Dice is not random at all

[Mart]

I have some serious doubt about the dice. I just played a few games in which it was nothing but 5's and 9's. Hardly any 7 or 6 or 8 was rolled. When I look at statistics after the game, a normal distribution cannot be seen in the times a certain number is rolled.
This game is far from perfect. It laggs, it crashes occasionally, but I at least expect that i can play the game in a fair way.

[N o i r]

fearenough eredeti hozzászólása:

sparky noir do not want to do anything but disagree. it is like telling a flat earth-er that the earth is not flat you will not get anywhere. according to noir Catan is supposed to almost always have a runaway winner sometimes it will be you some times anougher. It is not supposed to mimic a board game that is a close fun battle win or lose in at lest 4 out of 5 games that is really fun. No its supposed to be a boring runaway win, boring if win or lose. He will never see that he will only see what fits in his really small box and that is a bunch of losers upset that they lost

It's hilarious that you of all people say that, considering that statistics is an established field of science, and dice distributions is a mature field that is well understood by now.

The only one behaving like a flat earther is you, making empty claims fueled only by confirmation bias and fallacious anecdotal evidence.

Anyone with a cursory understating of statistics knows this very well - the reason I disagree is that no evidence of such claims of non-randomness has been presented, save for that 5 years old screenshot that cannot be easily reproduced.

The devs don't bother answering because, quite frankly, there is nothing to answer to.

[noob master]

author="N o i r" eredeti hozzászólása:

"Random" is not the same thing as "balanced" - it is not supposed to be,

So it seems to me you don't understand how the concept of randomness vs pseudo-RNG, and my math didn't seem to help (or you didn't read it).

What you see on the computer is never "true randomness", the random algorithm on a computer works by using the HDD size, Network speed, current position of the mouse on the screen, current time in miliseconds, etc to generate results according to probabilities. If any of these parameters gets stuck, or doesn't change as often as needed to provide for true randomness, this is reflected in a poor distribution in the results. There's extensive research on this.

Supposedly pseudo-RNGs are not only limited in true randomness, but also is potentially predictable and even controllable (i.e. rolling dice faster or later as your time runs out returns a different result, that may be predictable), and people have written algorithms to break online poker servers using this knowledge. Anyway, THIS IS HOW pseudo-RNGs WORK! . This is a mathematical fact that they're limited. Take this article that talks about pseudo-rng exploits in a Texas Hold'em game (and there are many historic examples):
http://www.bluffnakedpoker.com/PDF/developer_gambling.pdf

While the results over the long time are supposed to balance out, they will produce low-likely distributions that would never happen as frequently in real life. Pure and Simple.

So if you really want real "Random" on a computer, you need to "balance" it. And I've proven why in the posts above.

In the real world of course it's the opposite, if you want "random" dice on a physical Catan board that sits on a table, you need to NOT "balance" it of course. But this doesn't apply to pseudo-RNGs. And that's because the dice themselves are random, whereas the pseudo-RNG is not. It's deterministic. It's a function with specific inputs and deterministic outputs.

[fearenough]

N o i r eredeti hozzászólása:

fearenough eredeti hozzászólása:

sparky noir do not want to do anything but disagree. it is like telling a flat earth-er that the earth is not flat you will not get anywhere. according to noir Catan is supposed to almost always have a runaway winner sometimes it will be you some times anougher. It is not supposed to mimic a board game that is a close fun battle win or lose in at lest 4 out of 5 games that is really fun. No its supposed to be a boring runaway win, boring if win or lose. He will never see that he will only see what fits in his really small box and that is a bunch of losers upset that they lost

It's hilarious that you of all people say that, considering that statistics is an established field of science, and dice distributions is a mature field that is well understood by now.

The only one behaving like a flat earther is you, making empty claims fueled only by confirmation bias and fallacious anecdotal evidence.

Anyone with a cursory understating of statistics knows this very well - the reason I disagree is that no evidence of such claims of non-randomness has been presented, save for that 5 years old screenshot that cannot be easily reproduced.

