Chest opening chances are not cumulative and there is no “pity timer” that increases odds as you open more. Every chest theoretically has the same odds as any other chest of the same type.
When people say that opening 1000 gem chests gives you a “fair shot,” that’s because the odds of getting a mythic from a gem chest are approximately 1 in 1000. That does not mean you are guaranteed a mythic if you open 1000. You might get four from 1000, or zero from 5000. But over the long run, the entire game population will average about 1 mythic per 1000 gem chests.