Well, that first one looks kind of random, but...

An excerpt from the HP 12c Solutions Handbook.
For the record, the program does in fact work a bit better than they claim.

Question: is there any explanation on why so many manuals are never checked before printing?
So far, i have a ton of technical specifications that doesn't pass the simplest common sense test.

I don't get it. They got 5 random numbers.
If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.

@vt_mruhlin said:
If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
True, you can get the same number a million times if truly random. False, you never get that kind of results in real life when truly random is involved. Ever. Not a single gambler in the world ignores this. In that picture, you're looking a five times lottery win in a row with the same ticket. That said, given that i know not of any record in the world about someone getting this kind of random behaviour, and given that i work a lot with random numbers, and given that i gamble a lot too, i feel confident to say that it is a really WTF to not doubt about the randomness of whatever algorithm involved there.
Random means unpredictable, not undetermined. There is something that generates somehow the random effect. In case of software, that something and somehow are manmade. If you want to talk about probabilites, it's more likely to get a human error here than a true five times two digit decimal random repeat. No mistakes in "thinking somehow indicates nonrandomess" IMO. To be fair, no proof of it either.

@vt_mruhlin said:
I don't get it. They got 5 random numbers.
If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
True, but the probability of getting 5 random numbers all the same from 0 to 1 with 2 significant digits is 100,000,000:1
I think the chance of human error is higher really.

@vt_mruhlin said:
I don't get it. They got 5 random numbers.
If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
Pedant FAIL.

@vt_mruhlin said:
I don't get it. They got 5 random numbers.
If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
It's an example. They're contrived to prove a point. You know, like in your math books in high school where everything worked out to even numbers (or even numbers plus even fractions). The same number repeated 5 times doesn't work for "contrived randomness" unless the point you want to prove is that, yes, in an unusual case random numbers can be the same number repeated adnausem.

@donniel said:
@vt_mruhlin said:
I don't get it. They got 5 random numbers.
If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
Pedant FAIL.
Perhaps he was sarcastic...?
Any chance?

@Xelort said:
@donniel said:
@vt_mruhlin said:
I don't get it. They got 5 random numbers.
If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
Pedant FAIL.
Perhaps he was sarcastic...?
Any chance?
I think human error was involved here at some point.

@tster said:
@vt_mruhlin said:
So? The probability of getting the sequence [0.83] [0.98] [0.12] [0.37] [0.68] also is 100,000,000:1I don't get it. They got 5 random numbers.
True, but the probability of getting 5 random numbers all the same from 0 to 1 with 2 significant digits is 100,000,000:1If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
I think the chance of human error is higher really.
And yet some would say this is more random.

@Xelort said:
False, you never get that kind of results in real life when truly random is involved.
True random won't PREVENT you from getting the same result multiple times in a row. True random eliminates the possibility to predict the next result.
If a random number generator claims to be true random, but is designed to not allow (either explicitly or implicitly) for the same result to be repeated a number of times in succession, then it can't be true random
That cleared, I still think this is the case of human error

@bjolling said:
So? The probability of getting the sequence [0.83] [0.98] [0.12] [0.37] [0.68] also is 100,000,000:1
And yet some would say this is more random.
I'm suspicious of your mathematical, philosophical and psychological insights, but I will not call you names if you can also come up with the probability of having a sequence with only different numbers, or that of a sequence where not all numbers are identical...

Well speaking of Random, I've noticed something ... interesting in Windows Media Player sometimes. If I select a song, there's a decent chance the next song on random is going to be from the same band/album. Has anybody else noticed this?

@belgariontheking said:
Well speaking of Random, I've noticed something ... interesting in Windows Media Player sometimes. If I select a song, there's a decent chance the next song on random is going to be from the same band/album. Has anybody else noticed this?
This sounds like the meme that was going around a while ago about the "(lack of) randomness in the iPod shuffle". Take a look a few articles on it and it seems that the consensus is that the human brain is great at finding patterns.Personally I am from an age when albums were created as that  albums, not a collection of unrelated songs. So the thought of letting my computer troll randomly through my song collection is abhorrent to me.

Just for the record, here are the actual first five results that the supplied program produces:
.8310511
.5579467
.2728599
.04132030
.1963391

@belgariontheking said:
Well speaking of Random, I've noticed something ... interesting in Windows Media Player sometimes. If I select a song, there's a decent chance the next song on random is going to be from the same band/album. Has anybody else noticed this?
Some media players, including xmms and WinAmp, generated the random playlist ahead of time, so that selecting a song and hitting "Next" would always jump to the same song. Both used an algorithm that took the playlist and moved random songs up or down the list a random amount, thus causing songs which were in the original list close to one another to be more likely to play backtoback. I don't know if they still do it that way, or if WMP ever did, but it might be the cause. Or it could just be a case of you not noticing the mundane.

