It has been known for a while that giving away techs can reduce your beaker cost. Also, there always seems to be one Key Civ to whom tech-gifting triggers the beaker reduction. What has been unclear is the relationship between the Key Civ and the Human Civ. How do you know which civ to give techs to in order to effect beaker reduction? I think I have found the answer to this.
I hestitate to post my conclusions for two reasons. First, early announcements of "findings" often turn out false. And secondly my answer is pretty ridiculous, in my own opinion. Nevertheless, here it is.
The relationship between the Key Civ and the Human Player involves the Power ratings and Turn positions. Each civ's Turn Position is determined by its color:
|Turn Position||Power Ratings||
The Key Civ for tech-gifting can always be found occupying the Turn Position
which corresponds to your Power Rating using the above numbers.
For example, if your Power is 'Inadequate', the Key Civ will be Dark Blue.
Science beaker cost is the product of two things: the number of Acquired Techs (+1) that you have and a Tech Multiplier. One of the determinants of the Tech Multiplier is your relationship to the Key Civ as found by the above method. If you have the same number of Acquired Techs as your Key Civ, you get the nominal Tech Multiplier and pay an average cost. If you have fewer Acquired Techs, you pay less. If you have more, you pay more. By giving a sufficient number of techs to the Key Civ you can reduce your beaker cost.
If your Power rating corresponds to your own Turn Postion, you will always have exactly the same number of techs as yourself and therefore will always pay the average cost. You can give away techs till you're blue, it won't help. Well, it might. Power ratings are in part determined by how many techs you have. So giving away techs may lower your PR and get you out of the 'dead spot'.
If you're planning to spend a lot of time being 'Pathetic', don't choose White! Same for 'Supreme' and Purple. I know, this seems like a ludicrous design. Maybe that's why it has proven so illusive.
Let me know if you have questions or if you can show this to be wrong.
My testing was with V2.42, deity, 7 civs. I haven't tried fewer civs yet.