The devs don't bother answering because, quite frankly, there is nothing to answer to.

sorry i am a busy man i am well respected in my expertise but i have not got time for learning statistics. this is not a game about statistics there is no need if it was i would have no interest in playing

[N o i r]

sparky eredeti hozzászólása:

So it seems to me you don't understand how the concept of randomness vs pseudo-RNG, and my math didn't seem to help (or you didn't read it).

I understand it; it's been almost 20 years since when I learned this at uni, but I still remember, and can confirm it works the way you explained.

However, even pseudo-random can work well enough for something as simple as simulating dice: https://boallen.com/random-numbers.html.

The problem of Catan, as further exemplified in the colonst.io link that you provided, is that in the majority of situations, games are too short for the dice rolls to be distributed in any way that appears to be close to the expected curve.

sparky eredeti hozzászólása:

While the results over the long time are supposed to balance out, they will produce low-likely distributions that would never happen as frequently in real life. Pure and Simple.

What is your evidence for this statement?
EDIT: my Firewall blocks the link in your last post, something due to gambling.

[noob master]

author="N o i r" eredeti hozzászólása:

EDIT: my Firewall blocks the link in your last post, something due to gambling.

It's a research paper about how a bunch of programmers figured out the randomization algorithm used by an online poker site, and could infer on most hands what other people had in their hands with almost perfect accuracy, before any bet was placed.

author="N o i r" eredeti hozzászólása:

However, even pseudo-random can work well enough for something as simple as simulating dice: https://boallen.com/random-numbers.html.

Yes, for simulating 1 die. Not simulating distributions or combinations of 2 separately generated random dice. Read the Potential Issues section in here "https://en.wikipedia.org/wiki/Pseudorandom_number_generator".

Why do I have a feeling Catan Universe was coded using Java? Here's what they say about low quality pseudo-RNGs:

Java still relies on a linear congruential generator (LCG) for its PRNG,[6][7] which are of low quality—see further below.

Also, IMPORTANT: you'll notice on the Colonist.io, they are matching "total numbers" to get the "expected results". Again this is flawed, and you can have a look at https://boallen.com/random-numbers.html to see why totals don't equal good PRNG (i.e. look at the 2 images and notice they have each shade of grey appearing approx. the same number of times, but one of the php windows bitmap clearly the distribution is bad.)

author="N o i r" eredeti hozzászólása:

What is your evidence for this statement?

Ugh hello?? The numbers I've been posting? The fact that every 2-3 games I get 1 in 100 combinations of numbers, as well as sometimes one in a million combinations? I feel like you're not listening... I dare you to play a home game and see if you EVER:
1. get 2,3,11 or 12 (any single one) to show 10 times in 25 rolls
2. Or to get 4 or 5 not showing in 40+ rolls
3. Or to get 9 to show 11 times in 42 rolls

And even if you get any of these, it'll be once in many, many games. The fact that this happens so often in Catan Universe is blatantly unrealistic and typical of the php rand() on Windows from your link! Your link helps disprove your point that distributions don't prove pseudo-RNGs are bad! You see, scientists looked at the distributions and saw patterns, which helped them prove that the php rand() is a bad pseudo-RNG. I did the same with Catan Universe.

Instead of arguing with me on why Catan Universe is using a good pseudo-RNG, you should argue that the php rand() function is a "good enough" pseudo-RNG with those scientists... Their random distributions aren't as unlikely as the ones in Catan Universe, so you might have more luck there.

[noob master]

author="fearenough" eredeti hozzászólása:

sorry i am a busy man i am well respected in my expertise but i have not got time for learning statistics

Me neither, frankly I'm just having fun with all this math thing because it's hilarious how many people like "N o i r" simply say "oh well it's just random, it'll balance out and u just have to trust it" with the typical smugness of someone who doesn't really understand limitations of pseudo-RNGs.

