#66082: "Are dice results really random ?"
על מה דוח זה?
מה קרה? אנא בחר מהרשימה מטה
מה קרה? אנא בחר מהרשימה מטה
בבקשה בדוק אם יש כבר דוח על אותו נושא
אם כן, הצביעו בעד הדיווח הזה, דיווחים עם הכי הרבה קולות נחקרים ראשונים
| # | Status | Votes | Game | Type | Title | Last update |
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תיאור מפורט
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• אנא העתק/הדבק את הודעת השגיאה המופיעה במסך, אם יש כזו.
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... -
• בבקשה הסבר מה רצית לעשות,מה עשית ומה קרה
• מה הדפדפן שלך?
Google Chrome v102
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• בבקשה העתק והדבק את הטקסט המוצג באנגלית במקום בשפה שלך. אם יש לך צילום מסך (מומלץ) אתה יכול להשתמש ב Imgur.com כדי להעלות אותו להדביק קישור לכאן.
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... -
• האם טקסט זה זמין במערכת התרגום? אם כן, האם היא תורגמה במשך יותר מ -24 שעות?
• מה הדפדפן שלך?
Google Chrome v102
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• אנא הסבר את ההצעה שלך במדויק ותמצית כדי שיהיה קל ככל האפשר להבין למה אתה מתכוון.
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... • מה הדפדפן שלך?
Google Chrome v102
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• מה הוצג על המסך כאשר נחסמה (מסך ריק? חלק ממשק המשחק? הודעת שגיאה?)
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... • מה הדפדפן שלך?
Google Chrome v102
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• איזה חלק של הכללים לא היה מכובד על ידי עיבוד BGA
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... -
• האם אפשר לראות את הפרת החוק בשידור החוזר? אם כן, באיזה מספר מהלך?
• מה הדפדפן שלך?
Google Chrome v102
-
• מה היה המהלך במשחק שרצית לבצע?
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... -
• מה ניסית לעשות שגרם לפעולה הזו
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• מה קרה כאשר את/ה מנסה לעשות את זה (הודעת שגיאה, הודעת פס סטטוס משחק, ...)?
• מה הדפדפן שלך?
Google Chrome v102
-
• באיזה שלב במשחק הבעייה קרתה (מה היו ההוראות הנכונות)
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... -
• מה קרה כאשר את/ה מנסה לבצע פעולת משחק (הודעת שגיאה, הודעת פס סטטוס משחק, ...)?
• מה הדפדפן שלך?
Google Chrome v102
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• אנא תאר/י את הנושא המוצג. אם יש לך צילום מסך (מומלץ) אתה יכול להשתמש ב Imgur.com כדי להעלות אותו להדביק קישור לכאן.
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... • מה הדפדפן שלך?
Google Chrome v102
-
• בבקשה העתק והדבק את הטקסט המוצג באנגלית במקום בשפה שלך. אם יש לך צילום מסך (מומלץ) אתה יכול להשתמש ב Imgur.com כדי להעלות אותו להדביק קישור לכאן.
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... -
• האם טקסט זה זמין במערכת התרגום? אם כן, האם היא תורגמה במשך יותר מ -24 שעות?
• מה הדפדפן שלך?
Google Chrome v102
-
• אנא הסבר את ההצעה שלך במדויק ותמצית כדי שיהיה קל ככל האפשר להבין למה אתה מתכוון.
Hey, it seems that the dice results are clustering, in some games; what I mean by that, is that some specific combinations(sometimes just the results) are rolled one after another or sometimes in tandem with another result. the weird thing is that its throughout the game 1-3 specific results. it can be 6s or 9s (which seems not super unlikely), it also can be 4s and 3s that are going up to 15-20% rolls of the whole game - but the weird thing is not that, but that they are rolling one after another.
I know that is possible for that to happen, but in itself not likely - and at the rate Im seeing it, I think something might be wrongly implemented (?)
It might be since the last update (saw that before the update a couple times but in 100 games not in 10-15), it also might have been always a problem; But Im seeing it more now, because Im paying more attention... • מה הדפדפן שלך?
Google Chrome v102
היסטוריית דיווחים
since its pseudo random, it might, in combination, generate a pattern.....
PS: I try to post more games like that later
"Dice weirdness (since last update?)"
changed to
"Are dice results really random ?"
