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On Sat, 28 Jun 2014 19:53:08 -0500 |
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Canek Peláez Valdés <caneko@×××××.com> wrote: |
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> On Sat, Jun 28, 2014 at 7:37 PM, <gottlieb@×××.edu> wrote: |
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> > On Sat, Jun 28 2014, Canek Peláez Valdés wrote: |
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> > |
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> >> That doesn't matter. Take a non-negative integer N; if you flip a |
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> >> coin an infinite number of times, then the probability of the coin |
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> >> landing on the same face N times in a row is 1. |
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> > |
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> > This is certainly true. |
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> > |
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> >> This means that it is *guaranteed* to happen |
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> > |
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> > That is not as clear. |
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> |
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> Let me be more precise (and please correct me if I'm wrong): It is |
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> guaranteed to happen at some point in the infinite sequence of random |
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> flip coins, but we cannot know when it will happen, only that it will |
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> happen. |
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> |
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> That's the way I got it when I took my probability courses, admittedly |
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> many years ago. |
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The probability is 1 in the sense that the as the number of flips M |
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increases, so does the probability of getting N heads (or tails) in a |
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row also increases, and the upper bound for the sequence of |
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probabilities is 1. It's not a probability about something which |
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actually happens; no one so far has been able to flip a coin an |
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infinite number of times, not even a computer. |
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> In any way, even if I'm wrong and it is not guaranteed, the main point |
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> remains true: the probability of getting a large sequence of the same |
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> number from a RNG is 1 for every true random RNG, and therefore seeing |
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> a large sequence of the same number form a RNG doesn't (technically) |
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> means that it is broken. |
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It's true that that wouldn't *prove* the generator is broken. But it |
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might be a good reason to take another look at the algorithm. |
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> |
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> Regards. |
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