change the dice generator.

[Romain672]

According to my probability calculation, the chance of getting such a game is ~1:500,000, and in only 11% of these games the player would have a chance of getting 5 of the 8 fours rolled, so the value is far outside the norm at ~1:5,000,000 in around 4,600,000 games on BGA, a true phenomenon.
Add to that the luck of occupying both four fields at the beginning.

Yeah I just had a game where there were 27 8s and 2 5s, I based my strategy on those 5s and was sitting without any resources. So 5 has probability of 11 percent or whatever and rolled 2 out of 60-70 rolls, it is broken

Ok let's see that one.
So it was this game: https://boardgamearena.com/gamereview?table=624492989 .
So firstly those 27 8s and 2 5s are probabilities. You got 27% of 8s and 2% of 5.
Here is the real rolls:
2 3 4 5 6 7 8 9 10 11 12
0 2 4 1 8 7 14 5 6 2 2

So here you got 51 rolls, 1 being 5 and 14 being 8.
If you double that which I suppose is what CaptainDex did, you will find more extreme probabilities.

Zero or one 5 is at 1.82%
Forteen or more 8 is at 0.818%

So let's keep that forteen 8s, and let's apply my formula: 1-(1-0.00818)^22, we got 16.5%.

Which mean that if you play 6 games, you should have one game where one number is too much or too few rolled as unlikely as that one.

(Zero 2 in 51 rolls is 23.7%)

To be fair, that ^22 isn't great, but that's a way to be fast in calculation. I suppose I should do ^20 or ^18 instead since it's unlikely to get 2s/3s/11s/12s too few rolled being the weirdest thing. But then that should still be 1/7 game instead of 1/6.

[gmrsmrt]

If now you look at all numbers and try to find a number too much or too few rolled, I like to multiplay that probability per 22 (any number rolled too much or too few):
1-((1-0,0000757)^22) which now gives 0.00166, so 0.17%.

you are right I forgot to include the probability to have a low probability on the other dices
Once included this effect I find a probability of about
0.00048
which is obtained running a simulation of 100 millions of dice rolls

The reason we don't end up on the same number is that you are a bit overgenerous in your consideration. The point is that since the distribution
is not flat each number needs to be treated separately. The biggest effect comes from the low end of the tail, even for seven which is the most
likely outcome if you get 0 rolls you don't reach such a small probability so you should only consider the possibility to overshoot. Then to

[Kaladry]

I had a game earlier where there were ZERO (0) sevens rolled the whole game. It was crazy. Doesn't mean the dice are bad, but I've just never seen it before.
https://boardgamearena.com/table?table=624730962

[euklid314]

I had a game earlier where there were ZERO (0) sevens rolled the whole game. It was crazy. Doesn't mean the dice are bad, but I've just never seen it before.
https://boardgamearena.com/table?table=624730962

It was a short game with only 40 dice rolls. The probability of not getting a single 7 in 40 rolls is 0.07%. In other words it should happen in 1 out of 1470 games.

As you wrote this does not mean the dice generator does not work. Just the other way round, the dice would be broken if such games did not occur. It is a rare event for a single player but a common event for a site like BGA since thousands of games are played in a short period of time.

[Jellby]

In other words it should happen in 1 out of 1470 games.

Just to be clear: in 1 out of 1470 40-roll games. And if you've played 1469 40-roll games and it hasn't happened, it does not mean it will happen in your next 40-roll game.

[euklid314]

In other words it should happen in 1 out of 1470 games.

Just to be clear: in 1 out of 1470 40-roll games. And if you've played 1469 40-roll games and it hasn't happened, it does not mean it will happen in your next 40-roll game.

You are absolutely correct, Jellby.

As a matter of fact, if in the first 40 rolls of your game there was no 7, you will be probably close to the finish of this game.
Usually Catan games take more rolls to finish but if not a single ressource is lost because of a 7 rolled the game should finish much sooner (the ressources may change their owner due to trades and steals but ultimately they will be used for some build). Thus the 1 out of 1470 ratio might even be a not-so-bad estimate over all games...

[Theana]

Hi all,

This will be my first and last comment on this topic.

By now, we all have at least some understanding of how causality, randomness, and statistics work. Looking at the end-of-game statistics, we can agree that the results align with what is expected.

The only point of discussion I see regarding the dice is the frequency of consecutive identical rolls—sometimes the same result appears repeatedly, whether it’s a 6, 10, 7, or any other number.

So far, this is just a perception and isn’t reflected in the statistics. However, if someone wants to go through the matches, track all the sequences, and provide concrete data, then it would make sense to revisit the discussion.

[euklid314]

Hi all,

This will be my first and last comment on this topic.

By now, we all have at least some understanding of how causality, randomness, and statistics work. Looking at the end-of-game statistics, we can agree that the results align with what is expected.

The only point of discussion I see regarding the dice is the frequency of consecutive identical rolls—sometimes the same result appears repeatedly, whether it’s a 6, 10, 7, or any other number.

So far, this is just a perception and isn’t reflected in the statistics. However, if someone wants to go through the matches, track all the sequences, and provide concrete data, then it would make sense to revisit the discussion.

Sorry that I dont understand your point. What are you interested in?

My perception after many played games is, that after a 7 is rolled in 6/36 of all cases another 7 follows. After a 10 is rolled in 3/36 of all cases another 10 follows, and so on.

This is to be expected since the single RNG calls bga_rand(1,6) are completely independent of each other. Between successive calls for one game of CATAN there might be hundreds or thousands of calls of the same RNG function bga_rand() that are used for other games.

Nobody ever has shown me data that gives me a reason to doubt my observation.

[Theana]

Not sure what your point is, sorry.

What are you interested in?

Nothing?

My perception after many played games is, that after a 7 is rolled in 6/36 of all cases another 7 follows. After a 10 is rolled in 3/36 of all cases another 10 follows, and so on.

Great to hear that your perception gives you data...

This is to be expected since the single RNG calls bga_rand(1,6) are completely independent of each other. Between successive calls for one game of CATAN there might be hundreds or thousands of calls of the same RNG function bga_rand() that are used for other games.

Can the same value being rolled more times in a row? yes
Can the behaviour show in every game? questionable.

For example I am quite sure recently I played in a game where 10 started rolling like a crazy multiple times in a row.
Another time was with 5.

Now I am not paranoid so I don't really care, but if many people complain about the dices, there must be something that raises the concern.

IF this behaviour exists, game statistics will not show it, since one should be looking at the sequence, not the total percentage.

IF this happens, would explain the feeling that many feel.

Hence to prove something is wrong, who complains could start collect analyze and present the data.

Until that, is a pointless discussion

[Jellby]

IF this happens, would explain the feeling that many feel.

What, the same number being rolled multiple consecutive times? Of course it happens, because that's how random dice should behave.

The problem is not what happens or does not happen, but what people want to happen and what they believe is a random or non-random behaviour (hint: they're often wrong).