I think I already gave an example with the Luhn algorithm that is used for credit cards. The check that happens is to see if the serial you enter returns true when used in a function. There are multiple such keys, but the publisher only uses a subset of those. A very basic example (that I doubt has been used) would be to check if the number entered is odd or even, and only allow even numbers. The publisher creates serial in the range of 1000000-1500000, but the check would return true for the number 222222222 as well. That is how most of the keygens worked back in the days, though the scene groups usually tagged their keys by having the group's name in the generated ones.
So no, a key that passes the installer's check is not necessarily a valid publisher's key.

All the available games are gone now, right? Nothing up for connect at the moment.

It will be interesting to watch this space.

when you gaze long into the abyss. The abyss gazes also into you

This space will be empty for quite some time. Now with steam sales coming right after ours, no sane publisher would want to hand out free gifts, much less to DRM-FREE people, much less when we won't have discounts by then but full price instead.

But, couldn't you just pass the key through an if (key >= 1500000 && key <= 2000000) to immediately correct the misbehaviour? :P

But I assume you left it blank to make your example as simple as possible. It would be extremely funny if they went through the effort of creating a possibly complex algorithm to forget to check for the range, though!

An evil nemesis we call The Master
Bates me into all kinds of Disaster
On Galifrey or so i'm told
He gazed into a gaping hole
And ever since he's been an awful bastard!

Then what happens when the publisher does a second print and adds more keys to the list they used? They'd have to replace the algorithm with a newer one, so older installers would no longer work with newer keys.
Yes, there are ways to correct that behavior, but most require you to be able to modify the algorithm, something which would require updates. Considering the era of the software we are usually talking about, I don't think the developers planned for the ability to provide regular updates.

Ah, fair enough, I did not think of that possibility. Maybe they could use a second matching pattern instead of modifying the old one? Though it may become a source of confusion if used too liberally and without changing the range (e.g. one pattern for finding odd numbers between 0 and 1,000 and the other one for finding even numbers between 0 and 1,000, every combination would be valid, that's not good).

That would be a possibility, but it would also mean that old copies would reject the new valid keys. So you'd have a case where version 1.0 of the game accepts keys from list A, while version 1.2 of the game accepts keys from list A and list B. Version 1.0 would reject keys from list B, even though they would be perfectly valid publisher keys.

The second matching pattern is actually what Blizzard used (and most likely still uses) for Battle.Net play. The Diablo 2 installer required a key, which should pass the key algorithm, but online play required a valid key, which was only those Blizzard had issued. If you had used a non Blizzard key (from a keygen for example), you would get a "This key is not valid for Battle.Net play". And there was also the case of changing the key to something random, in which case you'd get the "This is not a valid Diablo 2 key", even though you could still play single player just fine.

Seems like it's a mess whatever system you choose, in the end; better do it right / get lucky the first time and hope that you won't ever have to update it.

Thank you very much for the explanations!

The chances are astronomical low, since there was already a second batch of games.

So this could only be a "two time" thing.