Need some clarification on the Research Agreement

Free stuff right now is more valuable than more free stuff much later.

And usually it is very easy to explain why. The “turns of empire science” you get from an RA makes things a little tricky.

Also, it's a bit naive to assume that a RA signed on T150 would shave 2 turns on an Information Era tech 150 turns later.

It is a contrived thought experiment to help illustration why the math needs to factor in the 30 turn delay. It does not seem like an obviously bad deal to me, but clearly I am in the minority on this point.

Well in that case, I state it as a fact that teching to Machinery first, rush-buying Crossbows to kill your neighbour and Annex his Cap with University leads to faster winning time than spending that gold on your own University OR Research Agreements!

Where does math figure into this assertion?
 
There was some concern [from the other thread] that a player could never get enough RAs going to make a difference. A fair benchmark for rush buying after NC is 3 universities and 3 public schools, hard building in the cap only. That would be enough gold for 12 RAs during the course of game, but if RAs out perform rush buying at 4:3, one would only need 9 RAs to test this. With 7 civs on a standard map, 9 RAs seems pretty feasible over the course of a game. Optimal would be a mixed approach: aggressive RAs with rush buying in lowest production cities, and rush buying in other cities only to the extent that RAs are not passed over for lack of gold.

Emphasis added, thinking about this more, the crux of problem is getting enough RAs in soon enough. 9 RAs over the course of a game is not too hard, but for RAs to be competitive with rush buyinging, those 9 RAs would have to be completed by Scientific Theory. That seems like a very tall order. Maybe on a huge map with lots of AI civs?
 
Responding late to a few hanging comments...

Here we go again....

Yes, no resolution on that thread, a little better this time around, I think.

If you make some good food per turn in a city and you have science buildings such as academies and universities etc,, you can obtain a good science per turn and won't need to rely so much in research agreements. AIs also often like to ask more from you if you have a tech lead in science.

I understand you to be saying that people have good science games without RAs, and that is true enough, but the math implies that your science game would be well served by more RAs. Yes, RAs come at the very significant cost of helping your opponents. I am only talking about beakers for the gold.

2. Assume you have four cities, and this city is a quarter of your science, so that's roughly 3 turns of empire science.

Faulty assumption.

Agreed, an expo city is almost always producing less than a quarter of your science, but that only makes rush buying less competitive with RAs. You are citing the line in my “proof” where I set a relatively high target for RAs.

You can theorize, but you cannot test your theories. They remain theories until you can test them. Your "math" is missing tons of stuff that all play a big factor in the end result. Until you can prove your theory covering all aspects of the game, or test it out with game samples, you have nothing but a theory.

If the math has faults, that would be enough to debunk it. I am not sure why what I see as a neutral observation seems to cause such hostility. In order to test this for yourself (with noticeable results), you would have to rush buy universities and still be in a position to get six RAs completed before Scientific Theory. That seems like a tall order, and certainly not something I can pull off in my games!

A mod that allowed arbitrary numbers of RAs could also demonstrate their efficacy in terms of gold for beakers.
 
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