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sleepsleep



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I am perplexed by this scenario,

A draw result contained 23 numbers, 1st, 2st, 3rd, 10 special and 10 consolation,

And most likely, the next draw result will be totally different from these 23 numbers.

There seems like no relationship in each draw,
There are equal chances to get one of the previous draw numbers,

But why one hardly get those exact number to reappear in next or third draw? There usually a period of few months (hundred draws) then only they reappeared,

Does having past information could somehow affect future information?
Post 27 Jun 2018, 21:08
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revolution
When all else fails, read the source


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sleepsleep wrote:
Does having past information could somehow affect future information?
It depends how the drawing is done. If it is truly random the the answer is "no". If there is some storage or memory in the system the the answer is "yes".

Or if the officials are corrupt then the answer will be "anything is possible".
Post 27 Jun 2018, 22:30
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sleepsleep



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i am slightly confused by what is the definition of your truly random,

now let say we use your truly random device and draw a series of dice numbers,
1,4,5,6,5,5,2

could we say in a higher certainty that such series wouldnt repeat in the next draw? (this is what i mean by having past information, it somehow dictates how future proceed)

then we use the truly random device to draw next series,
5,1,3,6,2,1,4

we are very sure that there is no relationship in each draw,
there is equal amount of possibilities and chances that each number from 1 to 6 could be drawn,

but why it looks impossible to have exact past draw series?

so could we predict the next number by having lots of past series by assuming it got lower chances to match previous drawn number series?
Post 28 Jun 2018, 18:24
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Furs



Joined: 04 Mar 2016
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sleepsleep wrote:
now let say we use your truly random device and draw a series of dice numbers,
1,4,5,6,5,5,2

could we say in a higher certainty that such series wouldnt repeat in the next draw? (this is what i mean by having past information, it somehow dictates how future proceed)
Yes, if you bet then it's extremely wise to bet that the next one won't be 1,4,5,6,5,5,2.

It has nothing to do with memory, it's because it's extremely unlikely to have an exact sequence -- MUCH more unlikely than having ANY other sequence.

If you bet on the next draw not being 1,1,1,1,1,1,1 then it would be the exact same thing. In both cases the probability is the same, which is really, really, really low.


Let's simplify it to a single dice roll. Say you just rolled a 6. You say with confidence that the next one won't be a 6, and you'll most likely be correct. This has nothing to do with memory. It's just that the next one being 6 is only 1/6 chance.

Clearly 5/6 (83%) is much more likely than 1/6 (17%).


On a similar note, a lot of people think that getting two 6s in a row means that the second one is much rarer than 1/6, but that is false.

It's no different than picking any sequence whatsoever. Two 6s in a row is not less likely than the sequence 6 followed by 5, they're equally likely as 6 followed by 4, and so on. Any other specific sequence has the same chance.

But remember that when you look for a specific sequence, it's "either THIS specific sequence, or ANY other sequence". It's not a specific sequence vs another specific sequence (which are equal), it's a specific sequence vs ALL the other sequences. All of them.
Post 28 Jun 2018, 18:57
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Tomasz Grysztar
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Joined: 16 Jun 2003
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Furs wrote:
On a similar note, a lot of people think that getting two 6s in a row means that the second one is much rarer than 1/6, but that is false.
I think this is loosely related to another interesting fact. If you roll twice in a sequence, probability of rolling 6 and 6 is the same as probability of rolling 6 followed by 5. BUT, if you roll two dice simultaneously and do not care which is which, rolling 5 and 6 is more probable than rolling 6 and 6, because there are two possible sequences that give you 5 and 6 (either 5-6 or 6-5) but only one sequence that gives you 6 and 6.

For the same reason when you roll a longer sequence, probability that all numbers will be different is higher than probability that all numbers will be the same.
Post 28 Jun 2018, 19:30
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sleepsleep



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does the nature of a truly random device ~ will not repeat its past sequence?

let use a truly random dice,
regardless of x count of roll, each number still has equal amount of chances to get rolled, am i correct here?

as mentioned by tomasz,
Quote:
If you roll twice in a sequence, probability of rolling 6 and 6 is the same as probability of rolling 6 followed by 5


so why past dice result sequence is a factor here?
Quote:
Yes, if you bet then it's extremely wise to bet that the next one won't be 1,4,5,6,5,5,2.


is the probability of rolling 6 and 6 and 6 then 6 still same? if probability of each rolling is same, why it seems harder to get 6,6,6,6,6,6 sequence?
Post 28 Jun 2018, 20:56
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revolution
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sleepsleep wrote:
does the nature of a truly random device ~ will not repeat its past sequence?
No. True randomness has nothing to do with repeatability. It has to do with unpredictability. The sequences can repeat, and they have to repeat eventually, else you run out of unique sequences. If you consider a coin toss. There are only two outcomes (ignoring the edge for the moment), so if you forbid repeats somehow then after two throws, one head and one tail, you have no more sequences available. So a head can be followed by a head. The whole point of randomness is to ensure that each sequences has the same probability to occur at each sampling. So if a sequence has already occurred, then that same sequences can occur again with the same probability as before.


