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That sounds right to me. The first few sentences of the article, talking about "picking numbers at random" without fixing any sort of probability distributions
by pzone 11y ago
That sounds right to me. The first few sentences of the article, talking about "picking numbers at random" without fixing any sort of probability distributions for those numbers, or even labeling those distributions as P1 P2 and so on, raised enough red flags that I stopped reading.
Whether or not the the conclusion of this article is correct (and my intuition still screams "not a chance"), the argument is hand-wavey enough that it doesn't reply to the objection raised here.
- pzone 11y agoUpdate: I read one of the comments below and now I'm convinced by the argument. Here's the intuition for what's happening. (I wish the article had spelled this out sooner) As long as A does not equal B with some positive probability, and as long as you choose a separator R with full support, then there is some probability that R lands between A and B. When that happens, you always win the game. Otherwise, if picking A or B randomly doesn't hurt you, then R landing somewhere else not between A and B doesn't hurt you either. So you've gotten a strategy that, once in a while, helps you separate A and B, and doesn't hurt you otherwise.
- StefanKarpinski 11y agoYeah, I'm not convinced anymore either. Specifically, I think that the assumption that R < A and A < B are independent events is incorrect, which means that P(R < A < B) = P(R < A)*P(A < B) is not necessarily true. I'll have to think on it more and maybe email Mark about it.