dice used in catan is biased

[Stroom]

I think the issue here is that the dice often get "stuck". I have seen, many times, the same number get rolled 5, 6, 7 times in a row. Sure, that is not impossible, but statistically it is very unlikely - and the number of times I see it are incredible. Nearly every game one or two numbers get rolled an incredibly high number of times. I have also seen many many games where a statistically probable number, say anything 5 through 9, do not get rolled at all. I have seen multiple games with no 7's for instance.

A better dice distribution would make for more competitive games and make the experience more fun. I am not talking about equal distribution, but perhaps some dice rule that says something like "no number should be rolled more than 4 consecutive times" or something? Something to make it "feel" like the dice are more random would make a lot of people happier.

Every individual dice roll is distinct. It is not affected by previous die rolls. This is what randomness is about. After rolling a 7 (16.7%), the probability of rolling a 7 again is still the same (16.7%). And after that, it is AGAIN the same. So it's easy to keep having the same number roll time after time. If you only look at it in retrospect, you start noticing weird patterns, but in reality, it's your confirmation bias.

Look again at 2 coin toss example - you can get heads-heads, heads-tails, tails-heads, tail-tails. If you say that only heads-tails or tails-heads is "fair" then it's only 50% of all possibilities. If you take this kind of "fairness" and apply it to Catan, I'd say that in a similar level, the unfair amount of games would happen, if not more (the order of dice rolls also matters - if all 8s are rolled at the beginning and not the end, it is also not "fair"). So you could basically say that in the span of one game of Catan, the majority of games dice rolls could be perceived as "not fair". And this is how randomness works.

You could play a game of Risk, trying to invade a territory containing 2 troops with 10 troops but still lose in the end. Bad dice rolls can happen. You can mitigate it but never eliminate it. If you do not like the randomness, pick a different game to play.

[Jellby]

So a little less than 1 game out of 11.2, you should get at any point 4 times in a row the same number rolled (accross all players).
Not that unlikely anymore huh

You have to add also the times where *I* roll the same number 4 consecutive times, and those where *everyone but I* rolls the same number 4 consecutive times, and those where the same number is rolled 4 consecutive times except for that different roll that doesn't count because I wasn't paying attention...

[Nekojin]

Yeah, I've definitely noticed that numbers come up often in a particular game, but without having access to all the data (which no one does outside of the game administrators) how can we know if the numbers are truly random. For instance, for me to roll a 7 with two dice 4 times in a row, the odds would be 1/4x1/4x1/4x1/4 so 0.0039% likely. That's very, very slim odds, but I've seen it happen too often to count. There is no way to make a computer program "random". What is the algorithm and is it applied to a game or to the entire community playing Catan and the millions of dice throws? IDK.

What you're failing to understand is that the Law of Averages is a fallacy, not an actual law. When you roll a pair of dice, you have a 1 in 36 chance of it coming up 2. After you've rolled a 2, that probability no longer applies - it has already happened, collapsing the numbers to 1 in 1 chance. It was a 2. When you look back at it again, it's still a 2.

While you're technically correct that it's impossible to make a computer program "random," that's more or less a fallacy at this point as there are algorithmic generators that can create numbers randomly enough to be indistinguishable.

Your asking what algorithm is belied by the follow-up in that sentence; the secondary question is functionally nonsensical, and exposes your ignorance on the matter. If we told you the algorithm (which has already been mentioned in this thread), do you have the CompSci background sufficient to actually understand what that means, and how it functions, or would you be going off some website that critiques the algorithms?

Would you be capable of explaining, in your own words, how Threefry is different from Philox, and which would be better in use for generating small numbers of dice rolls? (And if I do a search on your explanation, will I discover that you're plagiarising someone else's critique?)

For instance, for me to roll a 7 with two dice 4 times in a row, the odds would be 1/4x1/4x1/4x1/4 so 0.0039% likely.

... your math is wrong.

[Niluna]

After the update, the dice rolls became so unpredictable that I don't understand how this is even possible? In one game, crazy spam 11 or 5, in another 3 or 4 plays more often than 6 and 8. That’s spam! When one of the players takes two identical adjacent numbers, he can win in 10 minutes. Please check for a possible bug.

Agreed! I'm going to start taking screenshots of end statistics. I would suggest others do the same. Now that you mention the update, I agree, I think it began when the update was made. It wasn't always this extreme. It's wild. And I work with statistics daily. This makes no sense when it's game after game. A few games, sure. But most of them? No way.

[Xeen_Dread]

https://boardgamearena.com/table?table=568572548

No, nothing wrong with these dice at all.

Idk why the replay won't start from the beginning from my perspective, but like I said in the chat log: This was either going to be glorious or embarrassing depending on how I KNOW BGA dice can cluster-drop/favor certain numbers for/at a given table and are not anywhere near expected random results based on probability of dice combinations with even a moderately tolerable variance.

The odds of something like this happening are astronomical, yet it's pretty consistent to see these behaviors or patterns of rolls if you play as many matches as I have. I'm sure others have played more and noticed this as well. If you happen to pick the 'seed' of the table to park on, gg. If you picked the anti-seed..... embarrassing. Try to pick every number? I've played games where I had 3 4 5 6 8 11 to start, 9s and 10s roll... you know.