But I can assure you that the dice randomness is indeed random.
boardgamearena.com/7/catan?table=276157622
Dice result ratio: 2 (~3%) 0Dice result ratio: 3 (~6%) 2Dice result ratio: 4 (~8%) 11Dice result ratio: 5 (~11%) 15Dice result ratio: 6 (~14%) 21Dice result ratio: 7 (~17%) 17Dice result ratio: 8 (~14%) 14Dice result ratio: 9 (~11%) 9Dice result ratio: 10 (~8%) 11Dice result ratio
15 x 5, 21 x 6, 11x 10
seems not to special in the end stats ... but the first rolls seemed , lets call it "weird" again - and that it worked out from there as assumed, doesnt proof anything since it's just one game ( I know )
I was talking about patterns, because it's pseudo random - which can be greatly made, but might generate patterns, even if both dice individually are close enough to real random(a.i. atom decay)
boardgamearena.com/table?table=277046660 11 rolled 0
10 and 9 clusters in the beginning - (most notable in similar combinations) - also in mid game 11 clusterings happen to appear - 9 and 11 clusters reapper (with mostly same red and yellow dices)
Dice result ratio: 2 (~3%) 1; Dice result ratio: 3 (~6%) 5; Dice result ratio: 4 (~8%) 7; Dice result ratio: 5 (~11%) 6; Dice result ratio: 6 (~14%) 11; Dice result ratio: 7 (~17%) 20; Dice result ratio: 8 (~14%) 11; Dice result ratio: 9 (~11%) 16; Dice result ratio: 10 (~8%) 10; Dice result ratio: 11 (~6%) 9; Dice result ratio: 12 (~3%) 4
again as averages, they dont seem too weird - its that they(the clustering numbers- here 9 11 and 10 at start) are so often in quick succession to themselves, with often identical dice values for the red and yellow dice ...
but it showed 4 in the statistic.
this game is totally bugged with the dice
I found in both games the 8's and 10's are very under rolled. It seems the 6 is over rolled in comparison.
Just a gut feeling.
little clusters of 4s 5s and 6s ... later 9s and 12s (and 5s continueing)
For example in the last game I played there were more 5s rolled than 6s and 8s combined. Over a large sample size (100+ rolls) this can absolutely happen – but it happens game after game so there is likely to be a code issue here.
Are the dice rolls being calculated in real time at the point of rolling or is there an array of random numbers being created when the game is loading and worked through during the game – the game has the feel of the later, which in a game for which the core mechanic is a bell curve distribution of resources, makes playing the game farcical and the outcome determined after 2 or 3 rounds.
At best it feels like something very static is being used to seed the random number variation. Consider generating these in real team and seeding with something truly random, like the last player’s turn in milliseconds.
6s and 9s - again not suprising it is rolled often - but it was obv. from the start when there were the first , lets call it clusters again ...
boardgamearena.com/7/catan?table=281576357
what would be the difference between creating a table beforehand and generating it live, based on something like milliseconds ?
it is still determined either way, what the result will be, with the difference, that one would have the feeling to have control of it, if one knew how its generated [or believe to know should be enough :P] - if it's a good algorithm which creates the pseudo random results (low predictability in trends and next results), it should be just fine, shouldn't it ? (if there is no way for players to get that table, that is :P )
And yes, 7 is the most frequently rolled number, but to the point where more often then not it's the first roll in almost every game I've played, and if not the first, then ALWAYS in the first round, and then again, rolling a seven sometimes 3 or 4 or 5 times in a row being almost EXPECTED at this point from how frequently it happens that again the robber alone can basically determine the outcome of the every game? Really seems off.
In terms of a pseudo-random algorithm, it really seems like there might be something wrong in the coding.
Few things -
For Settlers, being able to predict the next dice roll isn't the most important thing as most of the decision making made on placement is made at the start of the game and is done so based on a bellcurve of 2D6 rolling which will peak at 7.
For every game I've played the abnormally highly occurring number has been on the 2nd from bottom row, on the hex 2nd from the left - importantly, players seem to be catching on to this - the highest ranked players are going straight for this hex and the hex with the corresponding number. Might be a conincidence but doesn't feel like it.
Populating the array at the start of the game will help in the performance of the game but removes the opportunity of adding genuinely random input into the psudo randow generator - the generator probably is producing a bell curve of numbers just now - but they're not piviting on the number 7 which a genuinely random input will give you over time.
