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Worth noting that after 900 case you still almost have 10% chance of not having one.
However, you pass the 75% treshold of getting at least one around 400-450
Id geuss whether that story is true is a gamble as well.
the chance doesn't accumulate
ex. 0.01% for every case, not 0.01% -> 0.05% -> 1%
If you don't have enough money to buy a knife, you definitely don't have enough money to open cases for a knife.
There is no way to "boost your luck." Skipspik's answer gives the mathematics. If you want to simulate the experience of opening cases without risk, look at
https://convars.com/case/en
with whatever case you were going to try.
Opening many cases is best left to people who can afford it: wealthy people, streamers and YouTubers who generate income from people watching the openings, and so forth. Most of us only open a few cases here or there if we have a little extra money in our Steam account, or not at all.