Write a query to display the patron ID and the average number of days that patron keeps books during a checkout. Limit the results to only patrons who have at least three checkouts. Sort the results in descending order by the average days the book is kept.

Sure, here's the SQL query:

SELECT patron_id, AVG(DATEDIFF(checkin_date, checkout_date)) AS avg_days
FROM checkouts
GROUP BY patron_id
HAVING COUNT(*) >= 3
ORDER BY avg_days DESC;

This query selects the patron ID and the average number of days that patron keeps books during a checkout from the `checkouts` table. It then groups the results by patron ID and only includes patrons who have at least three checkouts (specified by the `HAVING` clause). Finally, it sorts the results in descending order by the average number of days the book is kept (specified by the `ORDER BY` clause).