Firebase: set security rules depending on user roles

Question

I would like to implement "write" security rules in Firebase depending on users roles.
My data structure is like this:

+ myapp
  + users
    + john
      + email: "[email protected]"
      + roles
        + administrator: true
    + mary
      + email: "[email protected]"
      + roles
        + moderator: true
    + ...
  + documents
    + -JVmo6wZM35ZQr0K9tJu
      + ...
    + -JVr56hVTZxlAI5AgUaS
      + ...
    + ...

I want - for example - that only administrator users can write documents.
These are the rules I've come to:

{
  "rules": {
    ".read": true,
    "$documents": {
      ".write": "root.child('users').child(auth.uid).child('roles').child('administrator').val() === true"
    }
  }
}

But it doesn't work: not even administrator users can write documents...
Is my understanding of Firebase security rules totally flawed?

UPDATE: Just before Jenny's answer (believe it or not :-), I did implement the exact same solution he provides (of course based on Kato's comment).
Though, making some tests, I could not let the rules structure

{
  "rules": {
    "documents" {
      "$document" {
        ".read": "root.child('users').child(auth.uid).child('roles').child('documents').child('read').val() === true",
        ".write": "root.child('users').child(auth.uid).child('roles').child('documents').child('write').val() === true"
      }
    }
  }
}

work... I always got a warning like this:

"FIREBASE WARNING: on() or once() for /documents failed: Error: permission_denied: Client doesn't have permission to access the desired data. "

So I came up with this structure, instead:

{
  "rules": {
    "documents" {
      ".read": "root.child('users').child(auth.uid).child('roles').child('documents').child('read').val() === true",
      ".write": "root.child('users').child(auth.uid).child('roles').child('documents').child('write').val() === true"
    }
  }
}

Which indeed works, for me: if I set a roles/customers/read node to true on a user he can read all documents, otherwise he can't (and the same for write).

My doubts now are:

• why I could not let the first rule (as suggested by Kato) work?
• do you see any possible security hole in a rule like the one I did came up with?
• are rules using "$" variables necessary/useful even if you don't have to allow/deny the readability/writeability of each single document based on it's key, but you just want to allow/deny the readability/writeability of a node as a whole?

Solution

Based on the names of your user records, they don't match auth.uid, which is probably a Simple Login id, such as twitter:2544215.

Start by adjusting your users to be stored by their Simple Login uid:

+ myapp
  + users
    + twitter:2544215
      + email: "[email protected]"
      + roles
        + administrator: true
    + twitter:2544216
      + email: "[email protected]"
      + roles
        + moderator: true
    + ...
  + documents
    + -JVmo6wZM35ZQr0K9tJu
      + ...
    + -JVr56hVTZxlAI5AgUaS
      + ...
    + ...

Next, add a security rule so that administrators can access documents. You have a couple options here, depending on your specific use case.

1. To give administrators write access to contents of each document:

   {
     "rules": {
       "documents": {
         "$documents": {
           ".write": "root.child('users').child(auth.uid).child('roles').child('administrator').val() === true"
         }
       }
     }
   }
   

2. Or, alternatively, give them access to the whole collection:

   {
     "rules": {
       "documents": {
         ".write": "root.child('users').child(auth.uid).child('roles').child('administrator').val() === true"
       }
     }
   }
   

The difference between these two being the $documents variable that moves the security rule one step further into the hierarchy.

(This was mostly just an aggregation of comments by @Kato into answer form)