Yes. I implicitly assumed events were uncorrelated to make the math simple to understand and simple to explain. Its a sketch not a photograph. What you're describing is an optimization problem wherein the chance of failure P is some function of the trials per time frame n. So if you're doing it n times per week then the probability of not dying in a given week is (1-p(n))^n . The obvious question to ask is what is p(n)? Well we know some properties it must have. It has to only be decreasing in n (it shouldn't be possible to get worse with more experience). It has to have a diminishing return and eventually stop getting smaller with n (you can't get better than 0% chance of failure). It has to be smooth (your skill doesn't change in sudden discrete jumps). The obvious candidate distribution for this is exponential decay. e^{-rn} * (p_0 - p_inf) + p_inf where p_0 is the absolute worst no-practice value p(0) and p_inf is the is the absolute best attainable value. r is just some constant that determines how quickly the practice pays off. Now based on the assumptions so far the probability of dying in a given time frame becomes (1-e^{-rn} * (p_0 - p_inf) - p_inf)^n. The last step is to just take the derivative with respect to n and set it to 0. I'm tired so exercise for the reader yada yada.