This may be compounded by the the "Teela Brown" problem [1], where some candidates may be too lucky to end up with our company, causing them to appears later in the stream or not-at-all.
I see two possible solutions.
1) Most people won’t be using up most of their luck on this one thing. I mean they’ve got their whole lifetime worth of luck, so you just need to make sure to pick people who still have plenty left. In other words, ageism and/or picking people who’ve never accomplished much are the solutions!
2) We assume working for the company is a lucky outcome. If you make the company a really unpleasant place to work, people will have to use their luck to dodge it. However, luck can only be evaluated against other possible outcomes. The plan, then, should be to set up a competitor (possibly a front) that is a really nice place to work. They’ll act as the “lucky outcome expenditure dump.”
Ah yes, the much revered cosmological fairness constraint.
I’m not a whiz with the math involved, but I am of the opinion that 500 consecutive same-side flips is a large enough sample size to calculate that the coin in question is biased, so it would be unreasonable to assume that the next flip is 50/50.
https://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fai...
The coin can be assumed to be fair before the flips, but after the flips we have no mathematical reason to believe that the coin is fair, as our results heavily suggest that it quite simply isn’t fair.
However, for the purposes of discussion, assuming an ideal coin, the probability of 500 same flips in a row is so statistically unlikely that fairness of the flipping process and/or flipper must then be called into question.
Even if the coin, flipping process, and flipper are all ideal (which wasn’t stated, but we will also assume for the sake of argument that we have ideal immovable goalposts), the likelihood of the 500-in-row event is so improbable as to be unreasonable to use as an example or even a metaphor, because it doesn’t have much predictive power in a conversation, as ideal coins don’t exist any more than ideal coin flippers.
Even a coin designed to be fair would be fairly deemed defective after so many same-side flips, and any reasonable gambler would demand that the coin be replaced with another; at that point an argument could reasonably be made to also change the coin flipper and/or the venue.
I agree: the events are independent in probability, which was never under debate, and is a separate matter to whether or not the coin is fair.
As for your edit:
> Pretend I said 5 instead of 500 if it makes you feel better.
At this point, wouldn’t you say that’s a bridge too far? It’s uncharitable to ask of your interlocutor as that changes the entire context and implications of what you originally said upthread.
Asking me to just pretend that you made a different argument than you originally made, when the mathematical implications of your original argument are the context under question, is literally moving the goalposts.
If you had said it was 5 flips in a row instead of 500 flips, then I wouldn’t have said what I said, because there’s a difference so wide between the two statements in their degree of probability as to be different arguments entirely. You didn’t say that though, and so I don’t know what you’re trying to say now.
Any position you have these days is inundated with applications. Most don't meet the qualifications (because in a lot of places say in the US you must apply to jobs to keep with benefits, regardless of what you are applying for), and for the remaining, you'll find that there will always be some that are all similarly qualified. Who do you hire for one position? It sometimes just comes down to luck.
AI doing the job of filtering I can't imagine making the process easier, and more applications are just going to get tossed because of it.