The seed range from current time in Miliseconds (MS) is very small and relies on the system being called to return the time updating its response accurately every MS. For example I've seen reports of time related functions on Windows only changing their return value every few milliseconds so the same seed value will come back repeatidly.
Hope this is helpful - again, as players seem to be catching on to this and flooding where the high occurance is popping up.
Cheers
#284621586
4 : 20x
5 : 15x
6 : 19x
7 : 7x
8 : 14x
9 : 7x
10 : 7x
4 was actually the number on the hex described by Jimbobbery above : 2nd row from bottom, 2nd hex from the left
7s rolled 3 times in a row and not the first time I've seen it.
"if two succesful players roll two 3s on a row, then the probability to roll 3s in the whole game would be higher than normal"
That way, we can test that hypothesis, and see if it's true or not.
Atm, that post look just a collection of randoms games.
.... what i mean by cluster is some thing like that (lets use [1-6] with 1/6 each): 123561235644441235612356 ; this would be a 4 cluster - and if this happens once in a game this would happen prob. again later with same number ( not rarely with same combination of red and yellow dice number) - THAT is what I find curious, and way to often that it would be just random (obv. Id need a larger data set too proof that - super unlikely sequences can just happen - but it would be nice to have a number to put on, how unlikely that consistency is... )
9s were spun in clusters throughout the game and I'm fairly certain that they were spun more frequently than sixes and eights COMBINED. I'm not a premium member so I cannot see dice statistics, so if someone could double-check this game I would appreciate it.
Here is the 2s/3s/4s/5s/6s-7s-8s/9s/10s/11s/12s rolls done
0/3/2/9/8-13-10/18/8/3/2
18/76 rolls were a 9.
It has a probability of occuring of 0.14%, 1 out of 701.
Since you can do the same claim for every number, I will 'multiply properly' that probability per 11.
That now give 1.56%. Something unlikely like that or worst happen one game out of 64,2.
So you are slightly better than the game shared on the forum, but still far from finding a really strange game: I'm still waiting for a probability under 1/10k :D
And please note it was not the claim done on that bug report. Rolling the same dice accross one game =/= having many time a specific dice at one moment.
Percentage of 2's rolled: 7%
P(3)= 4%
P(4)=11%
P(5)=10%
P(6)=12%
P(7)=18%
P(8)=10%
P(9)=9%
P(10)=13%
P(11)=4%
P(12)=2%
P(2)=0%
P(3)=0%
P(4)=13%
P(5)=11%
P(6)=11%
P(7)=13%
P(8)=26%
P(9)=18%
P(10)=5%
P(11)=0%
P(12)=3%
P(2)=5
P(3)=11 (this is why I won)
P(4)= 11
P(5)= 13
P(6)= 6
P(7)=22
P(8)=13
P(9)= 3
P(10)=8
P(11)=3
P(12)=5
Predicted the dice would be in my favor after the first 6 rolls of the dice. Other players thought I was a bot. Really need to look at that RNG
P(2)=3
P(3)=7
P(4)=8
P(5)=8
P(6)=7 (less 6's rolled than 12's!)
P(7)=20
P(8)=20
P(9)=8
P(10)=5
P(11)=7
P(12)=8
P(2)=7
P(3)=7
P(4)=5
P(5)=21 (21 or more 5's in a game is 1 in 1000)
P(6)=9
P(7)=14
P(8)=7
P(9)=12
P(10)=9
P(11)=2
P(12)=7
P(2)=8
P(3)=10
P(4)=19 (1 in 2K chance of 19% or more 4's)
P(5)=11
P(6)=13
P(7)=14
P(8)=16
P(9)=0
P(10)=5
P(11)=3
P(12)=2
boardgamearena.com/table?table=303601034
25 eights in 90 rolls (1 in 10K chance)
The only numbers I didn't have in the initial setup were 2, 8, 11, 12. This is significant and affects the dice bias.
1 in 50K chance of starting the game with three 12's in a row
1 in 100K chance of no nines rolled in the game
This is the nearest to "normal" (pun intended) game I've had in a while, and still has several 1 in 100 events
Just six 6's out of 100 rolls
Longest game ever, and quite "normal" in the dice distribution. BUT, 9 was over-rolled (there were 15% nines, which is not too unlikely (13% chance). 3 was under-rolled. I predicted this would be the case in the chat box within the first five minutes of the game.
First consider boardgamearena.com/table?table=302620573
There were 63 dice rolls in the game, of which a 6 came up 4 times (moves 40, 61, 63, and 170).
