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You have an interesting thought and I was wondering the same thing. OP says that the probability of winning in the 3 cases are: (1) 50% win, (2) 50% win, (3)

by alister 11y ago

You have an interesting thought and I was wondering the same thing. OP says that the probability of winning in the 3 cases are: (1) 50% win, (2) 50% win, (3) always win If I understand correctly, you're saying that the probabilities might perhaps be: (1) 50% win minus some probability of case 3 happening, (2) 50% win minus some probability of case 3 happening, (3) always win Then the three cases even out to 50% and there is no winning strategy. But wouldn't your argument break down where you write, "But the interval less than X is finite, while the interval above X is infinite."? Since we're dealing with reals, then both (+∞, X) and (X, R) have an equally large and infinite set of numbers (i.e., the latter is not a finite set)[1]. So, Y is as likely to be found in (+∞, X) as in (X, R). I'm still wondering if there's a way to make your argument work. [1] https://proofwiki.org/wiki/Closed_Interval_in_Reals_is_Uncountable https://proofwiki.org/wiki/Closed_Interval_in_Reals_is_Uncou...

jdmichal 11y ago
> But wouldn't your argument break down where you write, "But the interval less than X is finite, while the interval above X is infinite."? Since we're dealing with reals, then both (+∞, X) and (X, R) have an equally large and infinite set of numbers (i.e., the latter is not a finite set)[1]. So, Y is as likely to be found in (+∞, X) as in (X, R). Yes, of course. I realized this about 5 minutes ago in the shower and was hoping no one had called me out on it yet! I think the real argument is actually a combination of this and landryraccoon's post, depending on the problem definition. [1] The problem is either defined in such a way that the (X, R) interval is finite, and therefore falls under my argument. -OR- the problem defines (X, R) to be infinite, and P(case 3) is zero. [1] https://news.ycombinator.com/item?id=10647331 https://news.ycombinator.com/item?id=10647331

by alister 11y ago

jdmichal 11y ago

> But wouldn't your argument break down where you write, "But the interval less than X is finite, while the interval above X is infinite."? Since we're dealing with reals, then both (+∞, X) and (X, R) have an equally large and infinite set of numbers (i.e., the latter is not a finite set)[1]. So, Y is as likely to be found in (+∞, X) as in (X, R). Yes, of course. I realized this about 5 minutes ago in the shower and was hoping no one had called me out on it yet! I think the real argument is actually a combination of this and landryraccoon's post, depending on the problem definition. [1] The problem is either defined in such a way that the (X, R) interval is finite, and therefore falls under my argument. -OR- the problem defines (X, R) to be infinite, and P(case 3) is zero. [1] https://news.ycombinator.com/item?id=10647331 https://news.ycombinator.com/item?id=10647331