pre-determined numbers for conversions and yields.

Values don't normally change based on situations, but in the case of GPP they do, as they scale with numerous factors, this is why picking any given situation and evaluating it isn't very useful in getting an idea of what GPP are worth.

[Tlalynet]

Actually, I'm being way to hard on this thread. Sorry all.


Screw the complex stuff like GA's and shrines, the basic, early game calculations arn't bad if we fudge out the randomness factor...

For settling:

1 GPP = The value of 1 GP turn per point 100 turns after the specialist is produced \ # of specialists produced.


EG.

1 Scientist = 3GPP+3Sci

1 Great Scientist = 1 Hammer+6sci

It will produce Great Scientist #1 after 34 turns, and #2 after 100 turns, #3 after 200 turns.

For the first 34 turns that Scientist is worth a whopping 3 hammers+21 sci, each GPP is worth 1 hammer and 6 sci each, but it won't get its payback till turn #134 of running that scientist. The payback is actually that huge though, but only for those 34 turns.

Turns 35-100 the scientist is worth 1.5 hammers + 12 sci, the GPP are worth 1/2 a hammer and 3 sci each and won't see its full payback till turn #200.

Turns 101-200 the scientist is worth 1 hammer + 9 sci, the GPP are worth 1/3rd a hammer and 2 sci, and won't payback till turn 300.

After turn 200 the scientist is worth .75 hammers + 7.5 sci, and the GPP are worth .25 hammers and 1.5 sci each.

#5 is worth .2 hammers and 1.2 sci, and #6 is worth .16 hammers and 1 sci, and after that it trails off into being worthless. The first 3 specialists produce incredible yields compared to commerce tiles around their time, but the payback is delayed, and by the 5th GPP you need REP or something to make the paybacks worthwhile compared to cottages. On the upside these are affected by modifiers. While that doesn't help the output calculation it does make it more favourable vs bulbing in the long term.


Now Bulbing, that's much simpler if we fudge out population. Is the 1500 value from earlier right? Then we have 1500/100/# of great people produced. It's worth 15BPT for the first one, 7.5 for the second, 5 for the 3rd, after that 3.75, 3, 2.5, 2.14 ect...

Mind that means a specialist producing 3 GPP is worth a whooping 45BPT on the first bulb... By the 7th bulb it's worth only 6BPT (still considerable). Pop growth helps this of course, but the trend is the same one way or another. Those values are absolute in the sense that they are immune to beaker modifiers.



GPP to your first GP is therefore worth either a flat, one shot 15 beakers (less if you bulb too early) or a base hammer+6Beakers every hundred turns (or food+6commerce or 3 hammers + 3 science or whatever). The second is worth half that ect...

No matter what you do, it proves the well known rule, early GPP are vitally important and vastly better than comparative commerce tiles (esp cottages). That starts to really change by your fourth GP though.

Settling consistently takes a base 100 turns to catch up to bulbing if we 'smooth over' hammers and food at roughly 1:1, but is affected by modifiers, so if you have +100% it'll be 50 turns for settling to catch up and with +200% 33 turns will suffice. If you have a large population bulbing fares better late game, I suppose a 40-50 turn payback should be the rule of thumb with a +300% city. 100 turn payback has long been my rule of thumb with artists going for cultural victory (bombing vs settling) but that's kind of another matter as those ratios are different.

[karadoc]

I don't think that analysis is quite sound.

For the first 34 turns that Scientist is worth a whopping 3 hammers+21 sci

. This doesn't make any sense to me.

Suppose you run that specialist until you get the great scientist, and then you settle the great scientist and stop running the specialist. For the first 34 turns, you get only 3 per turn, for a total of 102; but after that you get 1+6 per turn for the rest of the game regardless of whether or not you continue to use the specialist; and so the total value of the great person points during that 34 turns really depends on how long the game lasts. I don't really see why you'd take that to mean "For the first 34 turns that Scientist is worth a whopping 3 hammers+21 sci".

I reckon that if you wanted to evaluate the great people points in that way then you'd need to estimate how long the game will last, and apply a 'discount rate' to devalue the benefits gained later in the game as opposed to earlier; and of course there will be various multipliers and such which affect the value of the raw yields and commerce particularly later in the game.