Let X be the number of times you get a 6, when you roll a pair of dice 63 times. Then the probability that X is 0, 1, 2, 3, or 4 is:
0.000081 + 0.000824 + 0.004118 + 0.013504 + 0.032671 = 0.0512, or about 1 in 19.5.
You said, "Less than 1% chance of so few 6's" but in fact the probability of 4 or fewer sixes is greater than 5%.
Now consider boardgamearena.com/table?table=303184521
This game also had 63 dice rolls, of which none were 9's.
Let Y be the number of times you get a 9, when you roll a pair of dice 63 times. The probability that Y is 0 is:
(1 - 4/36)^63 = 0.00059895, or 1 in 1669.586.
You said, "1 in 100K chance of no nines rolled in the game" but in fact the probability is about 1 in 1,700, not 1 in 100,000.
I still think 1 in 1,700 is still too low of a chance to be random and that the dice are biased.
As to your main point (and that of some of the other posters in this thread), I believe it's an instance of the "rare events fallacy". Have a look at this article by mathematician David Hand: slate.com/technology/2014/02/the-improbability-principle-rare-events-and-coincidences-happen-all-the-time.html
It's understandable to ask, "In that game I just played, the probability of seeing zero 9's would be only 1 in 1,700 if these are fair dice. I haven't played anywhere close to 1,700 games yet so isn't it suspicious that I'm already encountering this 1-in-1700 event?"
The reason why it's *not* suspicious is, there are so many different things that could happen, any one of which looks unusual, and the chance of one particular thing happening is minuscule, but the chance that *any* of them happens is much much larger.
As a thought-experiment, what if you sat down before playing a game of Catan, and wrote out a list of specifically what results in the dice statistics you would consider unusual (assume each game has 60 to 70 throws). So the list would include, having two or fewer 5's show up, two or fewer 6's, etc. You might say it would be unusual if we get more than eight 2's rolled, or more than ten 3's. You might say it would be unusual if there's any sequence of six throws in which four of them are 3's. And so on. You could write a list, specifying exactly what you would consider unusual, on the understanding that any event which happens that is not on your list, you don't have the right to call it unusual after the fact. (It's important that you make this list before playing the game, otherwise the results are tainted by selection bias.)
Then you've got a list of events each of which is considered unusual, and you ask, what is the probability that *at least one* of the events on your list occurs in the game you're about to play, if the dice are fair. That is something that can be calculated exactly (because the list is expressed unambiguously).
What you'll find is, if you have exhaustively listed (before the game) *every* event that you would consider unusual, and then carefully calculate the probability that at least one of these events on the list occurs, you'll reach a probability that's pretty high, maybe over 0.5, of at least one of these events occurring.
Then if that's the case, it's actually not suspcious at all, that in most games of Catan you play on this site, something "unusual" occurs. In fact you would expect it to!
But, wouldn't you say that if I could predict the rare event within the first five minutes of the game, that there is a problem with the implementation of the RNG? I expect rare events. I should not be able to predict them.
Here's another game with 3 11's in 4 rolls (about 8 in 10K). This kind of occurrence is expected, but it's weird if it happens at the point in the game where 1 player has settled on every number except 11. This game also had 20% 8's and 20% 9's, leading to a quick victory for me, since I was depending on those rolls.
boardgamearena.com/6/catan?table=304559931
10 rolled more than either 6 or 8 (predicted this within the first few rolls of the game)
Predicted 8's rolling more often after 10 rolls.
Two 6's for entire game
Hope this message finds you well.
I feel like a couple of strange random distributions in rolling today
boardgamearena.com/table?table=305268260
99 rolls - 20 x 4's (20.2%) - expected is 6.94%
boardgamearena.com/table?table=305268260
92 rolls - 29 x 8's (31.5%) - expected is 13.9%
Maybe I need a larger sample of dice rolls for this to make sense, but it kinda put me off the game today. It made me perceive that the random number generator was not within expected parameters.
Really just need somewhere to vent - it was a frustrating experience. Did I get a couple of anomalies in a row? Please reassure me the dice rolling subroutine is working as expected.
Thanks for running a great site I am happy to contribute to and keep me happy for hours :)
Dave from Toronto
on table boardgamearena.com/table?table=305534566
there was only 4 times 6 at all!
