Speedrunning - A Matter of Time

In speedrunning, there's a common routine where the runner is focused less on improving skill and consistency and more on beating the Law of Large Numbers. At times it can feel like the payoff of "more practice" is just less than the benefit of "just do some runs." When does that happen, and when it does what does it look like? If a perfect run of a hypothetical game is 58 minutes, and I have a 50% chance of losing 5s every minute, how long will it take to get a sub-1-hour time? I think the answer is "about 20-25 attempts."1 Do be aware that it's been decades since I've had to do this kind of calculation, so I might be getting something wrong, but the overall ratios should be correct. This is a gross oversimplification of a model of course - very rarely does a run have nice evenly distributed coin-flip risks - but it's a good model to demonstrate some principles. The maths on this are really rough, as it's all about expectation and likelihoods. The specifics aren't the focus of this…