And I agree, the distributions on Catan Universe are simply unrealistic, and I feel like I've softly proven this in at least 3 different ways

[fearenough]

yes i think you have done a great job on maths

[N o i r]

sparky eredeti hozzászólása:

It's a research paper about how a bunch of programmers figured out the randomization algorithm used by an online poker site, and could infer on most hands what other people had in their hands with almost perfect accuracy, before any bet was placed.

I see. The thing is, a randomization algorithm can definitely be written to be fair, depending on the OS and language used. In the case of a casino they have a vested interest on it not being fair. The developer of Catan Universe on the other hand do not have this conflict of interest, and in fact has already replied to similar criticism on the official forums stating that the RNG of the game is properly random.

sparky eredeti hozzászólása:

Yes, for simulating 1 die. Not simulating distributions or combinations of 2 separately generated random dice. Read the Potential Issues section in here "https://en.wikipedia.org/wiki/Pseudorandom_number_generator".

Why do I have a feeling Catan Universe was coded using Java? Here's what they say about low quality pseudo-RNGs:

Java still relies on a linear congruential generator (LCG) for its PRNG,[6][7] which are of low quality—see further below.

That article refers to RNGs that are seed-based. Hardware-based RNGs - such as those that read the CPU clock timer when the request is called - are much closer to real random, to the point of being practically equivalent.

sparky eredeti hozzászólása:

Also, IMPORTANT: you'll notice on the Colonist.io, they are matching "total numbers" to get the "expected results". Again this is flawed, and you can have a look at https://boallen.com/random-numbers.html to see why totals don't equal good random algorithm (i.e. look at the 2 images and notice they have the same total of number of each shade of grey, but one of the php windows bitmap clearly the distribution is bad.)

I'm not sure I follow you here, or what exactly is flawed in the Colonist approach.

sparky eredeti hozzászólása:

sparky eredeti hozzászólása:

Ugh hello?? The numbers I've been posting? The fact that every 2-3 games I get 1 in 100 combinations of numbers, as well as sometimes one in a million combinations? I feel like you're not listening... I dare you to play a home game and see if you EVER:
1. get 2,3,11 or 12 (any single one) to show 10 times in 25 rolls
2. Or to get 4 or 5 not showing in 40+ rolls
3. Or to get 9 to show 11 times in 42 rolls

And even if you get any of these, it'll be once in many, many games. The fact that this happens so often in Catan Universe is blatantly unrealistic and typical of the php rand() on Windows from your link! Your link helps disprove your point that distributions don't prove pseudo-RNGs are bad! You see, scientists looked at the distributions and saw patterns, which helped them prove that the php rand() is a bad pseudo-RNG. I did the same with Catan Universe.

Your anecdotal evidence is simply not statistically significant.

As I said, launching a 6-faced dice X times results in 6^X different possible outcomes, some of which are necessarily going to be extremely rare; by applying the same logic, I can examine the dice rolls of any one of my victories, calculate the chances of obtaining exactly that series of rolls, and conclude - erroneously - of being the luckiest player in the world.

Again, the only evidence that would count is a statistically significant sample that diverges from the expected result - your examples is not evidence of the RNG being broken.

sparky eredeti hozzászólása:

Instead of arguing with me on why Catan Universe is using a good pseudo-RNG, you should argue that the php rand() function is a "good enough" pseudo-RNG with those scientists... Their distributions aren't as biased as the ones in Catan Universe, so you might have more luck there.

Yes, php's rand() is notoriously terribad. However, we don't know exactly what algorithm Catan Universe uses. The administrators on the official forums have publicly stated that the dice is not rigged and that they are properly random, before locking the thread because the usual uninformed people that don't understand statistics kept repeating their fallacies without reading the evidence he was posting.

[fearenough]

hey I've moved on to a more fun game risk. dice work well and very positive reviews

[fearenough]

maybe nior can move over to there can try forums there since i think there dice are great he can jack of his ego on how they not at all random

[noob master]

author="N o i r" eredeti hozzászólása:

I'm not sure I follow you here, or what exactly is flawed in the Colonist approach.