Here's a game with 20% 8's (not all that low probability, but really weighed the game against the player with the highest elo). I'm curious if anyone can comment on how the "average number of tiles around settlements" is computed I the end-game stats. In this game, you'll notice how the player with the highest average number of tiles produced the least number of resources by a significant margin.
boardgamearena.com/8/catan?table=305666720
By the way, I've noticed this non-randomness in other games on this site as well, particularly in Viticulture. It's subtle, but noticible.
boardgamearena.com/6/catan?table=307368873
[1] You said: "But, wouldn't you say that if I could predict the rare event within the first five minutes of the game, that there is a problem with the implementation of the RNG? I expect rare events. I should not be able to predict them." My question is, how do you predict within the first five minutes of the game exactly which rare event is going to have occured when the final stats are in. For example: here's the most recent Catan game I played, lasting 41 minutes: boardgamearena.com/6/catan?table=307408908 In 54 throws, there were quite a lot of 9's and 11's, with relatively few 6's, 7's, and 8's. But how would you have predicted that within the first 5 minutes? The first 7 dice rolls of this game (approximately 5 minutes) were: 11, 10, 5, 6, 4, 6, 7. As the first five minutes of the game had a couple of 6's but no 9's at all, how could you predict from that, that by the end of the game there will be *fewer* 6's rolled than 9's?
Or if this particular game is not a good example, could you choose another Catan game I played within the last week or two (boardgamearena.com/gamestats?player=88974824&game_id=1539) and explain how I could have predicted, within the first five minutes of the game, a rare event that shows up in the final dice statistics of that game.
[2] What do you think is a possible mechanism for the issue you perceive, with the dice not being random? Do you think that the code is written so that for each game of Catan, the code looks at which dice rolls will benefit a certain player in the game, and then produces those rolls at a higher frequency? How would the code decide which player to benefit in a particular game?
[3] I'm not asking these questions rhetorically. In one of the early responses in this thread, Darhf (one of the developers of the BGA implementation of Catan) said, "I can assure you that the dice randomness is indeed random." I find that entirely plausible. But I am keeping an open mind and I want to try to fully understand your position, which is the reason I asked [1] and [2] above.
[4] One of the reasons I find it plausible that the RNG is properly written, is that it's pretty easy to write code that simulates the sum of two dice. Other random processes, such as shuffling a deck of 52 cards, are much trickier to simulate, because the number of permutations of the deck is more than 8 * 10^67, and you need to make sure that each one of them is equally likely to occur. But a die has only 6 faces, so the code is straightforward.
2% chance of so few 4's. The player with the top elo had almost no cards at the beginning of game in spite of having high probability spots and not being particularly picked on by the robber.
Here's my analysis of table #307408908.
Based on initial setup, Nafnaf had 5,6,8,10,11
Jonas had 3,4,5,6,8
Mathew had 5,6,9,10
First rolls were 11 (only Nafnaf), 10 (poor Jonas), 5 (all get something), 6 (all get something), 4 (only Jonas), 6 (all get), 7 (Nafnaf gets to move robber), 12 (nobody)
6's at the beginning do not hurt or help anyone (everyone gets cards, so doesn't give much info about dice bias)
Based on this first set of rolls, Nafnaf has a very slight advantage. Even his unlikely numbers got rolled. At the end of game, 11 was rolled 13 times (an insane advantage for Nafnaf) while 3 was never rolled (hurting Jonas). I maybe should have written down a few more rolls to see that the dice are slightly hurting Jonas (game ending with few 6 and 8) and helping you and Nafnaf (lots of 11 and 9). I would be interested to know the average elo of each player at game start.
But I do believe that there might be a bias coded in to encourage players with low elo to keep playing and to make things slightly more challenging for better players. It's easy to code a function of elo that prefers rolling 7's for players with low elo or slightly avoids the initial placement numbers of players with high elo. I can only guess based on observations. It's not uniform since occasionally I've received the advantage in spite of having the highest elo among my competitors. The dice here just remind me too much of the dice of a Catan version I used to play against AI that would slow down rolling the numbers of the current winning player. In those games I would settle on every number and then the game would only roll 7's. On BGA I also tend to have better outcomes settling on all the numbers rather than the high probability spots. It's not as in-your-face as the online Catan I mentioned earlier, but the bias seems evident to me.
