=Henry Baker <hbaker1@pipeline.com>
What do you do if the interval is (-oo, oo) on the real line? Does this change things in any meaningful way?
Don't think so. As Don points out, the most significant effect is quantization in discrete v. I believe that the
What is the relationship of this game to continued fractions?
At 09:01 AM 1/29/2004, Don Reble wrote:
An infinite version of the game is easy to analyse. Here, one picks a real number in some interval; the guesser tries to shrink the interval containing the number as quickly as possible, but mustn't allow three consecutive same answers.
So, if the last two answers were the same, the guesser must waste a guess, to ensure the opposite answer.
If the last two answers were different, he splits the interval according to the golden ratio (GR), so that the new answer is more likely to be different from the last answer. If he gets the different answer, he has reduced the interval by GR; if he gets the same answer, he has reduced by GR^2, but must waste a guess. Either way, he reduces by GR per guess.
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