[kadoban]

This is the birthday paradox. The rough approximation is you need sqrt(n) values to get to a 50% chance of having a duplicate. Sqrt of a million is a thousand, and if they're every 30 seconds, that's ~8 hours or so. So you probably get a duplicate or 2 every day.

There's _much_ better approximations than the sqrt one, but I don't know them and the actual math is too hard.

[jakey_bakey]

Correct, the article actually mentions the birthday problem somewhere. Even with 10k codes (2 days) you get dozens of duplicates, so I'd say it's potentially even more common.

Sextuples are 1 in 100,000, so something like every 50 days (per account).

[kadoban]

> Even with 10k codes (2 days) you get dozens of duplicates, so I'd say it's potentially even more common.

Yeah I screwed up here, at the end:

> Sqrt of a million is a thousand, and if they're every 30 seconds, that's ~8 hours or so. So you probably get a duplicate or 2 every day.

You'd get 1 or 2 every day (approx.) if you're only, at any point, looking at the collection of codes generated in the past 8 hours. But of course that wasn't the question, and the odds go way up once the period we're looking at goes larger and larger over time.

I shouldn't have tried to go beyond "ballpark if you wait 8 hours you have a coinflip of having at least one duplicate", anything more than that requires different math.