The critical thing though is the discount rate. I think it's pretty obvious that settling a great person will end up netting more science points than you'd get from bulbing; but the advantage of bulbing is that it's instant, and getting that instant boost can turn out to be a lot more valuable. In my mind it's that immediate vs. long-term factor that makes this so difficult to calculate precisely.

[UnforcedError]

Originally Posted by karadoc

<snip>
The critical thing though is the discount rate. I think it's pretty obvious that settling a great person will end up netting more science points than you'd get from bulbing; but the advantage of bulbing is that it's instant, and getting that instant boost can turn out to be a lot more valuable. In my mind it's that immediate vs. long-term factor that makes this so difficult to calculate precisely.

Especially as bulbing also enables you to get good tech trades (at least on the higher levels) so your scientist might well be worth double or triple of the amount of beakers it originally bulbs.

[damerell]

Originally Posted by Tlalynet

Just plain no. You seem to be confusing concepts here.

Just plain yes, because when I originally wrote that about hammers, I was replying to karadoc, who was writing about how the utility of a GPP is highly situational. It's you who's completely missed the context.

Edited to add: in fact, you're now running through the whole deductive process again. Yes (I say to karadoc), the value of a GPP is situational, but so is the value of a hammer. That doesn't stop us working out the nominal exchange rate, just as we can by comparing tiles we can work, or thinking about whipping, or building Wealth. Then we compare those game mechanical exchange rates with our assessement of the situational utility to discover which tiles we actually want to work, whether we want to whip, etc. But for GPP we don't even have a way to assess the game mechanical exchange rate.

[damerell]

Originally Posted by Tlalynet

Mind that means a specialist producing 3 GPP is worth a whooping 45BPT on the first bulb...

It doesn't, because you won't in practice bulb 1,500 beakers worth of technology with your first GP, or anything like it.

[Tlalynet]

Originally Posted by karadoc

I don't think that analysis is quite sound.

. This doesn't make any sense to me.

Suppose you run that specialist until you get the great scientist, and then you settle the great scientist and stop running the specialist. For the first 34 turns, you get only 3 per turn, for a total of 102; but after that you get 1+6 per turn for the rest of the game regardless of whether or not you continue to use the specialist; and so the total value of the great person points during that 34 turns really depends on how long the game lasts. I don't really see why you'd take that to mean "For the first 34 turns that Scientist is worth a whopping 3 hammers+21 sci".

I reckon that if you wanted to evaluate the great people points in that way then you'd need to estimate how long the game will last, and apply a 'discount rate' to devalue the benefits gained later in the game as opposed to earlier; and of course there will be various multipliers and such which affect the value of the raw yields and commerce particularly later in the game.

The critical thing though is the discount rate. I think it's pretty obvious that settling a great person will end up netting more science points than you'd get from bulbing; but the advantage of bulbing is that it's instant, and getting that instant boost can turn out to be a lot more valuable. In my mind it's that immediate vs. long-term factor that makes this so difficult to calculate precisely.

I said I went with value over 100 turns... 100 turns after settling your specialist each GPP that went into that specialist is worth the value of the specialist. In the scientists case its 100 hammers and 600 beakers at a cost of 100 GPP... 1 hammer and 6 beakers per GPP that went into that specialist. 34 turns of running a scientist gives the 102 beakers you mentions, 100 turns of having a settles specialist gives 100 hammers + 600 beakers. That means that after 100 turns of having settled the GP those scientists 34 scientist turns are worth 100 hammers and 702 beakers, if you allow for rounding (you actually produced 102 GPP, but don't get paid for the last 2) you get exactly 3 hammers+21sci for running that specialist. That value doesn't count weather or not you run the specialist that next 100 turns, as the value of the specialist changes every time you produce a GP

Obviously over 200 turns that value doubles, and after 300 it triples. But you don't really need to evaluate the 'how long the game will last' factor so much as the 'how long till it pays off vs bulbing' factor. Even though that settle GS will pay back 1000 hammers and 6000 beakers after 1000 turns there has to be a reasonable time-frame for paybacks set, 100 turns isn't quite reasonable, but its not exactly unreasonable either, more importantly its a realistic time-frame to evaluate the initial investment, and it gives us smooth numbers to work with.

All of these numbers are working with only the first 7 specialists, so unless its an AP cheese game or rush-dom the game should have >200 turns to go. That's the time-frame for settling to catch up to bulbing without multiplier buildings.

I did mess up that number last game, I said 100 turns was the base payback, 50 with +100% and 34 with +200%, but its actually 200, 100, and 50 respectively.

