This members-only tutorial provides the steps to output the number of posts that have a User-type custom field's value i.e., a WordPress user matching with the currently logged-in user.
For example, let's say for a given post, the user (need not be the post author) has been set as User A:
Similarly, there are 3 other posts associated with User A.
With the code in this tutorial, we can show 4 (in the above example) on a Page titled say Profile or Dashboard on the front end when it is being viewed by the user, User A.
Each user will see the number of posts associated with them.