So, apparently we need to establish an estimate before I start working on a task.

Why not rather let me get on and do the task, see how many hours it takes and then pay me accordingly?

This is for a freelance gig, just FYI

I would love that! "Here, create something for us, just go crazy! The words 'costs' and 'budget' do not reside in our vocabulary.."

^^

I don't know! Crazy people that want to limit your costs and budget stuff... pff! Money grow in trees or we could just ask more injection from our venture capitalist, right?

Yes. Yes, we do. With estimates, it's your responsibility to deliver on time (but with certain conditions on the client). With open-ended, free reign, the client has zero confidence that you're not just wasting hours and charging them. That's simply not how it works in the real world.

Because money doesn't grow on trees.
You wouldn't go to a restaurant and order a dish if the chef told you, let me start cooking, and I'll tell you how much it'll cost.

Your estimation * 3 should be the response to the client. After your deliver, collect your payment. If it takes more than a week, ask for 50% or less up-front

Getting them to pay you by the hour, as I learned yesterday from an awesome YouTube vid, is illogical because if you complete the assignment in less time, you will be paid less when you might should be valued more due to your efficiency. Similarly, if you take too long, the client would have to pay you more for no increased value, which they won't be likely to do at all. So therefore, everything you do should be at a flat rate, AND each project should be billed and timetabled separately.