Perplexed by relationship of draw numbers

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revolution
When all else fails, read the source

Joined: 24 Aug 2004
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revolution

sleepsleep wrote:

True random means that there's no inherent bias and all are equally likely (or at least, are exactly as likely as specified).

Nooooooo. True randomness means unpredictable. You can still have bias in the generating system. Indeed many TRNG circuits have methods to remove the inherent bias from the input, but it isn't a requirement for randomness.

So to summarise. Randomness is not about un-repeatability, or being unbiased, or equal odds of each outcome. These are things we humans like to have, but they have nothing to do with being unpredictable. And unpredictability is the only criteria for randomness. A faulty dice can still generate random (i.e. unpredictable) outcomes, and at the same time be biased towards a 6 showing up. It would only be when the dice is so badly unbalanced that 6 shows up on every roll forever that we could say that it isn't random.

Last edited by revolution on 01 Jul 2018, 09:39; edited 1 time in total

30 Jun 2018, 22:01

sleepsleep

Joined: 05 Oct 2006
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sleepsleep

revolution wrote:

And unpredictability is the only criteria for randomness.

ok, noted,

you mentioned about truly random in before,
how is it this truly random works, what kind of result it is (expected) to outputs?

30 Jun 2018, 23:45

sleepsleep

Furs wrote:

I think there's more types of bias to measure here. C obviously has a probability bias for 6, and B for 4. A is statistically perfect in terms of probability. But it seems A has some sort of "memory" here,

but what if i tell you, we keep on rolling the dice for another 100k and now
dice A got 1=1%, 2=20%, 3=1%, 4=20%, 5=5%, 6=53%
dice B got each faces appears 16.6%
dice C got 1=20%, 2=5%, 3=3%, 4=40%, 5=10%, 6=12%

30 Jun 2018, 23:47

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17452
Location: In your JS exploiting you and your system

revolution

sleepsleep wrote:

but what if i tell you, we keep on rolling the dice for another 100k and now
dice A got 1=1%, 2=20%, 3=1%, 4=20%, 5=5%, 6=53%
dice B got each faces appears 16.6%
dice C got 1=20%, 2=5%, 3=3%, 4=40%, 5=10%, 6=12%

These follow-on results are so very^lots extremely unlikely that I would suggest that someone has manipulated the system. Maybe they replaced all the die with another set.

01 Jul 2018, 09:44

Furs

Joined: 04 Mar 2016
Posts: 1489

Furs

revolution wrote:

Nooooooo. True randomness means unpredictable. You can still have bias in the generating system.

This makes no sense to me, unless you literally mean 100% predictable as it happens if you "crack" a pseudo-rng.

sleepsleep wrote:

ok, noted,

you mentioned about truly random in before,
how is it this truly random works, what kind of result it is (expected) to outputs?

He meant that a statistical expectation is "true random" no matter the chance. But if you can accurately predict the next number with 100% certainty (because you know how the pseudo random number generator works, exactly) then it's not true random.

To be honest, I can't really imagine a "true random" thing actually be statistically compressible with e.g. arithmetic coding, but maybe revolution is right. I'll think about this some more.

01 Jul 2018, 10:44

sleepsleep

revolution wrote:

sleepsleep wrote:
but what if i tell you, we keep on rolling the dice for another 100k and now
dice A got 1=1%, 2=20%, 3=1%, 4=20%, 5=5%, 6=53%
dice B got each faces appears 16.6%
dice C got 1=20%, 2=5%, 3=3%, 4=40%, 5=10%, 6=12%
These follow-on results are so very^lots extremely unlikely that I would suggest that someone has manipulated the system. Maybe they replaced all the die with another set.

well, if i built a truly random device, most likely i will insert more than one dice inside (the device use one until the dice hit 6 then device change dice), even if they got their own bias, the output would be more unpredictable,

as you said, These follow-on results are so very^lots extremely unlikely
also mean totally unpredictable,

i think i am confused,
if let say a company built a truly random device, and want to sell it, it must proves it is truly random, so how will he proves the device is truly random?

A. roll the device for 100 million times and let us see the statistic of output (which i think is quite reasonable to request if i am a buyer)

B. construct a mathematical function that will output number based on the secret key you put inside before rolling, anyone who got this key, would know the next number,

is truly random equal to B? but B is not random, it just mathematical function that output number,

01 Jul 2018, 11:35

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17452
Location: In your JS exploiting you and your system

revolution

You can build a TRNG device from a resistor. You can measure small changes in resistance due to thermal noise. Your output will have some bias, it will generate more low levels, or more high levels, it doesn't matter which, but there will be more of one level than the other. So usually an unbiasing circuit is added to "even out" the low-to-high ratio. If you were to take the raw biased output you could compress it. There is no law of randomness that says you can't compress the output, only that the next output be unpredictable. You can have a random biased output with an expected outcome of 60% high level and 40% low level, and still not be able to predict the next output level.

01 Jul 2018, 14:23

Furs

Joined: 04 Mar 2016
Posts: 1489

Furs

Ok, that makes sense now, you're right with that Smile

01 Jul 2018, 20:59

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17452
Location: In your JS exploiting you and your system

revolution

sleepsleep wrote:

as you said, These follow-on results are so very^lots extremely unlikely
also mean totally unpredictable,

No, I meant that the outcomes you showed were unbelievable in the way that the distribution changed so radically. And since that type of behaviour is so unlikely then another reason is going to be more likely, i.e. that someone has changed the die to another set.

You can't have a dice give you 16.6% 1's after 100k throws, and then suddenly give you 1% 1's for the next 100k throws, that would seriously challenge the known laws of statistics. The probabilities are so low as to be virtually impossible that it is the same dice.

02 Jul 2018, 01:41

sleepsleep

sleepsleep wrote:

let say, in 10k draws of a dice,
dice A got each faces appears 16.6%
dice B got 1=20%, 2=5%, 3=3%, 4=40%, 5=10%, 6=12%
dice C got 1=1%, 2=20%, 3=1%, 4=20%, 5=5%, 6=53%

sleepsleep wrote:

but what if i tell you, we keep on rolling the dice for another 100k and now
dice A got 1=1%, 2=20%, 3=1%, 4=20%, 5=5%, 6=53%
dice B got each faces appears 16.6%
dice C got 1=20%, 2=5%, 3=3%, 4=40%, 5=10%, 6=12%

the first is 10k, the second is 100k, Laughing

02 Jul 2018, 09:01

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17452
Location: In your JS exploiting you and your system

revolution

Still an unbelievable outcome. The odds of such a thing happening by chance are so remote that some other explanation is more likely. I'd suggest that you simply relabelled the die.

02 Jul 2018, 09:55

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