Variable that has the path to the current ansible-playbook that is executing?

You can use playbook_dir variable.

There is no build-in variable for this purpose, but you can always find out the playbook's absolute path with "pwd" command, and register its output to a variable.

- name: Find out playbook's path
  shell: pwd
  register: playbook_path_output
- debug: var=playbook_path_output.stdout

Now the path is available in variable playbook_path_output.stdout

I was using a playbook like this to test my roles locally:

---
- hosts: localhost
  roles:
     - role: .

but this stopped working with Ansible v2.2.

I debugged the aforementioned solution of

---
- hosts: all
  tasks:
    - name: Find out playbooks path
      shell: pwd
      register: playbook_path_output
    - debug: var=playbook_path_output.stdout

and it produced my home directory and not the "current working directory"

I settled with

---
- hosts: all
  roles:
    - role: '{{playbook_dir}}'

per the solution above.

There don't seem to be a variable which holds exactly what you want.

However, quoting the docs:

Also available, inventory_dir is the pathname of the directory holding Ansible’s inventory host file, inventory_file is the pathname and the filename pointing to the Ansible’s inventory host file.

playbook_dir contains the playbook base directory.

And finally, role_path will return the current role’s pathname (since 1.8). This will only work inside a role.

Dependent on your setup, those or the $ pwd -based solution might be enough.