That unique luxury diversity is the ideal.
I have however played on a lot of maps where there is very low diversity of luxury resources.
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Note the wide variability of resource diversity is a minor positive on the Tradition side of the Tradition vs Liberty debate ledger. Liberty starts are much more dependent upon luxury diversity than Tradition.
Jon doesn't need me running around and co-signing his posts, but (again), this is very important to digest for the improving player
So many posts these days are about how to step up to Emperor or Immortal or above, and while there are many facets to that, one of them is understanding the balance between resources and city spots. As the the famous quote from the Matrix says 'There are rules here... some can be bent, others can be broken.'
It is neigh on impossible to play a good Liberty game (6+ city placements hard built) without lots of luxuries to offset the immediate happiness sapping of founding new cities. And nothing is more toxic to a player trying to step up a level than stagnant growth. That snowballs.
Conversely, a flexible Tradition game can see players wait and do a two-city National College start, and maybe just 3 cities for a long time, and then manufacture the happiness to finally plant the 4th. In doing so, you can be more selective on picking 'good' city spots even if they offer no new unique lux.
Indeed, often in a tricky start, the key is how to get strong cities, period. Good strategic and food resources, mountains and freshwater, trade routes to the capital, et al. Happiness can be manufactured. So long as you're growing your Capital, you can take the time to get the requisite happiness for a tall core-4 Tradition game.
You can do the Colliseum and Circus Max sequence if you must, albeit it takes time. A good land full of horses yields Circuses. My personal favorite is scout well and find that one Mercantile CS with two unique luxes, where allying them will give
eleven happiness. That is immensely strong. Maybe you can't buy that University as fast as you'd like, but you can nonetheless get the happiness to keep you growing. Going Left-side Patronage (Opener plus Increase Influence from Gold Gifts), can get you to 80+ Influence on a few CS provided you're on top of quests and selling things to the AI. Obviously, if you play a decent diplo game, you can often turn a starting land with 5 copies of Copper or Crab or Silk into a trading station. But sometimes all you can do is sell copies for 7 gpt (ideally 240 bulk) and then invest that gold in a CS.
Either way, a strong city spot devoid of luxuries is still a strong spot in a Tradition Tall Strategy; conversely, if you're thinking Liberty, but your scouted land doesn't have the large diversity of unique luxuries, it's time to re-think.