Could you post a link to that second game you were talking about? The stats link didn't work for me
1% chance of so many 7's
4 and 10 rolled 150% more often than 5 and 9 (predicted after a few rounds that 3,5 and 9 would be under-rolled)
Out of 49 rolls, only two 6's. Forty percent of the rolls were 8 or 9 (1% chance of that happening)
boardgamearena.com/1/catan?table=307950692
No 9's in 60 rolls (about 1 in 1000 chance)
1 in 500 chance of so few 8's and 9's. More 12's than 9's in this game
So many 9's (incidentally 9 was the only number that the highest elo player hadn't settled on)
To me, this game really shows evidence of the dice bias as a function of elo. I (with the highest elo) was the only player settled on 10, but it did not roll until the very end of the game. If you watch the game, roll by roll, you will see the evidence. I'll post the probability of so few tens below. I expect games with no 10's. But I don't expect them to coincide with incidences where the top elo player is the only one settled on 10.
1.8% chance of no 10's in the first 46 rolls (by coincidence the player with the highest elo was the only player settled on 10)
boardgamearena.com/5/catan?table=309150219
The probability of so many 5's in Alison's game (13 5's in 44 rolls) is 7 in 10K. It is not a coincidence that only one player settled on 5 in the initial placement.
boardgamearena.com/8/catan?table=311510699
12 8's rolled but only 3 6's.
I had the highest elo at the table and had settled on all numbers (3-11) except 4, 8, and 11. Is it a coincidence that these numbers were over-rolled?
More 5's and 9's than 6's and 8's
boardgamearena.com/8/catan?table=311543385
boardgamearena.com/1/catan?table=311557303
boardgamearena.com/4/catan?table=311807666
1 in 10K chance of 5 elevens and twelves in the first 8 rolls.
The player with the lowest elo only settled on two 8, 5, 10 locations at the beginning of the game. In my experience, this encouraged a truly exaggerated error in the dice. The dice gave a slight advantage to the lowest elo player, but this was evidenced by an extreme amount of 5's, 8's and 10's, especially at the beginning of the game. It was a long, long time before we saw a six or a nine rolled. I'll look at the game log and try to see if I can calculate the probability of so few 6's and 9's, as it was quite extreme. The initial placements of the players and their relative elo encouraged the dice to be more extreme.
boardgamearena.com/5/catan?table=312704062
In this same game, there was a second occurrence of three 12's in seven rolls (7 in 10K chance)
There were no nines in the first 50 rolls (1 in 500 chance)
Same game as the above two comments.
38 of the first 40 rolls were 5, 8, 10 (where the lowest elo player had settled) or 7,11,12 (where no one got cards). The probability of rolling 5,8,10,11,12,7 is 21/36.
The chance of rolling 38 of these numbers in the first 40 rolls is 1 in 5,000,000 (1 in 5 million chance).
This game is my best evidence so far that the dice are rigged.
No 4's in this game (6 in 1000 chance). Is it a coincidence that the player with the lowest elo did not settle on 4?
The lowest elo player settled on every number except 6. There was only 3 sixes rolled in 62 rolls (probability of that happening is 1%). Also 1% chance of so many 10's.
boardgamearena.com/4/catan?table=315991890
1 in a million chance of no 2,3,8, or 10 rolled in the first 31 rolls (the numbers which the highest elo player settled on)
6 in 10,000 chance of so few 2,5,9,10,11
There were more 12's rolled than 5's
Only 1 eight in fifty rolls (4 in 1000 chance)
5 in 100K chance of so few 7's, 8's, 9's and 12's
Just as many 11's as 9's and 10's combined.
The dice clearly favored one player from the beginning. 24 of the first 30 rolls were 2,5,6,7, or 11 (1 in 1000 chance). The favored player had settled on 5,6,11
More 11's than 8's. The high prevalence of 9, 11 and 4 benefitted the player with the lowest elo.
1. Ensuring one player's numbers come up mostly at the beginning of the game, while the other player's numbers are rolled mostly at the end (too little too late when the first player has already established cities)
2. Giving most of the sevens to one player
...
8s were not rolled at all until after move #100, and they weren't rolled all too many times throughout the game in general. Both 8s were brick, (and the other brick was 12,) so that made it very frustrating for us, especially for my two opponents when I blocked their 8 while my 8 was open :). So this is an unbiased report (as I won the game) that I believe something is wrong with the dice rolls on BGA.
