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gwern comments on Open Thread for February 18-24 2014 - Less Wrong
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Ah. The approach I was thinking of was to model it as a binomial or Poisson, infer the probability of success at each step by noting that it took 12 hours (or let's say, 720 tries) to have 8 successes in a row, and then calculate how many tries would be required to get 13 successes in a row. Unfortunately I wasn't sure how to go from '720 tries for 8 successes in a row' to 'probability of 1 success' and gave up there.
the probability of one success is 720^(1/8), so it should take 720^(13/8) tries, which is about a month. However, the fact that they could line themselves up for the last one just by pressing up and down, and not risking having to start over will make a huge difference.