If I had to guess, I'd say that it's often better because picking a few random numbers leads to actually thinking about the decision for at least half a minute.

In practice, guessing at numbers and running a calculation actually serves as a quick second opinion on your original intuitive decision. If the numbers imply something far different from the decision that System 1 is offering, I don't immediately shrug and go with the numbers: I notice that I am confused, and flag this as something where I need to consider the reliability both of the calculation and of my basic intuition. If the calculation checks out with my original intuition, then I simply go for it.

Basically, a heuristic utility calculation is a cheap error flag which pops up more often when my intuitions are out of step with reality than when they're in step with reality. That makes it incredibly valuable.

of which figures are chosen and how the are used.

On first pass, I read this as "which figures are chosen and how the arse is used". That seemed oddly appropriate.

I figure it works better about 80% of the time, so I'm going to go with it.

There's some good discussion in Thinking, Fast and Slow about when intuition works well.

Years later, this unsurprising intuition is spectacularly confirmed by the Good Judgement Project; details in "Superforecasting".

Well at least if you pull numbers out of your arse and then make a decision based explicitly on the assumption that they are valid, the decision is open to rational challenge by showing that the numbers are wrong when more evidence comes in. And who knows, the real numbers may be close enough to vindicate the decision.

If you just pull decisions out of your arse without reference to how they relate to evidence (even hypothetically), you are denying any method of improvement other than random trial and error. And when the real numbers become available, you still don't know anything about how good the original decision was.

IME pulling decisions directly out of my arse usually produces results so bad that it'd be hard to do worse, except in certain situations in which it wouldn't even occur to me to use numbers anyway.

That's a good point.

Plugging gut assumptions into models to make sure that the assumptions line up with each other generally produces better results for me. Beyond it just feeling better, it gives me things I can go away and test that I'd never have got otherwise.

Like if I think something's 75% likely to happen in X period and I think that something else is more likely to happen than that - do I think that the second thing is 80% likely to happen? And does that line up with information that I already have? Numbers force you to think proportionally. They network your assumptions together until you can start picking out bits of data that you have that are testable.

Intuitions aren't magic, of course, but they're rarely completely baseless.

Huh! I hadn't heard of that. Retracted. (Anyway, I propose to state that explicitly.)