You can place a value of about 7.5 commerce per turn on every great specialist if you value food and hammers at 1.5 commerce and EP and culture at 1/3 a commerce point. I suppose you should value food at around 1.75 or even 2, but that's why people say merchants are so good. With those numbers spy and artist are worth 7, scientist and engineer are worth 7.5, and merchant and preist are worth 8.

So, without modifiers or considering population bonuses the payback for settling starts at 200 turns so long as you can use the whole bulb.

Normally the early bulbs can't be maxed, but you should get a min of 500 beakers out of an early bulb. The 'liberalism beeline' bulbs Philo first, which is 800, and only bulbs paper (600) if you're in a bind. After that it's education for the full 1500.

If you for some reason bulbed for 500 the payback is 66 turns without modifiers. If you bulbed for 800 its about 100 with a lib, less if you got an academy. By the time you bulb for the full 1500 you have at least 2 +25% modifiers at your disposal, and probably have >200% to research in your research centre (lib\uni\academy\monasteries), that makes the settling payback somewhere under 100 turns for the rest of the game (your pop grows to buff bulbing, your multipliers grow to buff settling).

Settling very consistently pays back vs bulbing around 100 turns after you settled, that's another reason to choose 100 turns as the 'magic number' to evaluate settled specialists.

After 100 turns settled specialists start having been worth those juicy numbers like 6, 3, or 2 commerce per GPP, where even 2 commerce per GPP is pretty huge when every specialist is worth 3 GPP.

Especially as bulbing also enables you to get good tech trades (at least on the higher levels) so your scientist might well be worth double or triple of the amount of beakers it originally bulbs.

You can trade techs you self-researched. The points settled GP's produce get traded multiple times too, its just not as obvious, or as timely. The lack of timeliness being the main issue. Even the points an academy produces eventually get traded and thus multiplied. The multiplier is a non-factor, as you get it by trading eventually no matter what you do. The delay before payback putting you hopelessly behind is of course a major issue which favours bulbing. But even higher difficulties use academies in their plan, and those are delayed payback options like settling.

It's you who's completely missed the context.

Actually, I'm being way to hard on this thread. Sorry all.

It doesn't, because you won't in practice bulb 1,500 beakers worth of technology with your first GP, or anything like it.

I intended to mention that, but neglected too.

800 is a decent number though to work with, as its the first 'liberalism bulb'. 500 (Theology) should be the minimum its worth, you really shouldn't ever bulb anything below that. You probably shouldn't bulb theology either, unless your doing some kind of oracle slingshot. Some high end players bulb paper from time to time, which is only worth 600, but even they say they prefer to self-research that if possible.


That puts us at 23ish science per specialist\turn for the first GP's GPP, very close to what a settled scientist is worth after 100 turns. The settled scientist catches up faster with libraries ect... 23 science per point is realistic, and pretty major. If you use your second scientist to bulb philo (first went to an academy normally) you actually got 4 beakers per GPP in that conversion. That make the scientist worth 15 beakers per turn. If the next guy bulbs education he gets 5 beakers per GPP (1500/100/3), putting him up to 18BPT, and that's real game practical examples using a set often used strategy and without representation. When the fourth guy bulbs liberalism he's gimped though, both cause liberalism itself is cheap and he's #4. He gets 3.5 science per GPP no matter your pop. Still, 13.5 BPT is nothing to sneeze at. 16.5 with a library\uni\academy.

It takes ages for the value of a bulb-specialist to fall below 2 beakers per GPP when you consider pop growth. I suppose the three GPP a specialist produce is worth a solid 6 (unmodifiable) beakers for quite a long time when you're bulbing them all.

[karadoc]

So, when you said "the value of 1 GP turn per point 100 turns after the specialist is produced \ # of specialists produced", I think what you meant is output-per-turn of a great scientist * great scientists per turn * 100 turns. You aren't dividing by the number of great people produced, and obviously if you multiply the yield produced in 100 turns and then divide by 100 turns to get the effective yield per turn, you're back where you started.

In any case, the key point I want to reiterate is that these kinds of yield estimates are the easy part. The hard part is that the value of this stuff varies enormously depending on when you get what you get. Bulbing on the way to liberalism is one such example of when the effective payoff can turn out to be much larger than the raw beakers from bulbing - because if the bulbing makes you win a liberalism race that you wouldn't have won otherwise, then you effecitvely get a huge amount of extra beakers... But if you would have won the liberalism race anyway, or if you don't win the race even with the bulb, then you don't get that extra effective value.

