[dstick]

"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."

https://wiki.lspace.org/Million-to-one_chance

[grumple]

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.

[Agentlien]

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.

[Dylan16807]

How often did that code run? Even with one player, that would be too high for a per-frame risk...

[Agentlien]

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.

[grayclhn]

To be super pedantic, for one million ops it's closer to a 63% chance every day:

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.

[Dylan16807]

> for one 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".

[grayclhn]

Dude, it was meant to be mildly educational, not an "argument."

[Dylan16807]

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.

[grayclhn]

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.