ratio of extract to base grain in a partial mash brew

What percentage of fermentables in a partial mash should be extract and what percentage should be base grain?

Whatever works.  I’ve never seen any standardization.

The biggest reason to mini mash is to use grains that must be mashed to get their full goodness. The basic rule I‘ve seen is 1-2lb base for each 1lb of grains that must be mashed.

I haven’t either, which is why I was asking.
I’m working on a project that involves partial mash recipes, among others, and I’ve never done it.

I agree with Stevie, I’ve always used that ratio of 1-2 lb of base to specialty grains.  That is so that you have enough Diastatic Power in the mini mash to convert it all, erring on the higher side to be sure.

Maybe 1.5 lb of base malt per 5 gallons seems about right, but it doesn’t really matter.  Like the others said, there is no official standard mini-mash.  Could be a pound, could be 5 lb… it’s all over the place.  I think when I was partial mash, I essentially started small then with successive batches worked myself up to all-grain over the course of a half dozen batches.  But most people these days probably jump from “extract plus a few grains” straight to all-grain BIAB or cooler mashing, especially BIAB because it’s so friggin easy, a caveman could weave some netting to do it.

I’d say there’s no reason not to use as much as you can within equipment limitations. It’ll be less expensive and arguably improve quality.

This is your answer.  I would add that, when I have done it (and if I do it again) all of my specialty grains go into the mini-mash, so you need enough base grain to convert those.  The extract is there to get the gravity up to where I want it and I use the lightest possible dry extract (Breiss Pilsen, IME).