Looking at the total appearances of each dice roll, after 1 million rolls is a horrible measure of how good a pseudo-RNG is, because:
- even though total numbers balance out
- distribution includes many very low likelihood sequences, which do not correspond to sequence probabilities - i.e. if you roll the dice 1.5 million times, and you get 10-15 one-in-a-million likelyhood scenarios like 3 coming up 10 times in 25 rolls, or 2 coming up 6 times in 10 rolls, this alone is sufficient evidence the RNG is bad. I got 3 of these over 20 games.
- in addition, you can have way to many low likelihood scenarios that aren't as rare, i.e. if in 1 million rolls, you keep getting distributions of 50 dice showing 9 coming up 11 times in 36 rolls, etc., there's a LIMIT TO HOW MANY OF THESE YOU CAN GET before it becomes unrealistic. I.e. if I roll 2 dice 1 million times, I should get an average of 10,000 sequences that have a one-in-a-hundred likelihood of appearing. Clearly CATAN has several in 2-3 games, which means instead of 10,000 of these sequences, it'll be more like 1 million which is horrendous. And this happened on both Colonist.io AND Catan Universe.

It's weird that Colonist.io is now saying "Balanced" dice replicates "ideal rolls", which is also dumb. Balanced dice don't replicate "ideal rolls", they replicate "ideal RANDOM"

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author="N o i r" eredeti hozzászólása:

Your anecdotal evidence is simply not statistically significant.

In my sample size it is definitely sufficient grounds for further investigation. If you go to the casino, and pick 3 numbers in a row on a roulette, and win every time, security will escort you out. 3 one-in-a-million situations in a handful of iterations is sufficient grounds for reasonable suspicion. Your smug attitude calling it "anecdotal" evidence is simply not true.

author="N o i r" eredeti hozzászólása:

your examples is not evidence of the RNG being broken.

You're running around in circles here. You keep saying I can't definitely prove the RNG is broken. Without looking at the source code, and running it of course I can't. But the RNG is bad, and in my sample it has consistently been bad. Maybe I'm the only one for whom the PRNG doesn't work, but for everyone else it doesn't give one-in-a-hundred situations every 10 rolls. Is that your argument?

author="N o i r" eredeti hozzászólása:

That article refers to RNGs that are seed-based. Hardware-based RNGs - such as those that read the CPU clock timer when the request is called - are much closer to real random, to the point of being practically equivalent.

You're making assumptions and approximations without limits here: what is "practically equivalent" to you?

1. As I said before, equivalent to real random means distributions and sequences of numbers are within reasonable probabilities. As I have proven with my sample size, they simply are not.

2. There are also many bad PRNGs out there, done in much more famous software, sometimes involving money. Why would you think Catan Universe would even consider investing in better PRNG software, when I'm sure they have limited resources, as well as smug developers such as yourself who may well simply trust the PRNG provided by, for example, JAVA (which is notoriously bad)? Let the numbers speak for themselves: many low-probability sequences = horrible PRNG. That's what the numbers are saying so far, feel free to prove me wrong with numbers.

------------------------------------------------------------------------------------------
Let's play a game: I'm a casino and you are a player. I then propose the following rules:
- you place a bet
- you roll two 6-sided dice 30 times in a row, and record the results
- if you get any of the numbers from 2 to 12 (any single one) to appear at least 8 times (not necessarily one after another), I'll give you 5 times your money.
- otherwise, you lose your bet.
Would you play with real dice? Or using the CATAN dice roll algorithm?

Would you play this? Because with real dice you have under 15% chance to win, which means I have an edge. But if you play with CATAN dice this won't hold, and chances are these repetitions will appear more often than in real life, as I have proven and many players have also noticed. And I would lose my money if I played with the CATAN Universe PRNG. And in a "true" RNG these sequence probabilities would hold, and I should still take your money.

Sequences matter in how good a PRNG is. Period.

