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This is just plain ridiculous. I can not even achieve this at anything higher than noble, and you do it on deity?
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Practice rexing by playing Hannibal on Archipelago maps:
http://forums.civfanatics.com/showthread.php?t=326230
I learnt from several HoF players that taught me how to use that tactic to win on Immortal, and I was then able to win every Immortal game I played as Hannibal. The link is only a noble game though to see how much more I could rex.
Hannibal gets FIN for more

, CHA for more happiness (I would chop both the Stonehenge and GLH in my games, then rex like a maniac), and Cothons add an extra trade route which brings in loads of extra commerce on top of the GLH.
The normal Hannibal strategy is GLH + Collosus plus Stonehenge as an optional (really helps immensely with the extra happiness and free border pops), and tech to Compass ASAP, and use it as trade bait. Build a Cothon first in every city, plus a granary, library and courthouse, and thats all you need for every city to start making a huge profit. Settle near as many seafoods as you can get and later on use Sids Sushi Co.
Its more powerful than Darius is, but it requires an archipelago map.
There seems to be some confusion about Deity and "rexing"

The hard part here is not the upkeep, connect your cities and grab some commerce tiles..you will be fine
The hard part here is playing as Joao on diety - You dont have either FIN or ORG to help you with rexing. You dont have any early economic buildings like Ziggurats, Rathouse or Cothons to recover your economy after a rex. Proper rexing on higher difficulties is rarely ever done with anyone other than Darius or Hannibal, and by proper we are talking about 16+ cities in the BCs without crashing your economy.
You can see from Grashopa's pics that rexing with Joao on Deity is not 'just fine'. It definitely isnt in any of my attempts either - even with all my cities built on the coast for instant trade routes with GLH, my Science slider is down to 20% after just 8 cites.
Joao despite his traits has never been a recomended civ to play for rexing, not even on difficulties lower than Deity. He is actually far weaker for this purpose than even Holy Rome is.