"In the fragile reality of Discworld, and with the gods who like to play games, a million-to-one chance succeeds nine times out of ten."
Pr[something happens across 1_000_000 events]
= 1 - Pr[nothing happens across 1_000_000 events]
= 1 - Pr[nothing happens once]^1_000_000 ## assuming independence
= 1 - (1 - Pr[something happens once])^1_000_000
= 1 - (1 - 1/1_000_000)^1_000_000
≈ 1 - 0.378
= 0.632
It's still below 99% for 4 million ops.
Okay, but they said millions.
> It's still below 99% for 4 million ops.
I find this misleading, because it's... 98%.
Which completely undermines your argument. If something happens 98% of days, it's fine to call that "every day".
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.
ps — "to be pedantic" means "fun fact" but sarcastically.
> 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.