Random number generator - please make it more random

[Lord_WC]

Alright, I admit that I am not a mathematician and definitely not a statistician.
But...
I was just beating on the dummy till its death, 213 hits, and the results are:
No clusters of 13,16,8
2 clusters of 3 2's
1 cluster of 3 5's
2 clusters of 3 13's
1 cluster of 3 20's
and...
1 cluster of 4 3's

OK, so no large clusters of 1's this time (there were 2 in a row, but I didn't record those)...

Now tell me, is this just stupid old me, or does look just a tad weird?

My point was only that 3 numbers are just that, 3 numbers. It's only a coincidence that we think 1 has a special meaning, but it has not. 3 consecutive 1s have the exact same chance as any 3 (same or different) numbers. It doesn't matter.

And random is random. You can roll 1000000000 1s in a row, that does not tell anything about the randomness of the random generator.

My personal best was 4 20s in a row while vorpaling stuff, it looked great (knowing that those are actually 4 20s in 8 rolls)

[Drallac]

http://en.wikipedia.org/wiki/Birthday_problem

statistics is a funny think that is often weird, like someone else said this is a dead horse. "Clusters" of numbers as you say, are in fact proof it is random, otherwise if there were never clusters randomness could never occur, as Tim Minchin said "as we know things that have a 1 in 64 000 000 chance if happening, happen all the time"

[BurningDownTheHouse]

My point was only that 3 numbers are just that, 3 numbers. It's only a coincidence that we think 1 has a special meaning, but it has not. 3 consecutive 1s have the exact same chance as any 3 (same or different) numbers. It doesn't matter.

And random is random. You can roll 1000000000 1s in a row, that does not tell anything about the randomness of the random generator.

My personal best was 4 20s in a row while vorpaling stuff, it looked great (knowing that those are actually 4 20s in 8 rolls)

And yet I can't help but wonder.
So many clusters in such a small sample range? Some of them multiple times?
I guess that the only way to be sure will be to record each number and then analyze the entire data set.

I'm sure that in the long run it will add up just fine. But clustering like this in small samples are deterministic to this kind of game.

[Keybreaker]

how'd you work those out?

sincere curiosity since it's been a while since i played with statistics.

to my mind it's both questions are answered by the number of people minus one dived by the number of days in the (normal) year. or:

(N-1)/365

which i believe is right as you can only be 100% certain to have two people with the same birthday once you have 366 or more (as then you would have one person to match every day and then one left over to guarantee the duplicate day).

in which case you have a 50% chance at around 182 and a 99% chance around 361 (spreadsheet floating point accuracy not withstanding)

correct me if i'm wrong =)

The "Birthday Paradox" is a well known one and quite extensively explained here: http://en.wikipedia.org/wiki/Birthday_problem

In probability theory, the birthday problem, or birthday paradox[1] pertains to the probability that in a set of randomly chosen people some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (including February 29 births). But perhaps counter-intuitively, 99% probability is reached with just 57 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (except February 29) is equally probable for a birthday.

[BurningDownTheHouse]

http://en.wikipedia.org/wiki/Birthday_problem

statistics is a funny think that is often weird, like someone else said this is a dead horse. "Clusters" of numbers as you say, are in fact proof it is random, otherwise if there were never clusters randomness could never occur, as Tim Minchin said "as we know things that have a 1 in 64 000 000 chance if happening, happen all the time"

This is actually fascinating, yet it doesn't explain to me how I can determine the "expected" number of clusters in a given test.

If you can come up with something like that, it will either completely defeat my arguments and I will capitulate, or it will show that I am on to something.

[BurningDownTheHouse]

You have 213 samples from, i don't know millions of rolls a day?

The problem is you see significance in rolling the same number as before. You probably think rolling 2,2,2 is somehow different than rolling 3 numbers you just make up. But esentially those two examples are the same.

I understand that, that's why I said that I'll try to get a whole list and analyze it.

[Lord_WC]

And yet I can't help but wonder.
So many clusters in such a small sample range? Some of them multiple times?
I guess that the only way to be sure will be to record each number and then analyze the entire data set.

