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On Fri, Jun 8, 2018 at 9:37 PM, Steven D'Aprano <steve+comp.lang.python at pearwood.info> wrote: > On Fri, 08 Jun 2018 12:23:40 +1000, Chris Angelico wrote: > >> On Fri, Jun 8, 2018 at 12:15 PM, Steven D'Aprano >> <steve+comp.lang.python at pearwood.info> wrote: >>> If you truly were limited to 2**32 different values (we're not), then >>> it would be exactly right and proper to expect a collision in 2**16 >>> samples. Actually, a lot less than that: more like 78000. >>> >>> https://en.wikipedia.org/wiki/Birthday_problem >> >> 2**16 is 65536, so the figure you give is pretty close to the >> rule-of-thumb estimate that the square root of your pool is where you're >> likely to have collisions. > > D'oh! > > > I mean, I knew that, I was just testing to see if anyone was paying > attention. > Plus, you were making another very clear point: Humans are *terrible* at estimating exponentiation. Unless you've memorized specific values (2**16 and 2**32 are fairly common and familiar), it's really hard to estimate the value of x**y. Want to hazard a guess as to what 0.99**100 is? (That's the chances that a one-in-a-hundred event won't happen after a hundred opportunities.) What about 85**8? (Theoretical password entropy if you have uppercase, lowercase, digit, symbol.) What is the smallest n such that 26**n > 85**8? (That's the length of monocase password required for equivalent theoretical entropy.) Thank you for that elegant demonstration of an important fact about humans. :-) ChrisA

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