Many mathematical-minded people look at this problem and conclude that the maximum probability of freedom is close to (1/2)^50. But that's absurdly wrong. They

Many mathematical-minded people look at this problem and conclude that the maximum probability of freedom is close to (1/2)^50. But that's absurdly wrong. They're out by a factor of 10^14 !!! So, are there any important problems in computer science / software engineering contexts that have this form? If so, they may have speed-ups of several orders of magnitude that mathematically and algorithmically-minded people might completely miss?