@bjolling said:
@tster said:
@vt_mruhlin said:
So? The probability of getting the sequence [0.83] [0.98] [0.12] [0.37] [0.68] also is 100,000,000:1I don't get it. They got 5 random numbers.
True, but the probability of getting 5 random numbers all the same from 0 to 1 with 2 significant digits is 100,000,000:1If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
I think the chance of human error is higher really.
And yet some would say this is more random.
Actually, the probability of that sequence is 10,000,000,000:1 (1e10:1), so it is more random. tster's hypothesis proposes all the same digit, but you don't take the probability in the first instance and treat it as happenstance. The second one has a 100 in 1 chance of being the same, the next has another 100 in 1 chance, which multiplies, and the result of 1e8:1.
What ifevery (I tried 5 times to get a space there) decision made a difference to the whole randomness of everything? My bedtime is 10pm and it is now 11:30, will that be a mistake tomorrow? Time will tell...

@bjolling said:
@tster said:
True, but the probability of getting 5 random numbers all the same from 0 to 1 with 2 significant digits is 100,000,000:1
So? The probability of getting the sequence [0.83] [0.98] [0.12] [0.37] [0.68] also is 100,000,000:1I think the chance of human error is higher really.
And yet some would say this is more random.
OK, but I didn't say the chance of getting the sequence .83, .83, .83, .83, .83. I was talking about the change of getting ANY number 5 times in a row. I generalized the given example to include all the sequences which would be the same. In your example you have 5 unique numbers.
The chance of having 5 unique numbers (any 5 numbers, any order) would be 90,345,024 : 100,000,00. I other words about 90.3% of the time you will get 5 different numbers.

Wow, almost an entire page of posts and THAT xkcd hasn't been posted yet.
Impressive! Or sad. I can't decide.

@Zylon said:
Great, now you've done it...Wow, almost an entire page of posts and THAT xkcd hasn't been posted yet.
Impressive! Or sad. I can't decide.

@Zylon said:
Wow, almost an entire page of posts and THAT xkcd hasn't been posted yet.
Neither was [i]that[/i] Dilbert. ++faith[humanity];

@db2 said:
Just for the record, here are the actual first five results that the supplied program produces:
.8310511
.5579467
.2728599
.04132030
.1963391So, first one is 0.83. It indicates static seed. I say bad random.
@Resistance said:
@Xelort said:
False, you never get that kind of results in real life when truly random is involved.
True random won't PREVENT you from getting the same result multiple times in a row. True random eliminates the possibility to predict the next result.
If a random number generator claims to be true random, but is designed to not allow (either explicitly or implicitly) for the same result to be repeated a number of times in succession, then it can't be true random
Pal... @Xelort said:
True, you can get the same number a million times if truly random. (...) Random means unpredictable (...)
TryitYoursef: gimme 5 truly random 2 point decimal numbers in a row. Good luck.

@Xelort said:
@db2 said:
Just for the record, here are the actual first five results that the supplied program produces:
.8310511
.5579467
.2728599
.04132030
.1963391So, first one is 0.83. It indicates static seed. I say bad random.
Yeah, I never claimed it was a good RNG. Even the book with the program listing says the period is about 500,000. Not exactly cryptographically secure, but good enough for a game of Monopoly/D&D.
This is the algorithm:
f(1)=FractionalPart(0.5284163 * 997)
f(n)=FractionalPart(f(n1) * 997)

@db2 said:
@Xelort said:
@db2 said:
Just for the record, here are the actual first five results that the supplied program produces:
.8310511
.5579467
.2728599
.04132030
.1963391So, first one is 0.83. It indicates static seed. I say bad random.
Yeah, I never claimed it was a good RNG. Even the book with the program listing says the period is about 500,000. Not exactly cryptographically secure, but good enough for a game of Monopoly/D&D.
This is the algorithm:
f(1)=FractionalPart(0.5284163 * 997)
f(n)=FractionalPart(f(n1) * 997)
Oh, sorry, didn't meant to imply that you said something. Just an opinion. I say bad english.
BTW, i still wonder about the manuals. Clearly, if not copied and pasted, the values are all equal to the first one possible... are we seeing a five times first click scenario? Isn't that just TOO stupid?

@TGV said:
@bjolling said:
I didn't have time to calculate stuff yesterday and I seem to have misunderstood tster argument.So? The probability of getting the sequence [0.83] [0.98] [0.12] [0.37] [0.68] also is 100,000,000:1
I'm suspicious of your mathematical, philosophical and psychological insights, but I will not call you names if you can also come up with the probability of having a sequence with only different numbers, or that of a sequence where not all numbers are identical...And yet some would say this is more random.
But what I meant to say was that the probability of getting the sequence [0.83] [0.98] [0.12] [0.37] [0.68] is the same as for getting the sequence [0.83] [0.83] [0.83] [0.83] [0.83] if generating number n+1 is indepent from generating number n. Like when throwing a dice. When the first roll produces a six, the probability of rolling another six stays the same because the second roll isn't influenced by the result of the first roll.
RNGs are not independent, are they?

