In his Vulnerable World Hypothesis Nick Bostrom recently compared invention to drawing balls out of a giant urn containing at least one black ball (i.e. an invention that would destroy civilization). If this hypothesis is correct, there is a need to assess the global catastrophic risk associated with human ingenuity. Here, drawing on the theory of zero-failure data, we develop two methods capable of addressing this question. The first method uses a Monte Carlo simulation approach, the second method focusses on analytical derivation of the survival function. Taking past global patenting activity as a proxy for human ingenuity, we draw on available patenting data and model different future scenarios for the annual number of technological inventions to provide upper boundaries (method 1) or point estimates (method 2) for the annual probability of pulling out a black ball for the next 1000 years. While there are clear limitations in terms of data and the urn model's conceptual framing, both methods successfully enable first approximations of global catastrophic risk associated with human ingenuity.