Okay dudes, I just played my first HOF mod game and it was probably the worst game I have played yet, but I had an epiphony of sorts. I didn't even finish because I wasn't going to make the HOF list and probably not even win before the computer launched the ship. I did however come up with a slight twist to previous theories on a cultural win, and I look forward to your feedback.
Yes, one often learns more losing a game badly, than winning and not really understanding why the game went so well.
After reading everyones strategies and feedback and playing half a dozen or so cultural games to completion and a handful to defeat I'm convinced that the strategies for an early deity win are different than for immortal or lower difficulty levels. The following is for non-gods playing a small map, normal speed, ancient, HOF rules, peaceful opponents:
Yes, Strategies for Settler and Deity are vastly different and often have no commonalities. In my opinion, the greatest difference between adjacent Levels is Immortal and Deity, primarily due to the AIs extra Settler. In all Difficulty levels, the AI has the same advantages/disadvantages as a Player at Noble Level. This is especially important for Research rate, where at Deity Level the AI's Noble Level gives them possibly more than double the Research rate that what the player starts with. To help counter this at high Levels (Immortal and Deity), it helps to get two Gems/Gold Mines running ASAP.
Look here for the handicap differences between Difficulty levels:
C:\Program Files\Firaxis Games\Sid Meier's Civilization 4\Assets\XML\GameInfo\CIV4HandicapInfo.xml
1) I don't believe that a straight beeline to alphabet is the best strategy for immortal. In my experience it's almost always best to start with BW for REXion, then agriculture and maybe maybe maybe AH (preferably Masonry) depending on your setup although this is not optimal, then wheel, pottery etc. The reason being that the computer doesn't have enough techs to trade you to make it worth going straight for alphabet which often limits growth. They also don't have any gold yet, and if you refuse their demands which they often make you're already starting off on a bad footing, especially if trying to block the AI by not opening your borders right away and selecting a religion for the +25% OR bonus. In deity this is obviously much different, but on immortal the computer rarely has researched priesthood which is the precursor to CoL, so you end up doing it yourself and often lose the CoL race by 1-2turns.
A beeline to Alphabet isn't required. There are always alternatives, even at Deity Level. Put Mansa Musa is as an Opponent. If an Opponent offers Open Borders early (has Writing), it may not be long before the same AI has Alphabet to trade. In such a case, you will want to research something you can trade for Alphabet. You may also have to research Alphabet to some degree (1/4 - 1/3 complete), before the trade seems favorable to the AI.
Usually you want Open Borders with Civs that have any Religion you don't have, so that they can send you Missionaries or it can spread naturally (though I'm not sure OB is required in the latter case).
You may be right about Immortal and early Bronze Working. I recommend you use it to complete a Library right after completing Writing -> 2 Scientists -> GS -> Academy. Make use of Forest Chops or Slavery to build the early Library.
I also don't believe that 6 cities are needed, but it definitely helps to put down a sixth city later in the game around 500-700ad on the coast to get the ocean food resources after your borders expand. The best situation is to have all 5 cities completely landlocked. 5 cities cuz only 4 need to build temples for the cathedrals in the capital and 3rd legendary city. In almost every case no cathedrals will be built in the GAfarm, which you already know, so only 4 temples of each religion are needed. It's also helpful to put the 6th city down a little later to ensure grabbing a late religion because my slight strategy twist doesn't encourage bulbing philo, but rather trading gold and paper for it after trading CivilService for lots of stuff and lots of gold.
If the sixth City reduces your Research rate below 100% and later Culture rate below 100%, don't build it without great reasons like six Pigs in BFC of the sixth City (Super GA Farm)!
For Immortal, you should probably replace the second GS that normally bulbs Philosophy with a GA.
Consider researching Philosophy and getting there first. The AIs will back off Philosophy, because Taoism is no longer available.
Consider trading nearly everything you have, so the AIs spend their time researching what you don't have rather than one of the dozen Techs your hording. I suspect you may already be doing this.
2) I think that having stone is required for an early win with this strategy twist, again on immortal. First of all to build the pyramids, but also to double production speed for the cathedrals you are likely to get, and if you decide to build any early/mid wonders. You can almost always trade 2 surplus food resources for copper if you don't have it, but you usually do. Marble is rarely found in my games, and islam has never once spread to my cities, leave the hindu cathedral to the end or not at all.
For Cultural games, select the "Choose Relgions" option, just in case you can choose a Religion that has a bonus (Copper, Marble, Stone) that you actually have.
What Map Type are you playing? Some Maps have more Stone, Marble and even Copper than others.
3) By now you are probably shaking your head. I'm not going to use the pyramids for what you think I am and buy stuff with US... By the mid-end to end of the game on immortal (HOF earliest finish vanilla, normal: 1730ad "The Hawk" soon to be "Jayhawks"

) ALL of your cottages are towns. Looking at the civics, you're happy with LIB-CS-Merc-Pac but you're frustratingly stuck on HR, especially because you don't need it anymore so it's just a wasted civic. Additionally everyone knows the benefits of Rep early on after building pyramids for the science and happiness boost. This not only helps you research faster getting you to CoL first (working scientists in capital to pop GS during this period) but it also allows you to skip a line of research, and it saves you gold in warriors which would maintain happiness. Skipping monarchy (which they don't like to trade early anyway) and skipping theology (another pesky one to get from them sometimes, and you rarely build sistine without a GE anyway) allows you to focus your trades on getting other more important techs like lit-music-drama-calendar-math if you don't have it yet etc. This allows you to hold onto paper and civil service longer putting you further ahead in the lib race.
