We present a powerful and flexible method for automatically checking anonymity in a possibilistic general-purpose process algebraic verification toolset. We propose new definitions of a choice anonymity degree and a player anonymity degree, to quantify the precision with which an intruder is able to single out the true originator of a given event or to associate the right event to a given protocol participant. We show how these measures of anonymity can be automatically calculated from a protocol specification in µCRL, by using a combination of dedicated tools and existing state-of-the-art µCRL tools. To illustrate the flexibility of our method we test the Dining Cryptographers problem and the FOO 92 voting protocol. Our definitions of anon...