https://en.wikipedia.org/wiki/Digital_rights_management
Digital rights management (DRM) schemes are various access control technologies that are used to restrict usage of proprietary hardware and copyrighted works.[1] DRM technologies try to control the use, modification, and distribution of copyrighted works (such as software and multimedia content), as well as systems within devices that enforce these policies.
https://en.wikipedia.org/wiki/Digital_rights_management#Product_keys
One of the oldest and least complicated DRM protection methods for the computer games is a product key, a typically alphanumerical serial number used to represent a license to a particular piece of software. During the installation process for the software, the user is asked to input the key; if the key correctly corresponds to a valid license (typically via internal algorithms), the key is accepted, and installation can continue. In modern practice, product keys are typically combined with other DRM practices (such as online "activation"), as the software could be cracked to run without a product key, or "keygen" programs could be developed to generate keys that would be accepted.

And my question is:
How do serial keys "restrict usage"?
How do they "control the use, modification, and distribution" of games (or other software)?

Note: this is not about online activation.

if you dont have the serial key you cant use the softwarre
it either wont install or you cant unlock the rest of the features and it will stay in demo mode ( or shareware mode with nag boxes)

The game restricts (and thus controls) usage by preventing installation unless you have a valid key. And if you use a valid key copied from somebody else, one or both of you is likely to run into trouble when you try to play online (see NWN, etc.).

But you have the key, because you bought the game, and if you copied it from a friend, you just wrote it down. In both cases > no restriction of usage.
So then you say what if you didn't write down the key? But what if you didn't copy ALL of the installation files? (in both cases = same result, you can't play the game....) But nobody claims that the installation files are DRM, so why would the serial key be?

untill you lose the key
and believe me when you are installing windows 95 or 98 and the damn key is either missing unreadable or plain wrong ( oh yeah that does happen)
you wil know how and why serials are drm

Until your floppy "brakes"/gets corrupted, scratch on CD makes it unusable, etc. etc. .... and still, the data carrier itself is not seen as a form of DRM, so why is the key?

Because the key is a deliberate restriction by the publisher, whereas the CD or floppy getting damaged/corrupted is an act of nature / restriction of nature not specifically intended by the publisher, but unavoidable.

How is it a restriction?
You have the key or copied it -> use the software
You lost the key or didn't copy it -> act of nature / restriction of nature

You don't have a valid key, you can't run the software. Usage restricted.

Or, concerning multiplayer (which happened quite often): "Key in use"...

What exactly are you trying to argue?

That you can work your way around this rather primitive protection scheme? Guess what: all forms of DRM can be broken or worked around in some way. But the restriction is still there. There is no restriction when there is nothing to crack, nothing to work around.

Or are you nitpicking the language?

Nobody is claiming the series of letters and numbers itself is literally and wholly by itself DRM. It is a part of the scheme, the part that serves to authenticate the user that has the key as a legit user. The other part is implemented in the installer and/or game, which actually checks the validity of the key. And yet another part is in the distribution channel where the keys are delivered to legit customers. That people say a product key is a primitive form of DRM is just a simplification that names the most visible and obvious part of the scheme. Even a half-wit will understand the simplification isn't to be taken literally.

You don't have a suitable brain, you can't run the software. Usage restricted. BrainDRM!
Please read the posts above, I've already addressed what you're saying. And online play is not what this topic is about.

Losing the key might be an act of nature, but not being able to use the software without the key is a deliberate restriction by the publisher. Ah, semantics.

No, the brain work analogue. So that's ARM. You should know about it.

I am arguing the restriction. It's not restricting anyone from playing the game and it's not restricting anyone from distributing it.
I quoted that wikipedia article so that we have a clear context. It's not about DRM as a concept, but about what DRM actually DOES. And only in a world without pen and paper does a key actually restrict from illegally distributing a game.


Ok, so we can conclude that it's DRM, but only semantically. :-D
What about system requirements? A restriction made by developer and/or publisher, but also not considered DRM.

That's why it is an outdated form of DRM that has been replaced with more restrictive methods like online activation and account binding. I am not arguing that a simple product key is a very effective way of preventing unauthorized use of a software, but it requires an additional step to make a copy for someone, because you also have to provide them with the correct key. That will not stop you from making a copy for your best friend, and then him making a copy for his friend; however, the longer the chain gets and the more middleman are in this chain, the greater the chance of someone messing up and providing a wrong key or losing the scrap of paper on which they noted the key. Remember that this came from a time where you couldn't simply download 500 Mb from the internet because that would have taken you five day. You had to make a physical copy and give it to the other one in person.
Similar to the limitations of floppy or disc, system requirements are ispo facto, meaning they result from the product itself. If it was within the hand of the publisher they would make the software run on every hardware, because that will maximize sales, but that is not possible. There will be natural limitations that result from the engine used, for example. Using a product key is a deliberate choice that is not necessary, except the publisher decides to do so. Quoting the first line from your Wikipedia article: "Digital rights management (DRM) schemes are various access control technologies that are used to restrict usage of proprietary hardware and copyrighted works." System requirements are not used to restrict the usage of a software, they are unavoidable.