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Ladder

Optimal stopping — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. 01234560.000.100.200.300.400.50how many are looked at and passed overchance of taking the best14.3%35.0%41.4%40.7%35.2%26.2%14.3%every one of the 5,040 orders, for every threshold: looking at 2 of 7 and then taking the first that beats them wins2,088 times, which is 41.4%taking the first one wins 14.3% and so does taking the last, because both amount to choosing without looking —the rule beats them by a factor of 2.90

    When to stop looking

    Candidates arrive one at a time in a random order. Each must be accepted or rejected on the spot, with no going back and no way to know what is still to come. The best possible rule is to look at about a third of them and then take the first one that beats everything seen — and it works about a third of the time, however many there are.

    rung 1 · probability

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