technology was advancing pretty quickly in the past, so the difference between what was available between the 1st and 3rd games was actually very significant.
technology has stagnated so there's nothing mindblowing about a 3rd game anymore

>First game establishes the idea
>Second game refines the same thing
>Third game does something new

>>736212327
Famously many NES games had the opposite effect when it comes to the 2nd and 3rd game. 2nd game did some left-field shit to mixed results and then the 3rd game went back to basics with refinement in mind.

>>736212327
first game establishes the core identity
second game tries to refine the ideas but ends up too ambitious and messy
third game "returns to form" ie it's total slopification which attracts nu fans calling it the best
examples: mgs, dmc, witcher

>>736213170
>examples
Dark Souls definitely fits that bill, too, in my opinion. It shared fates with the Mario NES trilogy as the second one was made by different people to the first and third in both cases.

>>736211854
Diablo 3.
Mass Effect 3.
Torchlight 3.
Borderlands 3 (although presequel is shit too and, in retrospect, 2 was the beginning of the downfall to the point 1 is a separate franchise from 2 and onward).
Dead Space 3.
Half-Life 3.
Fallout 3.
Fable 3.
And so on. Although there are always HoMM3, TES 3 and other good things. But yes, like >>736212327 says, 3 is often a turning point, for the good or the bad. Doom 3.

>>736211854
First game establishes the series.
Second tries new things.
Third takes what worked from 1 & 2 and cuts what didn't.

It's not hard to figure out.

And then you have Max Payne 3