I'm sure that in the long run it will add up just fine. But clustering like this in small samples are deterministic to this kind of game.

You have 213 samples from, i don't know millions of rolls a day?

The problem is you see significance in rolling the same number as before. You probably think rolling 2,2,2 is somehow different than rolling 3 numbers you just make up. But esentially those two examples are the same.

[SiliconShadow]

We all know that some dice in DDO are weighted.

However some dice should not be, but for example when I roll to hit and strike a vorpal, if I get a 20 then most of the time the following striking will also be a 20, then looking at the values you often see the faster you strike the more numbers appear clustered as put.

This has led me to the conclusion that due to some code optimisation in order to make the random function perform better has caused this because no random generation that is true random or pseudo random has that sort of frequent clustering.

The "random" numbers in DDO do cluster more than any random set should when taken in close fast proximity, either due to weighting or optimisation it happens and is obvious, the most obvious is when using many shot with slaying arrows most of the procs when hasted double proc sometimes triple proc if there is lag.

Optimisation / Weighting... both?

[MrLarone]

The "Birthday Paradox" is a well known one and quite extensively explained here: http://en.wikipedia.org/wiki/Birthday_problem

sweet, ta!

[Draccus]

In over 500 UMD rolls recorded, I am four times as likely to roll a 1 as I am a 20.

My theory is that Turbine uses skewed dice rolls to try to balance the game that they completely unbalanced with ridiculous loot and exploitable monster AI.

[BurningDownTheHouse]

In over 500 UMD rolls recorded, I am four times as likely to roll a 1 as I am a 20.

My theory is that Turbine uses skewed dice rolls to try to balance the game that they completely unbalanced with ridiculous loot and exploitable monster AI.

There you go then.
Can anyone tell me if this is an acceptable sample size? And if so, is it an "acceptable"/ "expected" result?

[Keybreaker]

Part of the issue here is that humans are not evolutionarily programmed to recognize randomness. We are programmed to recognize patterns... even when such patterns do not exist.

In the dark... given limited information... a few blurry shapes...

Caveman A: Awww, prolly nothin'. Just something random.
Caveman B: Ack! Was that a face?? Was that a bear??

Imagine 10,000 caveman As and 10,000 caveman Bs... The nervous, pattern-recognizing Bs are more likely to survive and procreate. The laid-back, randomness appreciating As might be right sometimes, heck even most of the times... but sometimes they will be at the spear-end of a jealous neighbor, or bear-food.

We are programmed with an observer bias to see patterns, even when they are not there.

[Drallac]

This is actually fascinating, yet it doesn't explain to me how I can determine the "expected" number of clusters in a given test.

If you can come up with something like that, it will either completely defeat my arguments and I will capitulate, or it will show that I am on to something.

CHALLENGE ACCEPTED!

Think of it this way, the value of pi, is irrational meaning it in theory goes on forever. Lets look at pi, pi to 1000 places which is here: http://c2.com/cgi/wiki?ValueOfPi

within pi to 1000 places there is:
1 set of 000
2 sets of 111
1 set of 555
1 set of 999999 (six nines)

and no more sets of triples, granted these arent randomly generated numbers, but it is from a small sample of what could effectively be random numbers as it is just a list.

Repetition is almost required in an infinite sequence of numbers otherwise it cannot be random, if there is no randomness an algorithm must be applied, similarly if you want to remove clusters of numbers the randomness is removed.

I gotta head to an exam but i will be back and try to explain better

[Lord_WC]

We all know that some dice in DDO are weighted.

However some dice should not be, but for example when I roll to hit and strike a vorpal, if I get a 20 then most of the time the following striking will also be a 20, then looking at the values you often see the faster you strike the more numbers appear clustered as put.

This has led me to the conclusion that due to some code optimisation in order to make the random function perform better has caused this because no random generation that is true random or pseudo random has that sort of frequent clustering.

The "random" numbers in DDO do cluster more than any random set should when taken in close fast proximity, either due to weighting or optimisation it happens and is obvious, the most obvious is when using many shot with slaying arrows most of the procs when hasted double proc sometimes triple proc if there is lag.

