@Bob Morane:
Bob. There will be a turn when the game will say "1 more turn" until Acoustics, for your plan of teching there directly. On that turn, there is a certain difference from the actual cost of Acoustics, and your research in Acoustics.
If THAT AMOUNT is less than the free beakers you would get by exploiting overflow, then exploiting overflow will get you Acoustics faster. And if THAT AMOUNT is greater than the free beakers you would get, then exploiting overflow will not get you Acoustics faster. If the amounts are equal, then it won't get you Acoustics faster, but it does get you Acoustics + other stuff by the same point.
I am appreciative of the desire to test , as experiment is the crucible of thought.
And I misspoke some times.
Guh, I got the cap inverted. The cap is the greater of 5*bpt and the cost of the tech, not the lesser.
This still doesn't explain what phillipwyles observed. However, before I blame IGE, I have to ask more detail about what the setup was. Why were you sure your overflow was 25K? Why was Mobile Tactics relevant? I though you just gave yourself every tech before PArticle Physics.
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This process has six parts, which depend on six values. I've scrapped the diagram and am just going to program a simple interactive animation to show the computations involved. I just keep getting sidetracked with insights into Design I'm having while designing it.
- The cost of the tech
- The research modifier for the tech.
- The modifier to the cost owing to the science penalty
- The cap applied in the April patch
- Your beakers per turn
- Overflow
The parts are:
- The actual cost determination of the tech
- Accumulation of beakers into the tech
- The transfer of overshot beakers through the cap
- The transfer of capped beakers into overflow
- The movement of overflow into accumulated beakers each turn
- The modification of those overflow beakers by the research modifier
0. Research modifier is a modified modifier. It's not a modifier group, I got this wrong before.
[Research modifier] = [Civ tech diffusion modifier] * ( (100 + [World Congress tech modifier]) / 100)
Code:
[Civ tech diffusion modifier] = (Number of met civs know the tech) * [TECH_COST_TOTAL_KNOWN_TEAM_MODIFIER, from the Defines table] / (Number of alive civs)
[World Congress tech modifier] = 20 [U]if [I]Scholars in Residence[/I][/U] 0 [U]otherwise[/U]
1. The actual cost is given by:
Code:
[The cost defined in the database] * (100 / (100 + [The Research Modifier]) ) * [The science penalty]
This cost defines a moving finish line for beakers accumulated into this tech. Except for passing and then repealing Scholar's in Residence, or someone reviving a civilization who doesn't know the tech, this finish line only gets -closer- to you and your beaker count.
2. When you get beakers, you put them into this tech, all at once. This is e.g. when you bulb, when you spread the Interfaith Dialogue religion, and when your turn starts. By adding this amount to your current research, you may well exceed the finish line. That excess is recorded and fed into a process.
3. The excess is processed as follows. The amount is capped by the following value:
Code:
MAXIMUM([the cost defined in the database] , (5 * [your bpt]) )
That is, if the excess is greater than both, instead it becomes the greater one of these two.
By "your bpt", I mean the amount sometimes called "Your science". The measure of change in beakers that applies to your empire, which is conveniently made visible for you at the top of your screen after you settle your original capital.
4. The capped excess is added into your overflow.
5. When your turn starts, you get beakers automatically pushed into your current research. The amount of beakers added is given as:
Code:
[Bpt]+ [B]Modified overflow[/B]
6. Overflow is modified by taking:
Code:
[B]Modified Overflow[/B] = [B]Overflow[/B] * ((100 + [Research modifier]) / 100)
Your overflow is set to zero when it is pushed through this modification into your research.
I'm gonna make a picture, but it should only help with visibility and digestion of the information. I have no resource to offer those who do not know what the preceding sequence means.
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I didn't mention the moving finish line trait before. Even though the finish line moves, the cost of the tech is actually only calculated at the times you gain research. So if the cost moves under your research level, you won't get the tech until the next time you get a

beaker.* Actually, being awarded 0 beakers, depending on whether the programmers added a check like "If this is 0 do nothing" to the Interfaith Dialogue procedure, would be enough to get the tech.
This can -actually- happen if you meet a civ who knows the tech, or a met civ learns the tech, as doing so increases the research modifier by , apparently, 5% in a 6 player game, which will reduce the cost by (1 - 1/1.05) around 4.8% (of base). Differences of 2 beakers are common in my games for late ancient learns; for techs like Mobile tactics that's 440 beakers