Dice roll: percentage of 2 (~3%)
7
Dice roll: percentage of 3 (~6%)
5
Dice roll: percentage of 4 (~8%)
5
Dice roll: percentage of 5 (~11%)
7
Dice roll: percentage of 6 (~14%)
5
Dice roll: percentage of 7 (~17%)
9
Dice roll: percentage of 8 (~14%)
16
Dice roll: percentage of 9 (~11%)
18
Dice roll: percentage of 10 (~8%)
20
Dice roll: percentage of 11 (~6%)
5
Dice roll: percentage of 12 (~3%)
5

TLDR version 8 9 and 10 rolled about 18 *times* % apiece while every other number (including 2s and 12s) rolled about 6 *times* % apiece

[Xeen_Dread]

Yeah, I've definitely noticed that numbers come up often in a particular game, but without having access to all the data (which no one does outside of the game administrators) how can we know if the numbers are truly random. For instance, for me to roll a 7 with two dice 4 times in a row, the odds would be 1/4x1/4x1/4x1/4 so 0.0039% likely. That's very, very slim odds, but I've seen it happen too often to count. There is no way to make a computer program "random". What is the algorithm and is it applied to a game or to the entire community playing Catan and the millions of dice throws? IDK.

What you're failing to understand is that the Law of Averages is a fallacy, not an actual law. When you roll a pair of dice, you have a 1 in 36 chance of it coming up 2. After you've rolled a 2, that probability no longer applies - it has already happened, collapsing the numbers to 1 in 1 chance. It was a 2. When you look back at it again, it's still a 2.

While you're technically correct that it's impossible to make a computer program "random," that's more or less a fallacy at this point as there are algorithmic generators that can create numbers randomly enough to be indistinguishable.

Your asking what algorithm is belied by the follow-up in that sentence; the secondary question is functionally nonsensical, and exposes your ignorance on the matter. If we told you the algorithm (which has already been mentioned in this thread), do you have the CompSci background sufficient to actually understand what that means, and how it functions, or would you be going off some website that critiques the algorithms?

Would you be capable of explaining, in your own words, how Threefry is different from Philox, and which would be better in use for generating small numbers of dice rolls? (And if I do a search on your explanation, will I discover that you're plagiarising someone else's critique?)

For instance, for me to roll a 7 with two dice 4 times in a row, the odds would be 1/4x1/4x1/4x1/4 so 0.0039% likely.

... your math is wrong.

uhh odds of rolling a 7 are 1 in 6, you can basically put 1 die away (it could be any of the 6 numbers) and there is a 1 in 6 chance that the other die can match up with the first to make a 7

so to roll a 7 4 times in a row (most ive seen is 5 with easy start 7's spamming out and rerolling) it would be a 1/6^4 chance 1 in 1296 or .00077 roughly.

[Romain672]

So we got:
numbers: 2/3/4/5/6|7|8/9/10/11/12
rolls done: 3/2/2/3/2|4|7/8/9/2/2
Which doesn't look really weird, you got few number of low numbers, but that's it.

So now to show you numbers, let me take my Bernouilli table: https://docs.google.com/spreadsheets/d/ ... 1846324187 and let's see how likely to get those numbers a certain amount of time is (total: 44 rolls).
So for every number, I will take the most likely probability to roll too much or too few each number. And so it's extremely difficult for that probability to be above 50% because if the probability to roll that number at least that amount of time is 75%, then the probability to roll that number at most that amount of time will be around 25~30%.
- 2 (rolled 3+ times): 12.3%
- 3 (rolled 2- times): 44.5%
- 4 (rolled 2- times): 27.9%
- 5 (rolled 3- times): 26.5%
- 6 (rolled 2- times): 4.5%
- 7 (rolled 4- times): 12.2%
- 8 (rolled 7+ times): 41.3%
- 9 (rolled 8+ times): 10.9%
- 10 (rolled 9+ times): 0.94%
- 11 (rolled 2- times): 44.5%
- 12 (rolled 2+ times): 34.7%

Then let's put those probability in descending order: 45, 44, 41, 35, 28, 27, 12, 12, 11, 4.5, 0.94.

And so you are claiming that some clusters of specific numbers will appear. Here the cluster will be the '0.94%' and '4.5%'. You can see that your cluster of 9s is the same than the cluster of 2 & 7, so that 9 shouldn't count.

If we focus on the 0.94%, let's check the chance when you open a new game to have any number rolled too much or too few with a probability lower than your 10 in that game: 1-(1-0.0094)^(11*2)=18.7% .
Which mean every 5 games you should get something like that.

You didn't explained much what was weird, so I can't really goes deeper. But you can see that this game is totally fine, you get clusters like you should get every 5 games.

[Mathew5000]

https://boardgamearena.com/table?table=568572548
...
TLDR version 8 9 and 10 rolled about 18 times apiece while every other number (including 2s and 12s) rolled about 6 times apiece

No, that's not what happened.

You can see from your link that there were only 44 dice rolls total, 15+14+15. So eight, nine, and ten could not have rolled "about 18 times apiece".

[Jellby]

It says clearly in the table: "percentage of", not "number of"

[Xeen_Dread]

ya my bad, still, equal % of 8 9 10 vs same % of all the rest of numbers, its wrong either way