I’ve always been a bit wary about intuition. For a long time, I would avoid using the term, because I found it was creating a dangerous habit in terms of thinking clearly while solving problems. Your intuition isn’t always right. As such, instead of trying to guess when your intuition is correct, my advice was simply to throw it out, and work with what you have. This seemed like a much easier and straightforward way to go about reasoning, particularly within mathematics.
My family and I play a lot of Scrabble, which is a word game where you have to use tiles with letters on them to make words on the board. The board containes multipliers that also give you more points, as well as the tiles themselves, which each have a certain number of points associated with them.