Optimisation / Weighting... both?

If you had EVERY roll EVER made by ddo probably you could analyze it. Otherwise the samples you take are just too insignificant compared to the vast numbers. Statistically it can happen that in the first 2 years of ddo noone ever rolled a 20, and in the next two years the frequency of 20s was 30%, it still wouldn't say anything about the randomness.

(and by randomness I mean computer generated randomness, which is not true random strictly speaking)

By analyzing samples you could state, that this sample of say 10.000 results had only 0,01% of appearing in a random environment. That would mean that happens in every 100 million rolls. Considering how many people are online, how many servers are and how many rolls are made, this really couldn't take long.

[BurningDownTheHouse]

CHALLENGE ACCEPTED!

Think of it this way, the value of pi, is irrational meaning it in theory goes on forever. Lets look at pi, pi to 1000 places which is here: http://c2.com/cgi/wiki?ValueOfPi

within pi to 1000 places there is:
1 set of 000
2 sets of 111
1 set of 555
1 set of 999999 (six nines)

and no more sets of triples, granted these arent randomly generated numbers, but it is from a small sample of what could effectively be random numbers as it is just a list.

Repetition is almost required in an infinite sequence of numbers otherwise it cannot be random, if there is no randomness an algorithm must be applied, similarly if you want to remove clusters of numbers the randomness is removed.

I gotta head to an exam but i will be back and try to explain better

And yet my (almost 5 times) shorter list has shown more clustering than you have shown here...
Good luck with the test.

[Lord_WC]

And yet my (almost 5 times) shorter list has shown more clustering than you have shown here...
Good luck with the test.

The example was just an example to show that repetition happens. You cannot compare an irrational number (which is NOT random digits following each other) with 10 different outcomes (digits from 0-9) to a supposedly random sample with 20 different outcomes.

Just for fun, here is 213 d20 rolls from ddo:
10,10,19,6,16,11,16,6,6,1,19,9,17,7,5,8,18,8,18,9, 9,6,15,1,12,14,9,18,9,5,18,18,10,18,7,16,10,2,15,1 4,8,17,17,14,
15,17,15,13,12,17,19,12,11,20,16,8,8,9,15,5,3,7,6, 17,12,13,2,8,13,13,3,7,8,13,14,8,18,20,2,1,9,17,5, 16,2,3,2,5,4,
6,6,12,10,14,1,12,4,14,12,17,8,9,11,7,17,5,4,8,12, 9,10,3,19,17,12,4,15,9,17,3,2,11,3,1,13,2,6,12,5,1 1,20,10,10,2,
19,20,4,20,20,16,7,7,17,14,4,7,5,14,12,2,8,3,18,4, 14,5,6,15,10,14,16,12,10,1,7,4,7,18,17,12,16,8,1,1 5,15,6,5,19,
19,18,19,18,12,5,16,18,9,8,7,5,13,1,2,9,5,19,18,17 ,2,8,15,17,19,20,1,7,6,14,5,10,10,18,4

No triplets here as far as i can see. Does this mean anything? I don't think so

[sweez]

The thing I find most interesting about this thread is the fact that you decided to remove your HP bar from the screenshot.

[SiliconShadow]

If you had EVERY roll EVER made by ddo probably you could analyze it. Otherwise the samples you take are just too insignificant compared to the vast numbers. Statistically it can happen that in the first 2 years of ddo noone ever rolled a 20, and in the next two years the frequency of 20s was 30%, it still wouldn't say anything about the randomness.

(and by randomness I mean computer generated randomness, which is not true random strictly speaking)

By analyzing samples you could state, that this sample of say 10.000 results had only 0,01% of appearing in a random environment. That would mean that happens in every 100 million rolls. Considering how many people are online, how many servers are and how many rolls are made, this really couldn't take long.

It is impossible for these patterns to happen and they do happen for 14 months I have played this game they are obvious.

As I stated it is one of two things occuring, an optimisation in which results are only refetched from the randomiser every x ms, or the numbers come from a lookup table which means patterns repeat obviously on that CPU thread (in which case Jo blogs on another instance will have a different thread for the randomiser to himself) OR the dice are weighted.

