Evaluating my peaceful SV progress

All I can say is my best time was 272 a month or 2 ago. My best time was t252 a week ago, before purchasing most my science buildings. Since changing, I've had t246, t244, and t238 victories. It would appear that purchasing your buildings is superior. Then again, maybe it is the fact I've been prioritizing markets and banks more so than in the past, which allow for me to purchase all those buildings.

Do you have an initial turn 0 save from your t238 victory? :D
 
There are no “free hammers” because you are paying dearly for them. The rush just gets you turns you would otherwise spent building.

I am just asking about best beaker return on gold. It seems to me that it boils down to these two:
  1. Save up gold so you can rush science buildings ASAP. Leftover gold on RAs are okay, but skip RAs if they compromise your ability to rush buy science buildings as soon as they get unlocked.
  2. Spend gold aggressively on RAs. Leftover gold on science buildings is good too, but don’t rush buy unless you are already working RAs with all your allies.
List conventional wisdom is clearly in the (1) camp. All the best players too! I am asking for math behind this, because it’s not obvious. Sure it feels right. Other strategies are easily justified by the numbers. Why not this one?

I'm not arguing the fact that RA may be better raw BPT for gold (as said in my original post).

What I'm saying is that it's not the only thing that matters.

And there indeed are free hammers (well freed if you prefer). The one you don't use for building a science building. RA dont do that. While doing RA you still have to use hammer for the building. I really don't understand why you think you can dismiss it.

Look it should be very simple to understand the following:
Strategy 1:
Use gold for RA, build a university.
Strategy 2:
Use gold for university, build market.

For the sake of the argument, let's say both university and market take the same amount of turn (10 for example). We will also suppose that after these 10 turns, both strategy have the same bpt out of the university. And finally the same amount of gold was used in both strategy.

Value of strategy 1 after 10 turn = Value(RA) + Value(University)
Value of strategy 2 after 10 turn = Value(10 turns of fast university) + Value(University) + Value(Market)

What you did in your math post (which I feel overestimate the number of turns a RA gives) is to just say Value(RA) > Value(10 turns of fast university). And I say it's probably true at least on Deity.

But this doesn't imply:
Value(Strategy 1) > Value(Strategy 2)

The comparison isn't that simple and would depend on how much you value the "freed" hammers that went into an additional building compared to the difference between value(RA) and value(fast university).

There is also another thing not talked about here. Cutting a couple turns for researching a renaissance tech (rushing universities) is often more important to not miss opening Rationalism than to cut a couple turns 30 turns later.

Let's make something else clear too. Please play BnW and see how hard RA were nerfed. RAs were my bread and butter in GK. It was just clearly the best option and rushing the PT was important. The AI were also much more opening Rationalism giving them better bpt for the equation. Nowadays, I only do a couple in early eras, still unsure whether or not it was worth it when it gives 1 or 2 turns of science at turn 150.
 
There are no “free hammers” because you are paying dearly for them. The rush just gets you turns you would otherwise spent building.

I am just asking about best beaker return on gold. It seems to me that it boils down to these two:
  1. Save up gold so you can rush science buildings ASAP. Leftover gold on RAs are okay, but skip RAs if they compromise your ability to rush buy science buildings as soon as they get unlocked.
  2. Spend gold aggressively on RAs. Leftover gold on science buildings is good too, but don’t rush buy unless you are already working RAs with all your allies.
List conventional wisdom is clearly in the (1) camp. All the best players too! I am asking for math behind this, because it’s not obvious. Sure it feels right. Other strategies are easily justified by the numbers. Why not this one?

It is justified by the numbers. The formula you've been using is wrong*. Buying a science building with gold gets you X extra science for Y extra turns, where Y is the number of turns remaining in the game. This is a fact.

The catch, of course, is that science buildings have an alternative cost (hammers) and research agreements do not. If you don't have the gold for both buying science buildings and signing research agreements, you have the option of hammering out the buildings AND buying research agreements, but not vice-versa. Getting both would give you more science. However, as you yourself has shown, cash-buying science buildings doesn't just let you skip building them, it also lets you get them sooner than you would by building them, which reduces much of the science gap between "just buildings" and "both buildings and research agreements". So now you're looking at an equation with a bunch of hammers on one side and some science on the other side. I'm not sure the exact unit conversion for hammers to science, but experience-based intuition and the wisdom of other good players tells me that the hammers are worth more.

*[Basically the formula you've been using actually describes a situation where gold-rushing a science building allows you to get the science immediately but you still have to build the building. That's not the world we live in.]
 
I am using the conservative BNW estimate for RA, namely 2.5 turns of empire science.

Value of strategy 1 after 10 turn = Value(RA) + Value(University)
Value of strategy 2 after 10 turn = Value(10 turns of fast university) + Value(University) + Value(Market)

You are counting the 10 turns saved by rush buying twice. Once for university, then again for market!

