P(drop) = 1-((1-p)^n), where p is the average drop rate and n is the number of times you've rolled. (Multiply the statistics from FATEs and CEs before subtracting the result from 1 to get the aggregate.)
While p is higher for CEs than FATEs, the fact they take longer and spawn less frequently about evens out. From what I've observed instances of OC cycle CEs (and maybe FATEs) before stopping admission to new players and letting the instance die. While CEs have a higher p value, the fact you can raise n faster by doing overworld FATEs means if you're trying to get a specific color it's more efficient to roll the dice time and again outside of OC than waiting or hoping for one you need (or a CE) inside.



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