Open How a day gets its color from the calendar and you get the entire method, not a summary: every day number the engine can produce, what each one means, and how the traditions are combined into one mark.
We list all of them on purpose. An earlier version of that page showed only the common ones, which left a chunk of the year landing on numbers the page never explained.
The short version: several traditions read the same date independently. When they agree, you get a good day or a not-your-day. When they disagree, you get mixed — and the day card names which reading said what, so you can see the disagreement rather than take our word for it.
See the whole rule