281–290 of 361 posts
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Almost certainly not. Given a circle with diameter AB and a point on the perimeter C, is ABC an equilateral triangle?
It's impossible for ABC to be equilateral. Maybe you meant right triangle.
Exactly! This is why you can answer "no" to my question, not "almost certainly not".
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And funnily enough, you'll often hear this trait as being desirable in a pseudo-random number generator. People often want something that will jump around fairly unpredictably but that will come close to outputting all possible numbers once before getting into re-runs.
I’ve coded up this exact algorithm, it’s really fun. It’s useful for “shuffling” in the music sense (not the cards sense). I think it’s actually the prototypical real-world software engineering problem. User says they want X (random music). X is a term in software, so you give them that (you get a random song). They’re not happy. You dig and find out they really want A, B, and C (next song is unknown, songs don’t rep…
Took months and a lot of patience to extract that crucial piece of information from the customer. I actually coded a recursive algorithm which to my surprise generated every possible (three letter) sequence in an acceptable sequence, enough for them for several lifetimes.
> Extreme cases tend to be the most or least important.
Yeah, that's my suspicion.
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Any single sequence of numbers has the exact same probability of being produced by a fair die (that's how the definition of "fair" goes). The probability of getting all 6 is the same of any other one you get.
You work with crypto according to your profile. I hope that when you see a random generator return a series of a hundred 6s, you go and check what's wrong with it instead of assuming you just got lucky this time ;-)
(Looks like my profile is out of date, by the way.)
> so that if another person is shown your sequence of digits from 1 to 6, he/she should not be able to tell whether these numbers were produced by a real die or just “made up” by somebody. That instruction is a flaw in the experiment. It's always impossible to tell, for any given sequence, whether it was produced by a fair die. There's nothing an experimental subject can do to make the impossible more impossible. > t…
> That instruction is a flaw in the experiment. It's always impossible to tell, for any given sequence, whether it was produced by a fair die. There's nothing an experimental subject can do to make the impossible more impossible. Baloney! Say you measure the traffic to your website in the morning and the evening, every day for a week. And this is what you see: day: 1 1 2 2 3 3 4 4 5 5 6 6 7 7 time: M E M E M E M E M…
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I’ve coded up this exact algorithm, it’s really fun. It’s useful for “shuffling” in the music sense (not the cards sense). I think it’s actually the prototypical real-world software engineering problem. User says they want X (random music). X is a term in software, so you give them that (you get a random song). They’re not happy. You dig and find out they really want A, B, and C (next song is unknown, songs don’t rep…
I actually had an engineering ask from somebody to produce "random sequences" which turned out to be anything but random. Short version: letter sequences, no repeats in a sequence or in adjacent sequences. Took months and a lot of patience to extract that crucial piece of information from the customer. I actually coded a recursive algorithm which to my surprise generated every possible (three letter) sequence in an a…
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I suspect many of the “bad” responses are smart aleks saying “11111111” is just as likely a “62536164”.
Is 11111111 less likely than another sequence?
Think of it in terms of coin tosses. Two heads is less likely than a head and a tail, because there are two sequences, 10, and 01, that map to the class of having one tail and one head. But there is only a single sequence of 00 in the class of all heads.
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>It's always impossible to tell, for any given sequence, whether it was produced by a fair die. If the sequence is long enough you can model how likely it is to have been produced by a fair die. Are all numbers equally distributed? Are some numbers more likely to follow or not follow other numbers? Are some patterns repeating? Of course any sequence can be produced by a fair die, but you can still create some objecti…
Any single sequence of numbers has the exact same probability of being produced by a fair die (that's how the definition of "fair" goes). The probability of getting all 6 is the same of any other one you get.
The sequence length of a single die roll is 1. The probability of any particular roll is the same.
Let's do the next part with two-sided dice because it will be quicker.
The sequence length of a roll of two dice is 2. The roll is a bag; the probability of either [0] or [1] is lower than the probability of [1,2] because it's a set membership and [1,2] has the same members and is the same as [2,1]
> so that if another person is shown your sequence of digits from 1 to 6, he/she should not be able to tell whether these numbers were produced by a real die or just “made up” by somebody. That instruction is a flaw in the experiment. It's always impossible to tell, for any given sequence, whether it was produced by a fair die. There's nothing an experimental subject can do to make the impossible more impossible. > t…
Here are some numbers: 123456123456 Did I get them by rolling a die?
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I'm not really a gambling man, but I'd expect a crooked 20-sided die to produce a biased sequence, not a running straight. I don't know if it's possible to make a die that always rolls the same, and I'd expect any such die to fail a superficial inspection (all sides but one bulge; one side is larger than the others; the die has a weird magnetic field; the die is heavily weighted on one side). So I'd still expect a ru…
> All this is beside the point; the instructions invite the subject to produce a sequence that they think will convince people it was produced by a roll of dice. But there is no sequence that SHOULD have that power to convince. If you genuinely believe that, we can easily set up a sequence of bets where you will win infinite amounts of money from me. But of course, you don't genuinely believe that, so you aren't inte…
If you're offering me a bet, and you can easily set it up, then what bet are you proposing? You haven't been very specific. I'm no Turf Accountant[0], but I can spot a three-card-trick when I see one.
[0] https://en.wikipedia.org/w/index.php?title=Turf_accountant