Similarly for founding corporations - the payoff for the great engineer that founds Mining Inc. might be huge - but if you end up missing out because someone else gets it first, then the effective value drops to near zero. Because of the critical timing of something like that, you could say that the value great-person-points-per-turn does not scale linearly. because if you're only getting 1 GPP/turn, then you wont' get the great engineer (or whatever) to achieve your goal in time, and so the points are wasted. But if you're getting 20 GPP/turn, then maybe you can get your great person before the time runs out, and so none of the points are wasted. It ends up being worth way more then 20 times the value of 1GPP/turn. -- Even without considering any kind of time-limit like there is in this example, I think it's clear that if you account for any kind of discount rate in the expected payoff, then value of GPP doesn't scale linearly.

[Tlalynet]

By 'the value of 1 GP turn' I did mean the value of 1 turn of output by any given GP.

That is, 100 turns after you produce a GP each GPP going to produce that GP is worth what that GP produces in 1 turn.

I am dividing by the # of great people produced, that's vital to the value calculation. The first GP costs 100, while the next 200 then 300 and so on. So the value of the first is \1 (so = to) while the value of the second is \2 and the third \3. Each great person costs more than the last. I never did directly multiply any yields by anything, I think that may be where you're misunderstanding me...

I'll try to phrase it differently.

Given the specialist has been settled for exactly 100 turns, then

1GPP= 1 turns worth of yeild from the settled specialist/# of great specialists produced.

50 turns is 1\2 that, 200 turns is double that. If it's your 3rd GP and its been settled 300 turns then GPP->yeild value is the same as your first GP settled for 100 turns. The 3rd GP cost 3x as much, so takes 3x longer for each individual GPP to match values with the first.

Normal speed is also a given. Epic would make the baseline turn 150 and marathon would make it 300.


But putting situation values on things isn't too hard in terms of bulbing if you have enough intel. If you can see your opponents research and see that the only way you get lib is by bulbing, bulbing will be better. If you can get lib without bulbing, and diplo is settled enough you can expect 50-100 turns of relative peace then settling will payback. That's just a basic either\or comparison that even AI can do without too much programming trickery. If the AI's turns to lib>players turns to lib and you have a GS then bulb, else settle. In most cases if it came to that bulbing would make the AI win, but if you wanted to be really meticulous you could make it check weather that action would put it in the lead or not. (The AI would have to assume the player is beeline Lib and that they have a constant beaker output, both of which may be false, but are accurate enough to make a good calculation)

Calculating corp values is tough because they scale with map size and resource distribution, both of which vary from game to game. But I know what you're saying with that, I said that we have to really limit calculations to early game settling vs bulbing to get anything like a solid answer. Anything like Shrines\Corps\GA's just make calculating value conversions unrealistic.

[karadoc]

Originally Posted by Tlalynet

Given the specialist has been settled for exactly 100 turns, then

1GPP= 1 turns worth of yeild from the settled specialist/# of great specialists produced.

Originally Posted by Tlalynet

I am dividing by the # of great people produced, that's vital to the value calculation. The first GP costs 100, while the next 200 then 300 and so on. So the value of the first is \1 (so = to) while the value of the second is \2 and the third \3. Each great person costs more than the last. I never did directly multiply any yields by anything, I think that may be where you're misunderstanding me...

When you say "the specialist [has been settled]", I think you're referring to "the great person" or "the super specialist", correct? Not the ordinary specialist which produces the GPP.

And when you say "# of great specialists produced", you are referring to the total number of great people that the player has produced in the entire game; not the number produced by the ordinary specialist in 100 turns. Is that what you mean?

Presumably what you have in mind is that dividing by the "# of great specialists produced" is a shorthand way of calculating the number of GPP required for each new great person. But in actual fact, the number of GPP required for each great person does not scale linearly either. The rate jumps quadratically every 10 great people. So straight out dividing by the 'number of specialists produced ever' does not necessarily get you the correct rate of great people per point.

Consider the formula I mentioned in my previous post. "(output-per-turn of a great scientist) * (great scientists per turn) * (100 turns)". In particular, consider the units of each term in the formula.

