If you have millions of ops per day, a million-to-one chance of something means you'll see it every day! And it only takes a few noisy customers to bring these issues to light.
I saw this first hand when I was overseeing the crash reports during the release of an online AAA game. A game with millions of players.
A fairly frequent crash bug was caused by a line with a comment explaining that it could theoretically cause a crash but that risk would be one in a million.
It only happened on players connecting or disconnecting from the server. Unfortunately it was a server crash so once it did occur it discontented up to eight players.
Then present it as a fun fact rather than as a correction?
And I'm not trying to be mean but I think the way you phrased your last line is accidentally anti-educational. Your last line treats 1 million ops and 4 million ops as nearly equivalent, when the truth is that 1 million ops is far from "every day" while 4 million ops can easily be called "every day".
And if you dislike the word "argument" pretend I said "point"? I think you're reading connotations into that word that I didn't intend.
And yet... here you are, having applied that same mathematical principle to calculate the probability of observing a one-in-a-million event at least once in 4mil independent trials. That's probably something you already knew how to do, but if not, it's a pretty educational moment. ;)
ps — "to be pedantic" means "fun fact" but sarcastically.
The bulk of your post was educational, but it was misleadingly shown as an answer to both "million" and "millions", when those two scenarios actually have very different answers.
> ps — "to be pedantic" means "fun fact" but sarcastically.
It means that, but also sets it up as a correction. But "millions" being "every day" was right all along.
A fairly frequent crash bug was caused by a line with a comment explaining that it could theoretically cause a crash but that risk would be one in a million.