Pseudo random and true random are different and there are dozens of ways of optimising something like this that is a key element of such a system that could produce this clustering effect, the dice rolls are not, cannot be and will never be truely random and will always produce clustering in patterns if there is clustering in the first place.

The example was just an example to show that repetition happens. You cannot compare an irrational number (which is NOT random digits following each other) with 10 different outcomes (digits from 0-9) to a supposedly random sample with 20 different outcomes.

Just for fun, here is 213 d20 rolls from ddo:
10,10,19,6,16,11,16,6,6,1,19,9,17,7,5,8,18,8,18,9, 9,6,15,1,12,14,9,18,9,5,18,18,10,18,7,16,10,2,15,1 4,8,17,17,14,
15,17,15,13,12,17,19,12,11,20,16,8,8,9,15,5,3,7,6, 17,12,13,2,8,13,13,3,7,8,13,14,8,18,20,2,1,9,17,5, 16,2,3,2,5,4,
6,6,12,10,14,1,12,4,14,12,17,8,9,11,7,17,5,4,8,12, 9,10,3,19,17,12,4,15,9,17,3,2,11,3,1,13,2,6,12,5,1 1,20,10,10,2,
19,20,4,20,20,16,7,7,17,14,4,7,5,14,12,2,8,3,18,4, 14,5,6,15,10,14,16,12,10,1,7,4,7,18,17,12,16,8,1,1 5,15,6,5,19,
19,18,19,18,12,5,16,18,9,8,7,5,13,1,2,9,5,19,18,17 ,2,8,15,17,19,20,1,7,6,14,5,10,10,18,4

No triplets here as far as i can see. Does this mean anything? I don't think so

Dice number:Times - 1:9, 2:11, 3:7, 4: 9, 5:14, 6: 11, 7:12, 8:14, 9:12, 10:12, 11:5, 12:14, 13:7, 14:11, 15:10, 16:9, 17:15, 18:14, 19:10, 20:7
Mean 10.5493
Median 10
Mode 17
St Dev 5.643803
Clusters 14
Non Clusters 198
% clustered 7.07
Max cluster spacing 42

Is this random? It is pseudo random definitely the distribution is almost perfect
Is it weighted? No
Is it optimised in some way that makes this clustering happen? We can't tell from this set but from the small sample it could be worth checking if anyone is ever bored enough.

We do not know how the servers are put together, how "instances" are seperated, how and where each dice roll goes to for a number, but it is not true random.

What we are most likely looking at is something like:

[bokaboka]

Screenshot or it didn't....... nvm

[BurningDownTheHouse]

The example was just an example to show that repetition happens. You cannot compare an irrational number (which is NOT random digits following each other) with 10 different outcomes (digits from 0-9) to a supposedly random sample with 20 different outcomes.

Just for fun, here is 213 d20 rolls from ddo:
10,10,19,6,16,11,16,6,6,1,19,9,17,7,5,8,18,8,18,9, 9,6,15,1,12,14,9,18,9,5,18,18,10,18,7,16,10,2,15,1 4,8,17,17,14,
15,17,15,13,12,17,19,12,11,20,16,8,8,9,15,5,3,7,6, 17,12,13,2,8,13,13,3,7,8,13,14,8,18,20,2,1,9,17,5, 16,2,3,2,5,4,
6,6,12,10,14,1,12,4,14,12,17,8,9,11,7,17,5,4,8,12, 9,10,3,19,17,12,4,15,9,17,3,2,11,3,1,13,2,6,12,5,1 1,20,10,10,2,
19,20,4,20,20,16,7,7,17,14,4,7,5,14,12,2,8,3,18,4, 14,5,6,15,10,14,16,12,10,1,7,4,7,18,17,12,16,8,1,1 5,15,6,5,19,
19,18,19,18,12,5,16,18,9,8,7,5,13,1,2,9,5,19,18,17 ,2,8,15,17,19,20,1,7,6,14,5,10,10,18,4

No triplets here as far as i can see. Does this mean anything? I don't think so

This list doesn't even have many doubles, is this from DDO?