> I made a chatbot that rolled dice, and it was constantly criticized for being "broken" because four 3's would come up in a row.

> These accusations would come up even though they (all being computer science majors) know it's possible (although unlikely) for these events to happen. They just don't trust the black box.

I am reminded of the approach that GamesByEmail.com used to address this criticism: http://www.gamesbyemail.com/News/DiceOMatic