I printed off the list of techs and wrote 1, 2 or 3 beside each one, representing the order in which they are blocked. The first hidden "cycle" consists of all the "2" techs, but alphabet (cycle 2) is always available because of the designing feature that lets the first tech on the list that you have the pre-reqs for always appear on the research list (it was a programming safe-guard).
I then plotted the techs to research under columns for each "cycle," and looked at the best alternatives under each circumstance. There was no play-testing beyond making sure that I knew the start-cycle and that the researchable techs matched my prediction. It was largely an "ivory tower" theory.
The trouble with getting to republic is that writing and literacy are both absent on the same "cycle" (2), and that code of laws is a pre-req for literacy.
I'll list the possible research patterns, in this form: tech (cycle tech is absent)
(vertical list, because it is easier to type and keep neat)
Cycle-----------------Tech Paths----------------
2---Alphabet (2)-----Alphabet (2)-----Alphabet (2)-----Alphabet (2)-----Alphabet (2)------Alphabet (2)----Alphabet (2)
3--Code of Laws (1)--Off Path------Code of Laws (1)--Code of Laws (1)-Code of Laws (1)---Off Path---------Off Path
1---Writing (2)------Writing (2)------Off Path-----------Writing (2)-----Writing (2)--------Writing (2)---------Writing (2)
2----Off Path-----Code of Laws (1)--Off Path (CB for Mon)-Off Path-------Off Path-------Code of Laws (1)---Off Path
3---Literacy (2)----Literacy (2)-------Writing (2) (Mon (1)-Off Path------Literacy (2)------Off Path-----------Code of Laws (1)
1--Republic (3)----Republic (3)------Literacy (2)--------Literacy (2)------Off Path---------Literacy (2)--------Literacy (2)
2----------------------------------Republic (3)--------Republic (3)------Republic (3)-------Republic (3)-----Republic (3)
I think this covers anything relatively likely if you don't get techs before alphabet. Anything else you can do yourself.
As for pre-alphabet
2-----Off path------Off path
3--Alphabet (2)----Alphabet (2)
1--Writing (2)-------Off Path
2--Code of Laws (1)-Code of Laws (1)
3---Literacy (2)------Writing (2)
1---Republic (3)-----Literacy (2)
2------------------Republic (3)
This information gives more ability to pop huts on the way to republic without risking delaying the tech by more than the extra carrying cost of techs.
Does this all mean that you have been experimenting with Republic instead of Monarchy as a potential viable alternative in your own games?
The more I know about the benefits and pitfals of strategies, the better I can determine what is best and argue the case. Unfortunately, I haven't played a regular deity game for a while (or any game for that matter, asside from the succession game and GOTM), so arguing for monarchy comes from a habit developed a while ago, and from my recolection of game mechanics. And, of course, the recolection of game mechanics comes from what I have done most regularly, and prep for an early republic was not a frequent occurance in my deity games. A prep for monarchy and contemplation of a republican government will lead to different opinions than a prep for republic and contemplation of a republican government would.