But my observation is not beakers per turn, but beakers for gold (or beakers over the course of the whole game). If you look at a cherry picked 10 turn window, of course you can make rush buying look good. You would have to net at least 60 turns, starting early, to decide if RA were better than saving up for public schools.
 
I am using the conservative BNW estimate for RA, namely 2.5 turns of empire science.

You are counting the 10 turns saved by rush buying twice. Once for university, then again for market!

But my observation is not beakers per turn, but beakers for gold (or beakers over the course of the whole game). If you look at a cherry picked 10 turn window, of course you can make rush buying look good. You would have to net at least 60 turns, starting early, to decide if RA were better than saving up for public schools.

I really have no idea what you're talking about. This is nonsense.

I do not value rush buying twice.
I am not looking only at a 10 turn window.

I'm comparing what both strategy have in both situation after a similar amount of time, and I do value the future value of RA. The argumentation is exactly the same after 30 turns, you cannot ignore the value of the additional building. I'll let others argue or wait for you to give me a good logical/mathematical reason why you'd ignore the hammer you just freed by rush buying. I did it above for why you cannot ignore it, by comparing what both achieve in a similar time frame. Please do the same. It should become obvious that rush buying allow you to get more buildings, and that each of these additional building have a certain value that doing RA cannot provide.
 
The value of hammers is completely tangential to my question about RAs providing more beakers per gold than rush buying science buildings.

Buying a science building with gold gets you X extra science for Y extra turns, where Y is the number of turns remaining in the game. This is a fact.

That’s only true if you are comparing rush buying with not ever building!

I am simplifying things a little bit because, during the time it takes to build, your empire has grown. But, if RA are better gold value than rush buying, then one should also be able to begin building sufficiently earlier! (The whole point is about getting through the tech tree quicker.)
 
The value of hammers is completely tangential to my question about RAs providing more beakers per gold than rush buying science buildings.

No no. RA providing more science per gold than extra turns of a university is one thing (while ignoring the indirect science value of everything else rush buying provides). But I'm pretty sure you have been arguing earlier that doing RA is therefore the best strategy (at which point you cannot chose to ignore those extra benefits of rush buying).

2 very different things.
 
If RAs provide more beakers per gold than rush building science buildings, then how can it not follow that prioritizing RAs is a good general strategy? (There are exceptions of course, namely unlocking Rationalism, Oxford, NC.)

Really, I didn’t think I had a dog in this race...
 
If RAs provide more beakers per gold than rush building science buildings, then how can it not follow that prioritizing RAs is a good general strategy? (There are exceptions of course, namely unlocking Rationalism, Oxford, NC.)

Really, I didn’t think I had a dog in this race...

1) Rush buying the science building allowed you to build a market or bank, and then some. Leading to more gold to be able to buy other things, including RA's. Or some other key wonder/building.
2) Rush buying the science building gets you to important tech's sooner, as RA's take 30 turns to come around. This can lead to more growth and science.
3) Rush buying science buildings gets your Specialists going several turns sooner, allowing you to bulb a bunch of science sooner or plant an academy. (something not brought up)
4) Beating policy to rationalism is also big.
5) There is no risk of your RA partner stabbing you in the back before it is complete.
 
If RAs gets more beakers for the gold than rush buying, it does not follow that rush buying the science building gets you to important techs sooner (assuming limited amounts of gold makes one choose between the two strategies).

I concede that RAs are more of a gamble, not just the DoW from your RA partner, but the chance of your RA partner being eliminated. (Although I guess you could predict if they will be around in 30 turns.)

Thinking about this more, I must concede that gold rushing science buildings is not valuable only for n extra turns of beakers, but also the value of doing something else (anything else) during those n turns. Even if it were just building wealth, that amount would still have to be subtracted from the cost of rushing the science building — and the turns are more valuable than that.

Still, I am still surprised the math isn’t more obvious.
 
Hammers are a scarce resource. This is the fundamental thing that you're missing. If you choose to not gold-buy science buildings, that does not mean that you get them for free. It means that you have to spend hammers to get those buildings, and those hammers could be spent somewhere else.
 
If RAs provide more beakers per gold than rush building science buildings, then how can it not follow that prioritizing RAs is a good general strategy? (There are exceptions of course, namely unlocking Rationalism, Oxford, NC.)

Really, I didn’t think I had a dog in this race...

Because you were ignoring other benefits when concluding that therefore it's the best strategy. It's one thing to say it yields more bpt when you blindly ignore additional values of rush buying, it's another to conclude it's the best strategy in reality... where you can no longer ignore such additional values.

Thinking about this more, I must concede that gold rushing science buildings is not valuable only for n extra turns of beakers, but also the value of doing something else (anything else) during those n turns. Even if it were just building wealth, that amount would still have to be subtracted from the cost of rushing the science building — and the turns are more valuable than that.

Jesus finally.

Still, I am still surprised the math isn’t more obvious.

Because:
1. Your math take imaginary numbers into consideration
2. Your math still doesn't take into consideration the value of what you just conceded.+

That's why it's somewhat worthless.