First, we have yield/(GP * turn). Then we multiply that by GP/turn, which gives (yield*GP)/(GP * turn * turn). The GP on the top and bottom cancel, and so that's yield/(turn*turn). Then finally we multiply by turns, which cancels one of the turn factors on the denominator giving us yield/turn.

As an example, I'll put in the numbers from your first calculation.

(output-per-turn of a great scientist) is 1+6 / (GP * turn)
(great scientists per turn) is 1 GP / 34 turns = 0.0294 GP/turn
(100 turns) is 100 turns

You can see that the 0.0294 GP/turn times the 100 turns is where the factor of three comes from to give the answer of 3+18 (+3 from the ordinary specialist itself)

In this calculation, there is no dividing by the number of great people produced. After the first great person is born, the GP/turn rate drops - and in fact it happens to drop by a factor of 2.. But we're still talking about GP per turn; and that's ultimately calculated with GPP per turn / GPP per GP.

[damerell]

Originally Posted by karadoc

In any case, the key point I want to reiterate is that these kinds of yield estimates are the easy part. The hard part is that the value of this stuff varies enormously depending on when you get what you get.

But, again, so does the value of a hammer. That doesn't stop us calculating the food/hammer conversion rate for whipping.

I'm only trying to do the easy part. I appreciate the hard part wrinkles the foreheads of AI programmers, but such is life.

[Tlalynet]

When you say "the specialist [has been settled]", I think you're referring to "the great person" or "the super specialist", correct? Not the ordinary specialist which produces the GPP.

Yes, you can't 'settle' normal specialists. I suppose Great Person is the proper term though, I understand the confusion.

And when you say "# of great specialists produced", you are referring to the total number of great people that the player has produced in the entire game; not the number produced by the ordinary specialist in 100 turns. Is that what you mean?

Yes. Specifically those produced by GPP, as ones obtained by other means don't affect this value.

Presumably what you have in mind is that dividing by the "# of great specialists produced" is a shorthand way of calculating the number of GPP required for each new great person. But in actual fact, the number of GPP required for each great person does not scale linearly either. The rate jumps quadratically every 10 great people. So straight out dividing by the 'number of specialists produced ever' does not necessarily get you the correct rate of great people per point.

Yes, but none of these calculations goes past 5-7 GP. After that point you'll almost universally be better off using GA's, special abilities, or founding corps. I suppose if you where Phi heavy you might want to know the value of settling your 10th GP, or if you're doing an OCC. As you pointed out, you'd need another formula to calculate their worth.

For what its worth the value of settling GPP when a GP costs 1000+ GPP is pretty small, getting to the point of being negligible.

Consider the formula I mentioned in my previous post. "(output-per-turn of a great scientist) * (great scientists per turn) * (100 turns)". In particular, consider the units of each term in the formula.

That formula would be (1H\6S)(3)(100) and produce a value of 300 hammers and 600 science... But it doesn't actually solve for anything. I think I may be misunderstanding that formula.

First, we have yield/(GP * turn). Then we multiply that by GP/turn, which gives (yield*GP)/(GP * turn * turn). The GP on the top and bottom cancel, and so that's yield/(turn*turn). Then finally we multiply by turns, which cancels one of the turn factors on the denominator giving us yield/turn.

You seem to be unnecessarily over-complicating things here. Yeild is the yeild of any given GP? Or is GP the yeild of a GP? Or is GP meaning GPP?

As an example, I'll put in the numbers from your first calculation.

(output-per-turn of a great scientist) is 1+6 / (GP * turn)
(great scientists per turn) is 1 GP / 34 turns = 0.0294 GP/turn
(100 turns) is 100 turns

You can see that the 0.0294 GP/turn times the 100 turns is where the factor of three comes from to give the answer of 3+18 (+3 from the ordinary specialist itself)

Ah, now I understand, great scientists per turn is how many turns it takes to create that Great Scientist. And I can see how that gives the same answer in this situation. The caveat I see with that is that you don't factor actual GPP into the equation. Say you're running 3 scientists.

(output-per-turn of a great scientist) is 1+6 / (GP * turn)
(great scientists per turn) is 1 GP / 12 turns = 0.0833 GP/turn
(100 turns) is 100 turns

That gives you a value of 8.3+50(+9)

I suppose given the rounding errors (100 isn't divisible by 3 or 9) it does give the same result. Now that I see how it works I have to say its a very tight formula. Nice work.