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My question seems simple but I can't figure out how to get to a mathematical answer. It has something to do with the binomial coefficient as it is 73 choose 4 but I'm not sure how to represent repeating that over and over again til all 73 options have been chosen.

fyi, I created a little sim in python as it was the only way I could get my head around solving this and came up with an answer of 88.5 ish but it seemed pretty variable, unsurprisingly. I still would love to see a mathematical derivation of this though so I can create some graphs and standard deviations and whatnot

RobPratt
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Lucas G
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  • This is a variant of the standard Coupon Collector Problem. Exact analytic methods are probably not available, but backwards induction should work. Just create a state variable representing the number of unseen options and solve that system (with a machine). – lulu Mar 31 '20 at 22:35
  • Do you select each day's options without replacement, or is it possible to have repeated options in a single day? – WW1 Mar 31 '20 at 22:42
  • here is a relevant question. A compilation of the methods used to address the standard coupon collector problem. – lulu Mar 31 '20 at 22:54
  • @WW1 they can repeat on the same day, so good point, its not exactly 73 choose 4 each day, I hadn't thought of that – Lucas G Mar 31 '20 at 23:06
  • @lulu thankyou lulu, I'll take a look those links – Lucas G Mar 31 '20 at 23:07
  • The title and body of the question don't quite seem to match. In the title you ask for the average. You don't repeat that question in the body of the question, but at the end you say you want standard deviations (in the plural – I don't understand which plural scenarios this plural refers to). You can't get the standard deviation from the average. Please clarify whether you're interested in the average and/or the standard deviation (or possibly in the entire distribution), and, if the plural in "standard deviations" is not a typo, which scenarios you envisage other than the one described. – joriki Apr 01 '20 at 00:03

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