And based on this alone, I'm not sure the admin actually understands what "properly random" actually is... I get that most people make dumb arguments, as well I may right now. But from my understanding it seems the inherent probabilities in sequences of dice on Catan Universe do not match expected probabilities of sequences from rolling real dice.

Yes, you get the same totals. Yes each number has an approximately equal chance to appear. But the order in which they appear determines how good the random algo is. And if the order is too unlikely, too often, it's a bad PRNG. Which they are not looking at. Because they're all smug thinking sequences don't matter, which all mathematicians and high level computer scientists agree that they do.

[noob master]

Let me repeat my concluding statement:
Sequences matter in how good a PRNG is. The frequency and distribution of low likelihood sequences of dice rolls on Catan Universe do not match expected probabilities of sequences from rolling real dice. The distribution lacks uniformity, the distribution is poor and distances between where certain values occur are not distributed as expected, according to probabilities.

And the proof for this is in the numbers I have been posting above. Many 1-in-100 roll situations in the same game (average of under 50 rolls), and frequent 1-in-1,000,000 situations in games not too far apart (max 100-150 rolls)

N o ir Please have a look at https://en.wikipedia.org/wiki/Pseudorandom_number_generator
in the Potential Issues section. What I'm describing here is 4 out of 5 issues:
* Lack of uniformity of distribution for large quantities of generated numbers;
* Correlation of successive values
* Poor dimensional distribution of the output sequence
* Distances between where certain values occur are distributed differently from those in a random sequence distribution.

[N o i r]

sparky eredeti hozzászólása:

Looking at the total appearances of each dice roll, after 1 million rolls is a horrible measure of how good a pseudo-RNG is, because [...] distribution includes many very low likelihood sequences

Yes, distributions may include very low likelihood sequences. This is also true for "real" random sequences.
As I explained before, the outcome of most random distributions are fairly rare, and that's completely normal.

sparky eredeti hozzászólása:

if you roll the dice 1.5 million times, and you get 10-15 one-in-a-million likelyhood scenarios like 3 coming up 10 times in 25 rolls, or 2 coming up 6 times in 10 rolls, this alone is sufficient evidence the RNG is bad

It is not, and stating this betrays your inexperience with statistics, I'm afraid. And please note, I am not saying this with intent to belittle or disparage you or your reasoning. As I said before, the probability of observing a random unspecified unusual occurrence without specifying beforehand neither the occurrence nor the timeframe of the observation is INFINTE.

Almost ALL random sequences will be extremely rare in some way, after the fact - this is your key misunderstanding.

sparky eredeti hozzászólása:

In my sample size it is definitely sufficient grounds for further investigation.

That's your opinion, and you are entitled to it. I will welcome, of course, any further investigation efforts from you or anyone else.

sparky eredeti hozzászólása:

You're running around in circles here. You keep saying I can't definitely prove the RNG is broken.

If you continue to present invalid evidence, I will have no choice but continue to reply that you are, in fact, not presenting valid evidence.
It is definitely possible to prove that the RNG is broken, and it is not difficult to try doing so. You just haven't done it so far, and I sincerely doubt anyone can.

sparky eredeti hozzászólása:

You're making assumptions and approximations without limits here: what is "practically equivalent" to you?

From https://en.wikipedia.org/wiki/Hardware_random_number_generator:

"These stochastic processes are, in theory, completely unpredictable for as long as an equation governing such phenomena is unknown or uncomputable, and the theory's assertions of unpredictability are subject to experimental test. This is in contrast to the paradigm of pseudo-random number generation commonly implemented in computer programs."

sparky eredeti hozzászólása:

Let's play a game: I'm a casino and you are a player. I then propose the following rules:
- you place a bet
- you roll two 6-sided dice 30 times in a row, and record the results
- if you get any of the numbers from 2 to 12 (any single one) to appear at least 8 times (not necessarily one after another), I'll give you 5 times your money.
- otherwise, you lose your bet.
Would you play with real dice? Or using the CATAN dice roll algorithm?

