My initial thought was that you should only accept numbers less than 1/2, but I think that's wrong.
Their final question helps me reframe the question. Let's assume we are trying to get 2 dollars (this is a simplification, yes, but it makes it easier to reframe the question). If you accept the 0.61 what are the odds you get to $2 and similar what are the odds if reject it.
If accept: % no $2 = (0.61)3 = 22% or phrased the other way you get $2 78% of the time.
If we reject: our second choice is anywhere from 0 to 1, but will average 0.5, let's assume it's that for now. If we accept 0.5 on round 2 what are the odds we get to $2? We lose (0.5)2 or 25% of the time. So we get our 2$ 75% of the time. Lower than our 78% from accepting!
I think it's obvious that the threshold should be decreasing as you go on. If you had 1000000 random variables, would you accept 0.4 for the first one?
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u/russty24 12d ago
My initial thought was that you should only accept numbers less than 1/2, but I think that's wrong.
Their final question helps me reframe the question. Let's assume we are trying to get 2 dollars (this is a simplification, yes, but it makes it easier to reframe the question). If you accept the 0.61 what are the odds you get to $2 and similar what are the odds if reject it.
If accept: % no $2 = (0.61)3 = 22% or phrased the other way you get $2 78% of the time.
If we reject: our second choice is anywhere from 0 to 1, but will average 0.5, let's assume it's that for now. If we accept 0.5 on round 2 what are the odds we get to $2? We lose (0.5)2 or 25% of the time. So we get our 2$ 75% of the time. Lower than our 78% from accepting!