Thanks. a few more questions:
1) With all that gold you make what do you usually buy? Rush Buildings, Units, or get allied city states?
2) How often do you make the war/wait 6 turns/collect tribute rotation? on cooldown?
3) What turn or era do you start the war/wait 6 turns/collect tribute rotation?
1) It is a bit hard to give a clear answer. I would answer that you should put the gold in what you feel that you need at that time. In the early game it is surely a good idea to buy the settlers if you afford them, and as a priority after that, even 1-2 workers if you couldn't steal how many you need. Other times, it might be a good idea to pay some CS especially if they have investment or gold gift quests... for example early game paying 500 to a Religious CS can make the difference between having a religion or not. Other times, Militaristic CSs with nice units can be a good use of money. For example Longbowmen, Keshik, Camel Archers, ChuKoNus, Siege Towers. I always try to look out to see if there is such a CS to try to profit from it.
Beyond this, It's always a good idea to try to buy buildings in the cities which have lowest production in the empire. My general priorities for a new city, if there are no special need to buy something in particular, would be //////. Defensive buildings only if absolutely necessary (but having Castles is nice after Neuschwanstein wonder).... Another thing to mention is that in those cases where you try to get an ideology from having 3 factories, saving up 3000 gold to buy them out is always a good idea. But I think in general it's easier and better to simply tech to Radio instead.
2) It might depend on how convenient it is... for example let's say we got 50 gpt out of a far away civ in the first war. It might be convenient to simply profit from this deal until it expires. Otherwise if it looks as if we could DOW and get more gpt after 6 turns, it might be worth to do it. It might also matter if they have CS allies or not, or if the war hurts us in any way (i.e to not risk having caravans pillaged or units killed). In any case, let's not forget to always first pay them to DOW as many other civs as possible first, so as to make sure they get their army weaker and to distract their attention.
3) To give a clear answer, in a Huge size game (best setup for the tribute strategy), it might be worth doing it even early in the game. (in the early game wars, it might be a better idea to try to take hard cash instead of GPT in peace deals. For example early game after we improve our first Luxury, there is often the possibility to DOW somebody who has a gold reserve, and after 6 turns, sell Embassy + Luxury for 275 gold.
But maybe the best way to fully profit from getting huge amounts of GPT is to do the following:
step 1. Stay peaceful and simply tech to Radio tech as fast as possible (or get 3 factories, if this is faster). Even get DOFs and get loans to buy Universities, Public Schools, etc). I think as a benchmark maybe turn 175 with an average civ and 4 city tradition.
And turn 160 with better civs. However as long as we are first to ideologies, the exact turn doesn't really matter.
step 2. Once we have ideology, get Freedom and Voluntary army as fast as possible in order to make sure we have a good Soldiers Value (those 6 units with 42 strength will make sure we can also attack somebody) If somebody else picked Freedom, I would take something else, it feels wrong to sacrifice a free tenet... nowadays I prefer Autocracy and take Industrial Espionage to steal techs super quickly, and go towards "Total War" policy ( +25% prod for units + 15 XP...very good)
step 3. DOW everybody, (backstab all friends by stealing their Cash first) and try to have an artist for a golden age on standby to use during the peace-deals. Also any caravan/sea route could be used for route to a CS to increase gpt so as to profit the most from peacedeals. Everybody will hate us for the rest of the game, but who cares, honestly.
step 4. After 6 turns, people will start wanting to make peace and we start to take the gold starting with the poorest one.... It's not impossible to get to +500 gpt around turn 175-200 in a Huge Size game (11 opponents) by doing this. In a standard game with only 7 rival civs, probably +250-400 gpt is a more realistic target, 4 less civs to take gold from.
step 5.With such a high GPT, it becomes easy to win in whatever way. Simply buy buildings and have strong empire, buy army and conquer everybody, or buy out all CSs.... it almost feels like an exploit... I mean, most people already see it as such