I tried a naive Monte Carlo on the homework...

I tried a naive Monte Carlo on the homework problem you posed and found a mixed strategy with average score 1+12.7b. That said, it had a surprisingly fat tail, and I suspect you could do a lot better either with a lot more samples (I generated random submission-time distributions with 1-minute granularity from 0 to 10(N-1) minutes, with N=10, and was reluctant to go over a million) or better rules/heuristics for shaping the distributions. I don't know much about this area; algorithm thoughts?

Anonymous

I think I got a full solution, but I haven’t written it up properly yet. The expressions are kind of gross. For now, let me say that the probability of submitting on time should be:
1 - (b / (1 + b))^(1/(N - 1))
Stay tuned.
Also… why are you on anon for this?
1. graatrunk said: math bullies duh
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