I'll try to include more about RAs in my next LP to show what is meant by 'median shifting' and how to use them effectively.
Effectively though, always try to keep a 'high beaker cost' tech available to ensure you get a better return for the RA.
Example:
Let's say you had Compass, Theology, Civil Service, the Wheel and Mining available for research.
You have RAs coming due and you're headed to Education. The plan is to finish Theology and Civil Service, then Education.
Deciding to grab Theology first, you can 'shift button' select Civil Service as the next tech. (and Education to be safe if you had multiple RAs finishing at the same time)
An RA finishes, so you're getting 50% of the beaker value from the median beaker cost tech. In this case, Compass is the most expensive, with Mining the least expensive. Theology and Civil Service have the same costs, but the wheel is cheaper and removes one of them. So you end up with 50% of the cost for, let's say, Civil Service. (random aside, it may be less than Theology at this point since the AI goes there first)
The next RA is a bit tricky, as you've now (likely) completed Theology. So the middle two techs would be Civil Service and the Wheel. If an RA came due here, you'd get 50% of the value of (Civil Service + the Wheel)/2. Which is much less than the previous one. So while tech blocking isn't important, ensuring you have the right 'median' is important. You can get in trouble if you don't manage the median well before the RAs come due. It would have been better to get 3 RAs (150% of Civil Service in one shot) signed on the same turn to complete Theology + Civil Service and then open Education for the next few RAs.
Conversely, had you cleared mining up, and had Metal Casting open instead (with the Wheel still there) :
Depending on the timing, you could have either cleared from Mining->Iron Working/Construction to open Metal Casting (same costs as Civil Service) or opened the Wheel to have Horseback Riding and Mathematics available. (less than Civil Service, but 'more' than the average of the Wheel and Civil Service) With the latter, trying to clear HBR out of the list is good, though finishing Mathematics opens Currency, which is a higher beaker value.
First RA has a split between Theology/Civil Service/Metal Casting. (all same beaker costs) The next one splits between Civil Service and Metal Casting. Finally, once you have Compass, Education, Metal Casting and the Wheel open, all RAs would give 1/2 of (Compass + Metal Casting) /2 = ~350 beakers (more than 50% of Metal Casting) as Education is a higher beaker value than Compass and you ended up with four open technologies.
Clear Education and you're back to Compass, the Wheel and Metal Casting. So the next RA would drop in value again (50% of Metal Casting) until Compass or Metal Casting is completed. (for this example Compass should be completed next since it'll open Astronomy vs. opening Steel) At this point you can assume the Porcelain Tower (Engineer Rushed as soon as you hit Education) and now get 75% of the beaker value of the median tech.
Finish Compass, Bulb Astronomy with the free GS from the PT and now Navigation is the 'high beaker value' tech. Take the Rationalism opener (if you didn't go Piety) and you get 100% of the median beaker value technology. That is, if you select the 'median' technology when the RA comes due, you'll get a free tech. This is an easy way to RA spam up through Gun Powder. If you need to 'shift' the median again, to get 100% of Metallurgy or Chemistry, then a GS bulb of Navigation opens Archaeology as the new high beaker tech. Finishing Acoustics and Economics also open Scientific Theory.
If you also had Chemistry finished, you'd have three 'late Renaissance' techs open (Archaeology, Scientific Theory and Military Science) to go with Metallurgy. Meaning you'll get 100% of one of those with each RA. This effectively gives you 2 free 'top beaker' techs with the RAs. If you chose Military Science and Scientific Theory, that opens Steam Power as the new high tech. To get to Artillery, a few RAs getting 100% out of Archaeology or Biology, will speed you through to Artillery.
GSs should be used to open technologies where there's multiple branches leading out from it to ensure that the median keeps moving in an 'upwards' direction. (Gun Powder, Steam Power, etc) There are points in the tech tree where you'll get 'more' beakers by using a GS early, than by saving it until later. There are definitely points where you can get 100% of a 'top' beaker value tech, which can be used to clear an entire line of low beaker techs to ensure you 'catch up'.
But actually AI is very impressive in this particular game in terms of taking cities.
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