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> there is no way to show that P[A < R < B] > 0 As the puzzle and strategy are stated, the methods for choosing A/B/R are all left unspecified. If we don't kno
by fenomas 11y ago
> there is no way to show that P[A < R < B] > 0
As the puzzle and strategy are stated, the methods for choosing A/B/R are all left unspecified. If we don't know how they're chosen, it stands to reason that we can't rule out the possibility of R falling between A and B, hence there's a nonzero chance of it happening. If you want a rigorous way to show this even for any given opponent strategy, the player can choose R from an unbounded distribution - which is nonzero everywhere, and therefore nonzero between A and B, for any choices of A!=B.
- umanwizard 11y ago"Can't rule out the possibility" isn't the same thing as "nonzero probability". E.g. pick a number uniformly at random between 0 and 1. It might be rational, but the probability of that is 0.
- fenomas 11y agoYou're moving the goalposts from what the article claims. The opponent's strategy is unknown and unspecified, per the puzzle. The point of the article is that there is a strategy that never does worse than chance, and may do better, depending on the opponent's choice of numbers. Sure, the opponent can make your advantage arbitrarily small - the article says that directly. But the notion that they are trying to do so is not part of the puzzle, and finding a strategy that prevents them from doing so is not what the author claims to have done.