Last edited by revolution on 28 Jun 2018, 23:04; edited 1 time in total
Post 28 Jun 2018, 21:57
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revolution
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sleepsleep wrote:
is the probability of rolling 6 and 6 and 6 then 6 still same? if probability of each rolling is same, why it seems harder to get 6,6,6,6,6,6 sequence?
It is just as "hard" as getting the exact sequence 1,4,3,2,5,3 or 6,4,2,6,5,3 or any other sequence you want to think of. It is only your mind that thinks the 6,6,6,6,6,6 sequence is special, it isn't.
Post 28 Jun 2018, 22:00
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sleepsleep



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somehow i was thinking about this,
does world event affect random, earthquake, volcano eruptions, flooding, solar flare, etc,

could we say in higher confidence that it is harder to get repeat observed sequence?
Post 29 Jun 2018, 08:26
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sleepsleep



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revolution wrote:
sleepsleep wrote:
is the probability of rolling 6 and 6 and 6 then 6 still same? if probability of each rolling is same, why it seems harder to get 6,6,6,6,6,6 sequence?
It is just as "hard" as getting the exact sequence 1,4,3,2,5,3 or 6,4,2,6,5,3 or any other sequence you want to think of. It is only your mind that thinks the 6,6,6,6,6,6 sequence is special, it isn't.


very true,
but 6,6,6,6,6,6 sort of breaking the nature of random ( which is probably why i perceived it as harder to roll )
Post 29 Jun 2018, 09:50
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Furs



Joined: 04 Mar 2016
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Tomasz Grysztar wrote:
Furs wrote:
On a similar note, a lot of people think that getting two 6s in a row means that the second one is much rarer than 1/6, but that is false.
I think this is loosely related to another interesting fact. If you roll twice in a sequence, probability of rolling 6 and 6 is the same as probability of rolling 6 followed by 5. BUT, if you roll two dice simultaneously and do not care which is which, rolling 5 and 6 is more probable than rolling 6 and 6, because there are two possible sequences that give you 5 and 6 (either 5-6 or 6-5) but only one sequence that gives you 6 and 6.

For the same reason when you roll a longer sequence, probability that all numbers will be different is higher than probability that all numbers will be the same.
Ah yes, I hadn't thought of that, good mention Smile

sleepsleep wrote:
as mentioned by tomasz,
Quote:
If you roll twice in a sequence, probability of rolling 6 and 6 is the same as probability of rolling 6 followed by 5


so why past dice result sequence is a factor here?
It's not a factor. The factor is that you are asking for a specific sequence here.


Do this experiment. Flip a coin 5 times. Getting 5 heads in all of the flips is rare, right? Ok, so now ask for a specific sequence like: head,tail,tail,head,tail.

See how often that pops up.

Really just put all the sequence together. To simplify, toss the coin twice. You want heads twice in a row. Let's look at true random possibilities.
Code:
head->head  < what you want
head->tail  < nope
tail->head  < nope
tail->tail  < nope    
So out of 4 random possibilities, you want ONE of them, of course it's going to be rare! 25% to be exact. You have a 75% chance to lose this bet. It has nothing to do with the first one "influencing" the rarity of the second one. Just because the first one is head doesn't mean second one is rarer. The reason is that if first one is tail, you've already lost, but there are many sequences that start with tail too, just as many as those that start with head, and equally likely.
Post 29 Jun 2018, 11:50
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revolution
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sleepsleep wrote:
somehow i was thinking about this,
does world event affect random, earthquake, volcano eruptions, flooding, solar flare, etc,
We don't know. It depends upon how you generate your random numbers. If your RNG is seeded/controlled/generated by something that can be affected by one of those events then the answer is "yes". But to be truly random it should still be unpredictable. Adding influence doesn't necessarily mean you can suddenly predict a random event. The outcome can still be completely random and be influenced by some event you choose.
Post 29 Jun 2018, 12:21
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revolution
When all else fails, read the source


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Location: Squiddler's Patch
sleepsleep wrote:
but 6,6,6,6,6,6 sort of breaking the nature of random
It is just as likely as every other sequence. If it never comes up after millions of tries then you should be worried that your dice might be faulty.
sleepsleep wrote:
( which is probably why i perceived it as harder to roll )
Harder than what? Do you mean it less likely than other sequences?
Post 29 Jun 2018, 12:26
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sleepsleep



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revolution wrote:

Harder than what? Do you mean it less likely than other sequences?

ya, less likely to roll 6,6,6,6,6,6 since it is hardly random, compare to 6,4,1,5,5,3

revolution wrote:

If it never comes up after millions of tries then you should be worried that your dice might be faulty.

but historical sequence is unrelated in the sense, each number has equal chance to get roll

how about 1 dice to roll 6,6,6,6,6,6 versus 6 dices to roll all 6 at the same time?
which one got higher probability, i would bet 6 dices but why?

