Quoting TfL Conditions of Carriage
7.7 National Rail Railcard discounts
For details of how to obtain a National Rail Railcard, see 5.9.
If you hold a Young Persons, Senior, Disabled Persons or HM Forces Railcard and an Oyster card with the National Rail discount loaded on it, your Oyster daily price cap will be 34% lower than the equivalent adult-rate cap.
This discount is only available to the cardholder. If you are travelling with other people who are entitled to a discount on any printed tickets bought in association with your Railcard, the entire group must purchase and use printed tickets.
In short: Oyster + Rail Card = 66% daily price cap
But how does one get this discount?! I’m off to the ticket office to check it out…