Would you play this? Because with real dice you have under 15% chance to win, which means I have an edge. But if you play with CATAN dice this won't hold, and chances are these repetitions will appear more often than in real life, as I have proven and many players have also noticed. And I would lose my money if I played with the CATAN Universe PRNG. And in a "true" RNG these sequence probabilities would hold, and I should still take your money.

Of course I would not play such a game, because the chances of rolling a number 8 or more times in 30 rolls is significantly lower than 20%.
Also, this specific occurrence will happen very rarely also in Catan Universe. Just because it happened once to you, it doesn't mean it will keep happening regularly.

sparky eredeti hozzászólása:

Let me repeat my concluding statement:

Sequences matter in how good a PRNG is. The frequency and distribution of low likelihood sequences of dice rolls on Catan Universe do not match expected probabilities of sequences from rolling real dice. The distribution lacks uniformity, the distribution is poor and distances between where certain values occur are not distributed as expected, according to probabilities.

You did not prove that the distribution of Catan Universe "lacks uniformity" or "is poor". The cherry-picked rare occurrences in your rolls are no evidence of this - you simply examined the rolls and noticed an arbitrary pattern that happens to be rare - you can do the same with most random sequences.

[noob master]

author="N o i r" eredeti hozzászólása:

Yes, distributions may include very low likelihood sequences. This is also true for "real" random sequences.
As I explained before, the outcome of most random distributions are fairly rare, and that's completely normal.

This were true if I asked the question: "How likely is it that we get the exact same distribution again". However, the question I'm asking is: "when rolling the dice 30 times, how likely is it that any single 2-12 result is repeated 8 times". In true random, and an infinite sequence, any sequence of 30 rolls will adhere to this probability. This is a mathematical fact, do you agree?

author="N o i r" eredeti hozzászólása:

It is not, and stating this betrays your inexperience with statistics, I'm afraid. And please note, I am not saying this with intent to belittle or disparage you or your reasoning. As I said before, the probability of observing a random unspecified unusual occurrence without specifying beforehand neither the occurrence nor the timeframe of the observation is INFINTE.

I appreciate you specifying, and I can definitely understand why you would say this. I've said as much to others and I completely understand your point: sequences of numbers are irrelevant when dealing with any single random unspecified event.

Again, you are right in general, but not with PRNGs, because with PRNGs you're not dealing with a single random unspecified event, but with all generated numbers by the PRNG. PRNGs are judged by 3 things:
1. likelihood that each number appears as many times as probabilities suggest
2. no patterns, correlations or predictability between the results
3. the time at which each number appears in the sequence is consistent with probabilities with high confidence.
You're continuously thinking of 1. and 2., but you're never considering 3. Do you understand 3. ? Because again, this is mathematical fact. And I'm not implying predictability, but rather if you roll the dice N times and 7 doesn't come up, the likelihood of 7 not coming up in the next 5-10 rolls goes up, in a completely random scenario. That's why roulettes at the casino have betting limits (which causes many to lose their life savings)

author="N o i r" eredeti hozzászólása:

Of course I would not play such a game, because the chances of rolling a number 8 or more times in 30 rolls is significantly lower than 20%.
Also, this specific occurrence will happen very rarely also in Catan Universe. Just because it happened once to you, it doesn't mean it will keep happening regularly.

Exactly, you shouldn't play this game with real dice. But let me tell you that if you were using Catan's PRNG, I would definitely play this game with you, me as the player, and you the casino. Because this type of repetition happened too frequently for me. You may well say it's anecdotal, which it is, but that doesn't disprove my point.

And where I'm getting at with this is a consistent method for judging whether a PRNG is good or bad, based on this simple 8-time repetition test: Take a PRNG and get N results (N>1,000,000). If the number of sequences of 30 dice rolls showing any single number (2-12) repeated at least 8 times (if 2 numbers are repeated at least 8 times, then the sequence is counted twice) is greater than 0.15 * N, then the PRNG is bad.