and what is truly random device? if the device is on earth, i assume most likely it would gets affected by earth condition,

Furs wrote:

Do this experiment. Flip a coin 5 times. Getting 5 heads in all of the flips is rare, right? Ok, so now ask for a specific sequence like: head,tail,tail,head,tail.

for a head tail 10 equal comparison, you might need to extend the sequence to 33 flips,
1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0

at least i am quite sure it is near difficult to row the sequence as i written above in 33 flips, eg.
Post 29 Jun 2018, 16:25
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Furs



Joined: 04 Mar 2016
Posts: 1301
sleepsleep wrote:
ya, less likely to roll 6,6,6,6,6,6 since it is hardly random, compare to 6,4,1,5,5,3
This is wrong. They're both equally random.

sleepsleep wrote:
how about 1 dice to roll 6,6,6,6,6,6 versus 6 dices to roll all 6 at the same time?
which one got higher probability, i would bet 6 dices but why?
They're the same.

Keep in mind that, say, assuming you rolled 6 five times already, the next one being 6 will be 1/6 chance (six-faced die) so quite high to be 6 again. However this completely misses the fact that you are extremely unlikely to even get to this point (i.e. roll 6 five times) since you already got 5 out of 6 of the entire sequence correct.

Any failure up to this point would effectively stop you before you continued, but people don't think of that.

sleepsleep wrote:
and what is truly random device? if the device is on earth, i assume most likely it would gets affected by earth condition,
True random is a mathematical/statistical construct so it's not affected by anything Wink Your questions are of that nature anyway, not of a practical random sense in the real world.
Post 29 Jun 2018, 16:57
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sleepsleep



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i assume historical sequence of random output (required) in order to determine if a random output is quality, good or bad,

which mean, if 6,6,6,6,6,6 occurred in less than 30 dices roll, it is bad random?

Furs wrote:

True random is a mathematical/statistical construct so it's not affected by anything

i would hope if you could elaborate about this, true random,
Post 30 Jun 2018, 01:06
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revolution
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sleepsleep wrote:
i assume historical sequence of random output (required) in order to determine if a random output is quality, good or bad,

which mean, if 6,6,6,6,6,6 occurred in less than 30 dices roll, it is bad random?
You will need more than 30 rolls to test the validity of the dice. You could get 6,6,6,6,6,6 on the very first try, but that doesn't mean anything is wrong. Instead you need to do many hundreds or thousands of rolls to see if your dice is well balanced or to try to find any bias.
Post 30 Jun 2018, 11:56
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Furs



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sleepsleep wrote:
i assume historical sequence of random output (required) in order to determine if a random output is quality, good or bad,

which mean, if 6,6,6,6,6,6 occurred in less than 30 dices roll, it is bad random?
Man, you don't get it do you? 6,6,6,6,6,6 is equally likely as any other specific sequence. There's nothing "less random" about it than, say, 1,2,3,4,5,6 or 1,3,6,2,5,4.

However if you get any sequence twice within 30 rolls (like your 6,6,6,6,6,6 sequence), it's probably biased and not true random, or it could be a coincidence but very rare so...

True random means that there's no inherent bias and all are equally likely (or at least, are exactly as likely as specified).
Post 30 Jun 2018, 14:36
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sleepsleep



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true random means no inherent bias, which mean the historical sequence must conform to the nature of balance, am i correct?

in order to know if an object produces true random, we must rolls the output for thousand or million times and check if the result got bias or not,

but doesnt it conforms to nature of balance equal to some sort of bias?

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%

but
dice A got 50% repeated sequence,
dice B got 10% repeated sequence,
dice C got 20% repeated sequence,

which is a better true random dice?
Post 30 Jun 2018, 17:05
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Furs



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sleepsleep wrote:
true random means no inherent bias, which mean the historical sequence must conform to the nature of balance, am i correct?

in order to know if an object produces true random, we must rolls the output for thousand or million times and check if the result got bias or not,
You'd technically have to roll an infinite amount of times Wink That's why I said it's a math construct: it is an ideal property, which is defined, NOT measured. Nothing in math is measured, you don't need "data" for math since it's theoretical, it's not like natural sciences. In math, of course, we deal with infinitely small things or infinitely large all the time, so you shouldn't be surprised it deals with ideal/true randomness too.

sleepsleep wrote:
but doesnt it conforms to nature of balance equal to some sort of bias?

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%

but
dice A got 50% repeated sequence,
dice B got 10% repeated sequence,
dice C got 20% repeated sequence,

which is a better true random dice?
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, which should not exist for true randomness, since you get repeated sequences too often. (assuming the sequences are long enough, otherwise it's fine if they repeat, it depends on their length, you can easily calculate the sequence's probability btw)

(I know your example is fictional, but in the real world, things do have memory, even if the ideal true randomness statistically should not -- that's beyond statistics though, it's more like looking at either computer code or molecular structures or the person who throws the dice... computer pseudo-random code could even be doing it on purpose!)
Post 30 Jun 2018, 18:40
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