Ethics approval for an independent project akin to a survey The self-funded project being planned involves participants doing a variant of a Random Number Generation task, involving just typing "randomly" for a couple minutes on a computer program to study/cluster the bias in what was thought to be "random". Since currently the authors are not affiliated to any university, how would they (if needed) get an ethics approval for such a project?

The project involves no intervention, no risks to the participants, the informed consent form includes a fully disclosed data handling policy and the materials are "open", i.e. open source program, open source analysis scripts (after the completion) and the like.

Would an ethics approval still be necessary for such a project? If so, how would independent researchers go about getting one?

I am also curious behind the logic of an ethical approval in such scenarios; all the "best-practices" guidelines available from many good sources are already being followed, and would an ethical approval add any extra layer of surety of adherence to these guidelines?
Let an IRB or equivalent make the call on this, not random strangers on the internet. I suspect, but haven't seen the research design, that you would get permission. But if you don't ask them, you don't have permission. 

But, if you do it without permission, and are asked by a journal for your documentation on ethics approval but don't have it, you are a bit stuck as retroactive permission is (many places) not permitted. 

It isn't you (or us) that gets to judge this. It is whatever ethics board is appropriate and whichever journals you might want to submit the research to. 



For the record, there are some exceptions under the law (some places) to the requirement of getting permission, but most things require it whenever human subjects are involved.