Do you understand and agree with this test? Because then we can generalize this to include even rarer situations like 3 repeating 10 times in 25 rolls, and see how many sequences with such low likelihood, exist over N rolls. Can we agree that failing these tests will definitely prove (at least for the purpose of our conversation) that the PRNG is bad? And if these sequences don't appear as much as I am suggesting, then, obviously, my argument would have no basis.

author="N o i r" eredeti hozzászólása:

If you continue to present invalid evidence, I will have no choice but continue to reply that you are, in fact, not presenting valid evidence.

Fair enough, except you also have to justify why it's invalid, and so far it's not that clear to me. I've given extremely unlikely scenarios, happening in close proximity, as well as fairly unlikely scenarios, happening much too often for my games. What is your justification for this being an invalid proof that the PRNG is bad:

1. Is it because you assume it just so randomly happened to me a few times, but wouldn't happen again or to others as often, thus admitting that these numbers make the PRNG look at least suspicious if everyone had similar experiences? The assumption of low likelihood you're making is contested by many players' experience and testimonies, and also by the fact that it keeps happening to me

2. is it because you don't believe the scenarios? I've provided screenshots, and I can play 2,3 catan games, and I can almost guarantee at least 4 or 5 1-in-100 scenarios (at 50-60 rolls per game, in 2-3 games should only get 2-3 one-in-100 scenarios on average), and at least a 1-in-10,000 scenario (which is absurd if I can actually predict this), so we can do this experiment if you'd like

3. is it because you don't believe sequences matter in assessing a PRNG's success? Again, I can go over this and explain why sequences and the frequency of various sequences matters. This again is a mathematical fact which I can easily prove.

4. is it because you disagree on the mathematics of why these low likelihood scenarios should only occur, on average, once in many games? Again, I can elaborate on this and present more math to back it up.

The proof is easy, let's do the 8 repetition in 30 dice test (which is not the lowest likelihood scenario I've seen, the 3 repeating 10 times in the first 25 rolls is a much stronger proof, but let's use the frequent events instead):
- if we assume a 60 dice rolls per game, and play 10 games => 600 dice rolls
- we record the first 30 dice rolls in every game
- We then count the # of times any number is repeated 8 times.
- this gives us the answer to a simple probabilities problem: given 10 sequences of 30 random dice rolls each, what's the likelihood any of these will have any number repeat 8 or more times? 15% as you saw in the casino test.

Math, statistics and probabilities say, in true random, we expect this to happen 15% of the time (any of the numbers repeated 8 times over the first 30 dice rolls of a game).
- We have 10 of these exclusive uncorrelated sequences => approximately 1.5 numbers will get repeated 8 times in the first 30 rolls, over 10 games. This means in 10 games, you should see a maximum of 2 numbers in total (not per game) repeated 8 times in the first 30 dice rolls. By pigeonhole principle, in at least 8 games out of 10 on average, you shouldn't see this kind of repetition in the first 30 dice rolls IF the PRNG is good.

=> Since I've had 2-3 numbers repeating 8 times in the first 30 rolls every 3-5 games or so (sometimes more often, and sometimes multiple numbers repeating like that in the first 30 rolls of a single game - I have screenshots), it means this expectation based on probabilities does not hold with Catan Universe, hence the PRNG is bad ... And you'd probably take my money in the casino game above, if I was the casino running the dice on the Catan Universe algorithm.

Looking forward to your reply

[noob master]

In fact, I can write a program for that test and attempt to run it over 1000 random dice rolls from random.org. Should my assumption of rarity of 1-in-100 situations hold, then I can go ahead and run this test over 1,000 dice rolls in Catan Universe (I'll play 10-15 games or something). Sound good ?

Even something as simple as rolling dice on Random.org over 100 dice has yielded much better distributions consistently for me over 30-40 dice rolls than Catan Universe: https://www.random.org/dice/?num=2 . Try it!