First step would be to take a real world scenario. Then see how big the difference between RA and rush buy is. And then discuss whether or not that difference is worth the missing opportunity of getting an additional building.
 
If RAs gets more beakers for the gold than rush buying, it does not follow that rush buying the science building gets you to important techs sooner (assuming limited amounts of gold makes one choose between the two strategies).

Umm...it takes 30 turns before you get RA benefits, you get rush buying benefits immediately.

The other part of the equation, which is far more murky, is how all the earlier beakers effect the game by the time 30 turns are up.

Getting to those techs sooner for 30 turns, will further give you beakers, growth, hammers, gold, great scientists and possibly other things. Does the end result at turn 30 make up for those losses up until then? My experience says no. All the fastest players seem to agree.

Now here is one other bit of info you have to take into account; it is not the amount of beakers you gain, but the amount of turns you shave off your victory. This is because as you tech further ahead, it also costs more beakers to earn techs. Since one gives you immediate results, you can't compare their beakers directly to the one with delayed beakers. This also makes the comparison very tough, and why testing is the only thing that seems to work. And from our experience, RA's do not beat rush buying science buildings.
 
Ok, so here is a test that should provide a little more light on the subject. I took a game where I reached Education on turn 102. I took a screen shot of my tech tree before I purchased 2 universities, and after. I was ~100 gold short of buying my 3rd university, so this is comparing 2 universities, versus waiting ~10 turns to build them.

Before Universities.jpg
After 2 Universities.jpg

As you can see, it dropped the tech time on Acoustics from 13 turns, to 9. Roughly, buying those 2 universities saved me about 4 turns immediately (after those ~10 turns, things should be comparable). It would take roughly 3 RA's to make that difference, ignoring gold and hammer differences which is harder to compare. Oh, and you get a great scientist 10 turns sooner as well.
 
Umm...it takes 30 turns before you get RA benefits, you get rush buying benefits immediately.

After Universities, RAs are available before your other science buildings. So you get the benefit of RAs sooner, starting all that science snowballing sooner.

Ok, so here is a test that should provide a little more light on the subject. I took a game where I reached Education on turn 102. I took a screen shot of my tech tree before I purchased 2 universities, and after. I was ~100 gold short of buying my 3rd university, so this is comparing 2 universities, versus waiting ~10 turns to build them.

As you can see, it dropped the tech time on Acoustics from 13 turns, to 9. Roughly, buying those 2 universities saved me about 4 turns immediately (after those ~10 turns, things should be comparable). It would take roughly 3 RA's to make that difference, ignoring gold and hammer differences which is harder to compare. Oh, and you get a great scientist 10 turns sooner as well.

Well 3 RAs are cheaper than 2 Universities, but you cannot start RAs until you or an AI has Education anyway. So sure, rush buy Universities, then prioritize RAs.

I think you have to test this between Education and Scientific Method. Which ends up with Public Schools built faster?

Do most people have 60 turns between Universities and Public Schools (or Public Schools and Research Labs). Since it seems like 2 rounds of RAs might be necessary to shave 10+ turns to these key techs, there might not be enough time for the beakers from RAs to pay out.
 
beetle, the main problem with this is that the gold is limited. You gotta save the money for these schools. I don't see how will this happen if you do RAs meanwhile - these are not exactly cheap in the early stages of the game, where you don't have 100+ gpt.

Also, I wonder - how do you need 10 turns to build Public Schools everywhere ... While this might be so with a salt or heavy strategic start, I don't think I have ever build schools that fast in at least 2 of the cities. Sometimes the 4th city has so low production so it would need 25+ turns to build it ... I usually buy 2 - one in the cap, and one in the city with lowest production. Saving 3k after buying universities, libraries, tiles and sometimes observatory is not that easy.
 
After Universities, RAs are available before your other science buildings. So you get the benefit of RAs sooner, starting all that science snowballing sooner.



Well 3 RAs are cheaper than 2 Universities, but you cannot start RAs until you or an AI has Education anyway. So sure, rush buy Universities, then prioritize RAs.

I think you have to test this between Education and Scientific Method. Which ends up with Public Schools built faster?

Do most people have 60 turns between Universities and Public Schools (or Public Schools and Research Labs). Since it seems like 2 rounds of RAs might be necessary to shave 10+ turns to these key techs, there might not be enough time for the beakers from RAs to pay out.

At that point, after you buy your Universities, it might be worth a couple RA's, but I'm not sure it is worth not buying the university for a couple RA's.

As far as that game goes, I bought universities on turn 102, and public schools on turn 146, and research labs on turn 180. That example is better than any other game I've had, however. Interestingly enough, it was Russia, and not a science civ.
 
Beetle, putting everything else aside by how much research agreements give to buying buildings, you have to understand that in BNW it is a pain to friend more than 3 civs at once which is needed for the research agreement. I really don't understand why this debate is still continuing...
 
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