@bjolling said:
RNGs are not independent, are they?
This one sure isn't, kind of by necessity. The previous output becomes the seed for generating the following output. If you got the same result twice in a row, then you'd keep getting that same result indefinitely.

@vt_mruhlin said:
I don't get it. They got 5 random numbers.
If you think the same number 5 times consecutively somehow indicates nonrandomess, you're gravely mistaken. There was just as much probability of that result as any other arbitrary set of 5 numbers.
While it is true that one set of numbers is just as likely as another set of numbers, the odds that all 5 numbers are the same is pretty small.
Take a simple example like Craps. Two 6 sided die, generate 36 possible combinations. The odds of getting a pair of 2's is 1 in 36. The odds of getting 4 then 5 is also 1 in 36 (assuming order here.) BUT there are only 6 possible pairs, so the odds of getting a pair is 1 in 6, the odds of not getting a pair is 5 in 6.

@chrismcb said:
BUT there are only 6 possible pairs, so the odds of getting a pair is 1 in 6, the odds of not getting a pair is 5 in 6.
What have combined odds got to do with this? You're muddying the issue.@chrismcb said:
So when you get a sequence of identical numbers like that from a random number generator, it is a statistical anomoly.
If you're getting a sequence of identical numbers like that from a pseudoRNG, then it's not only an anomoly, it's likely wrong (unless it's been specifically written to 'allow' such sequences.)However the odds of getting, say [0.86, 0.86, 0.86, 0.86, 0.86] in that order in a 'true' RNG (we've had threads on what 'true' actually mean before,) then the odds of getting that are identical to getting, say, [0.68, 0.51, 0.15, 0.43, 0.53] in that order. The only difference between the two groups is the human perception that the first isn't 'random enough.'

@PJH said:
It has everything to do with this. He is saying that this is like playing craps but with 5 100sided die. Your chance of winning in this game is very small, same as what we are talking about.@chrismcb said:
BUT there are only 6 possible pairs, so the odds of getting a pair is 1 in 6, the odds of not getting a pair is 5 in 6.
What have combined odds got to do with this? You're muddying the issue.@PJH said:
@chrismcb said:
So when you get a sequence of identical numbers like that from a random number generator, it is a statistical anomoly.
If you're getting a sequence of identical numbers like that from a pseudoRNG, then it's not only an anomoly, it's likely wrong (unless it's been specifically written to 'allow' such sequences.)However the odds of getting, say [0.86, 0.86, 0.86, 0.86, 0.86] in that order in a 'true' RNG (we've had threads on what 'true' actually mean before,) then the odds of getting that are identical to getting, say, [0.68, 0.51, 0.15, 0.43, 0.53] in that order. The only difference between the two groups is the human perception that the first isn't 'random enough.'
There is a very big difference, you seem to not be able to see this though. I think it's because you are very smart and clever, but have not studied enough number theory to see what we are saying.

I would say that the first sequence is just as probable as any other, but it is not very representative if you consider the features of the sequence, such as the variance. What I beleive that the human mind does is to guesstimate the probability that the sequence originates from a RNG given its features, which in this case is pretty slim (100:100^5) if you treat the sequence as taken from the set of sequences with repeated unique numbers. If you consider the sequence to be just 'any sequence', it instantly becomes just as probable as any other. The problem here is merely that the human brain focuses on the most obvious features.
So maybe it suffices to say that the first sequence is equally probable as any other, but not representative for the set as a whole (it does not posess the average variance of the sequences from the set)?
EDIT: This in combination with the fact that the human brain likes to make estimation based on far too few samples

@Obfuscator said:
I would say that the first sequence is just as probable as any other, but it is not very representative if you consider the features of the sequence, such as the variance.
That's pretty much it. There are two different probabilities being talked about here: (a) the probability of getting any particular sequence of 5 values, and (b) the probability of getting a sequence of 5 identical values. Putting it another way, getting any value, then the same value as the last repeated four times.
Assuming the range of values is 0.00000000.9999999, we get P(b)=1 * 1/10^7 * 1/10^7 * 1/10^7 * 1/10^7 = 10^28. A very small probability, which matches the intuition that 5 random numbers being identical is weird.
Further, any PRNG that uses only the previous value as a seed and returns the same value for some seed value, would have a pretty massive bias, since it would then get stuck on that value forever. Hence it cannot reasonably be such a PRNG, unless it is an exceptionally badly designed one. It still could be a sequence from a true random source, even if winning the lottery three times in a row is several orders of magnitude more likely.