The Pyramids can be quite good for a Cultural Victory, but you need to make good use of any GE that may result and generally do things to prevent a GE or reduce the chance of generating one. The best thing about Representation is the extra Happiness for the largest Cities. The Research boost is nice too and will allow substantial Research after the Culture slider is pegged at 100%.
Additionally, this ties in with building only 5 cities early because your growth will suffer from building the pyramids anyway, as will your economy from REXion if you build 6 or more without some lucky resources.
The biggest disadvantage of building any World Wonder is the sacrifices required to do so.
4) The true strategic value of the pyramids is switching first to REP for the early happiness and research, then HR to grow to sizes 10-13+ early allowing you to get your cottages worked early and NE GA etc. while skipping the trade for monarchy/theology. These warriors will likely run your enonomy negative from support costs for 8-12 units, not to worry. You will benefit once you shut off research and HR is obsolete by switching to US for the lower civic cost.
Ideally, you will want no more than 1 Warrior per City.
I would never go from Representation to Hereditary Rule. Representation is a better source of Happiness than Hereditary Rule and requires no extra military units.
There is another often overlooked strategic factor to building the pyramids on immortal, after you build the pyramids the computer will have gold because they didn't complete it and nearly all of the AI will be trying to complete it, so it will be an early pad to your coffers allowing you to run research at 100% increasing your chances for CoL. With 100% research, Rep, and 2scientists working in the capital you are almost assured to be first to CoL.
With only 4 Opponents you may be overstating this effect. It's quite possible that no one else may be building The Pyramids.
The switching/revolting path is Rep and slavery > HR and OR > Bureaucracy and CS > Pacifism and Liberalism > US and Merc. Then an additonal revolt for adopting a religion at some point. This is more than other strategies, but I think this will allow you to maximize growth as I don't feel/understand whipping to be worth the pop cost mid to later in the game, and would rather be working my cottages, building culture, AND building cathedrals all at the same time.
Play Saladin (Spiritual, Philosophical) to avoid anarchy and for half price Temples.
Not sure Universal Suffrage would be worthwhile.
You should be running Caste System mid-game and end-game, so Slavery isn't an option. Unless, you are playing Saladin (Spiritual, Philosophical)!
4) The final benefit of the pyramids is once adopting US the hammers from the towns in your auxiliary cottaged city (worker farm early on) will increase gold as you are building wealth and likely have at least one merchant and probably a marketplace, allowing you to run at 100% culture for longer before briefly returning to 90% for a turn or three.
You can always work Merchants in non-Cultural and non-GA Farms for extra Wealth (in addition to building Wealth).
Not to mention the increased production for your capital and 3rd legendary city building those pesky cathedrals. This benefit will start small with 2-3hammers but will increase rapidly and cut the turns to build in half or more, and added with stone and copper it's only 6-8 turns per cathedral by the end, far more efficient than whipping at a cost of 7pop or more.
Your Cathedrals should be completed before you have Towns. Well, at least most of your Cathedrals should be completed before Towns.
5) You will likely get a GE as everyone knows from the pyramids, and this is not assumed to be a benefit unless building the Sistine. I disagree. I believe that building the hanging gardens with the GE or even the hermitage in the 3rd legendary city are comparable on immortal as the game lasts longer than deity. With the hanging gardens you would obv not build it in the cap which has pyramids so you can dilute the GP gene pool to not pop another GE. With the hanging gardens and Merc you are assured to get your GAfarm to 10specialists even with a less than optimal placement. You don't even need fresh water in most cases for the GAfarm with these 2 additional specialists.
Avoid a GE as much as possible. You don't want even a single GE to build The Sistine Chapel. There are alternatives, like Chopping The Sistine Chapel or not building it at all. The Sistine Chapel in BtS is a must build though.
6) One final tiny point. I think that it's almost always better to add the first GA to a city, unless you need to expand the borders of your GA farm, a common problem, to get all the food resources that the AI annoyingly trys to take from you. The 3 gold helps more than it may seem, and the 12 culture it adds is raw culture, applicable to multipliers, which over the turns makes up for it in most cases. 4000/12=333, but with multipliers it's more like 140-160. Negligible of course considering the fastest immortal, small, normal, game took 256 turns, but the added 3 gold could make a lot of difference. 3*150= 450+paper = cost of trade for philo. Every bit counts.
No, not always better. The best City to settle a GA in is the one with the highest Cultural Multiplier. Except when that City would go Legendary prematurely. Then City the second highest Cultural Multiplier, except ... Settling a GA into a GA Farm is almost certainly a mistake, since it should have no Cultural Multiplier other than Free Speech. OK, you did say almost, but I don't think its even "almost always better" either.
Wow.... I'm starting to sound like Jesusin with my calculations.... Immitation is the best form of flattery. Next step is to actually implement this strategy
Opinions gentleman??
Try winning without any Wonders, especially The Pyramids. You will never know how high a price you are paying for The Pyramids until you Win without building it or any other World Wonder.
After Winning without any World Wonders, try Winning with just The Pyramids. Just as an exercise use the same Start (a HOF violation, so don't submit it) and even with prior knowledge of the Map, you may be hard pressed to match the Date with No World Wonders.
Try BtS. Early Cultural Victories are much easier in BtS than either Vanilla or Warlords.
Sun Tzu Wu