Txurce and mad-bax: Interesting discussion! Many of the tradeoffs on the route to 100K are difficult to quantify but it seems worthwhile to try.
Regarding when research should stop, my feeling is that Steam Power is a good choice in most games. But it would depend on how quickly domination can be reached. Most of the time I think Steam Power won't require much additional research and will pay back in added production in core cities and in a boost for the last stage of growth.
Regarding the relative priority of expansion vs. rushing culture in existing towns, my thinking is that expansion comes first because:
1) Each new town contributes one gold and one shield per turn to the economy. The gold is of course nice when multiplied by 100 or more. But the shields are the bigger win - when the time comes to rush cultural improvements, the accumulated shields at one shield/turn/town will provide a substantial boost.
2) I think that usually it is easier to take land from opponents earlier vs. later.
3) Score is higher from both territory and population.
Of course each specific game situation will vary - there might be periods while waiting for a particular tech that it makes more sense to build than to fight. And of course the above applies only to the corrupt regions - in the core it makes more sense after a while to build improvements than to continue spewing out settlers
The argument that cost to build should be measured against total long-term culture gained, not culture/turn, is compelling. But I disagree. I can't see a way to quantify the arguments each way and measure them. But my gut feel is that the long term benefits of rapid expansion will outweigh the earlier culture gained by building improvements first. I.e. that sometime before the 100K total is reached, the approach of expansion before improvements will catch up with and then accelerate past the approach of improvements before expansion.
When I first tried a 100K game I thought it would be good to get at least some temples and libraries built as early as possible, to take advantage of culture doubling after 1000 years. I now think this doesn't matter - in a fast 100K game the vast majority of the culture will come from improvements built during the last 1000 years. The contribution from improvements built before that period is small enough that I don't think doubling it will make as much difference to the final date as using the early shields for other purposes (military, infrastructure, expansion.)
Regarding which improvements to build in corrupt towns and in what order:
For a non-religious non-scientific Civ I figure that a library comes first at .038 culture/turn/shield, then a temple at .033 culture/turn/shield. The other possible improvements are university at .020 culture/turn/shield, cathedral at .019, and colosseum at .017. I don't think any of them are worth building in corrupt towns until every possible nook and cranny of land already has a town with a temple and library. After that start rushing universities if 100K hasn't been reached yet. The game should not last long enough that every town has a university, so cathedrals and colosseums should not be built at all in corrupt towns.
As well as ROI on construction, maintenance cost is an important factor to consider. Temples cost .5 gold/culture/turn, libraries .33, universities .5, cathedrals .66, and colosseums 1.0! Regarding maintenance cost libraries are good, temples and universities ok, cathedrals expensive, and colosseums brutal.
If a Civ is religious then things change a bit - temples move to come before libraries and cathedrals become more tempting at .038 culture/turn/shield. But cathedrals come after temples and libraries everywhere - libraries are as good as cathedrals in terms of shield cost and are cheaper in maintenance.
If a Civ is scientific then libraries stay in first place and universities move up. Universities not only become worth building, they even move up to come before temples.
If a Civ is both (Babylon
) then I think the build order should be libraries, temples, universities.
A final note: I think it best to rush each improvement in the priority sequence in every town before rushing the next priority anywhere. E.g. if not religious, rush a library in every town before rushing a temple anywhere. The reason is to maximize the value of both the gold used and of the shields accumulating (at one per turn) in every town. After the last improvement has been rushed in a town, its 1 shield/turn is of no further use and it should switch to wealth.
A reference table of the numbers I've used above, with an asterisk beside the cases which seem good to me:
Code:
Regular Religious Scientific Maintenance
culture culture culture culture gold/turn
shields /turn /shield /shield /shield /culture
Library 80 3 .0375* .0375* .0750* .33
Temple 60 2 .0333* .0667* .0333* .50
University 200 4 .0200 .0200 .0400* .50
Cathedral 160 3 .0188 .0375* .0188 .67
Colosseum 120 2 .0166 .0166 .0166 1.00