3 ms·

But couldn't you make the same argument for guessing that it's higher iff the number is greater than 42? Therefore, if the number is 9, both strategies tell you

• CaptainNegative 4y ago
  > But couldn't you make the same argument for guessing that it's higher iff the number is greater than 42? Yep. > Therefore, if the number is 9, both strategies tell you to do different things, yet in each case, your probability of winning is >½. There must be a hole in the logic somewhere… For any nonnegative value C, the probability of Gaussian draw x being larger than (iid) Gaussian draw y is strictly bigger than 1/2 when conditioned solely on x > C. The particular choice of C might change which specific draws of x and y the strategy succeeds with, but as you noticed for every C a thresholding strategy of the above form does give you some pointwise nonzero advantage over random guessing.