Hello cvikar,
I took the Secret tour offered by the Dodge's palace about 20 years ago and again last September. You will get a guided tour through the prison cells, bureaucratic offices, parliament rooms and the upper prisons including Casanova's cell and the torture chamber.
The tour adds a lot of context to just how strange and convoluted politics in Venice had become. For example the Dodge had ultimate power but they were so afraid he would use it he was essentially held in the palace and needed permission to leave it. So it add context and historical background like any good tour will do. Afterwards you will inserted back into the regular Dodge's Palace tour near the start. The current tour has fewer great rooms than the older one that followed kind of a different theme but I think some of those old rooms are now shown in the general tour.
Those tours are 32e or 20e if you qualify or have some of the many discount cards.
https://palazzoducale.visitmuve.it/en/pianifica-la-tua-visita/special-itineraries/secret-itineraries-tour/
This is probably the information about the discounted purchase you were looking for. In general with discounts cards you buy the cheaper on-line tickets but you will be expected to present the card when you used your discounted tickets.
Whether it is worth it to you I can't answer. I think that Venice is a unique enough place with a specific history that taking a tour, if you have the time, can really add some context to your visit. Whether it needs to be an expensive tour of a site or just a walking tour of city is up to you.
=Tod