There were 16% 3's rolled (more than 5's and 6's combined!) There was only one 5 rolled the whole game. Coincidence? I think not.
boardgamearena.com/7/catan?table=321798773
boardgamearena.com/7/catan?table=321798773
1-((1-p)^11)
So like if you said that your rolled X sixies, and this or more sixies has a probability of 1%, you apply my formula which give 10.5% (>10%), and instead of saying
"on that game, the probability of rolling X sixies or more was 1%"
you can said
"on that game, the probability of rolling X sixies or more, or rolling any other number with an even more unlikely event was 10.5%"
Most of your events will be way more likely. But that's normal since you choose to check a specific number after seeing which number was the most unlikely.
And if you want, you can count your 100 next games, and write all your most unlikely event. That should give a second good sample of what is going on. (but start at any moment like just after you read it, not at a moment you choose)
If my suspicion is correct, then the highest elo player at the table should settle on as many different numbers as possible, while maintaining spots with high probability of rolling, while the lowest elo player should settle on as few different numbers as possible (but high probability spots). In my experience, incorporating these two strategies encourages the dice bias and the likelihood of rare events.
boardgamearena.com/4/catan?table=322151166
Although I try to counter this reality by placing my initial settlements close to as many different numbers as possible, almost invariably the dice decide to fixate on the numbers to which I am not adjacent (i.e. 5s and 9s - or worse - when I am near both 6s and 8s.)
Although I really like the game concept, this flaw has led me to quit one or two games in extreme frustration and consider giving up playing the game entirely.
P.S. I agree with one poster about the box set. Correcting with different sets of dice is an innovative solution that I must try to remember.
Please use science (math, cs) to prove your assumptions not your feelings.
What you are doing is called cherry picking : en.wikipedia.org/wiki/Cherry_picking
Check this also : en.wikipedia.org/wiki/Fundamental_attribution_error (low elo having better luck)
en.wikipedia.org/wiki/Confirmation_bias
Dice do not have a will, randomness does not have biases, only humans have. We, as humans, will always have difficulties to correctly understand randomness, because our brain is made this way. We have all sort of biases and feelings that are corrupting our judgement relative to random events. It's ok that you'll are concerned about this topic and if dice were not random it would be indeed a big problem. But nothing here objectively tells me that it is the case.
The day you are using science to prove your point, tell me I'll be happy to check the work and to admit you are right and that dies are rigged.
One last piece of advice : in probabilities your personal experience is not relevant. One game is not relevant. A few games is not relevant. You need data, a lot of data. ~ 1,000,000 random dice throws could be a starting point. Taken from all of the catan games ever played at random. Then you can start working on something.
I am hypothesizing that the developers have coded in an advantage for players with low ELO on all the games on BGA.
1. Have the lowest elo at the table
2. Settle on two initial spots with the same three numbers (two 8,3,4 spots for example)
I predict that the distribution of dice rolls will be far from "normal" (especially if you plot the dice rolls for the first half of the game - I have noticed that occasionally the dice try to correct the skew somewhat at the end of the game). I have not been able to test this hypothesis often because I find it hard to be the lowest player at the table, but I encourage others to try.
(I don't mean this to brag, but just so you know, I have a graduate degree in science, my thesis was the awarded the best in the faculty of science, and I've published in journals with people at NASA and Harvard)
It just asks for two numbers between 1 and 6. That's all.
There is no link anywhere in the code betweeen a random call and whatever it will be used for. The Random function doesn't "know" it's used for a dice roll, a card draw, who is playing right now or anything, that is not how game adaptations work.
boardgamearena.com/7/catan?table=324605871
The lowest elo player had the worst starting position (only 18/36 chance of getting a card on any roll)
The highest elo player had the best starting position
But 5 and 9 were only rolled 8% of the time instead of the expected 22% (the chance of this is 3 in 1000), giving a strong advantage to the player with the lowest elo and the worst starting position (who easily won the game)
2 rolled 0%
3 rolled 3%
4 rolled 15%
5 rolled 17%
6 rolled 15%
7 rolled 7%
8 rolled 19%
9 rolled 5%
10 rolled 12%
11 rolled 3%
12 rolled 3%
5 and 10 are the answers. 9 is one of the numbers the lowest elo player did not settle on.
46% of the rolls were 4, 5 and 10 (chance of this happening is 1 in 1000)
boardgamearena.com/5/catan?table=326667525
Double as many 3's rolled as sixes. The only numbers I didn't settle on were 3 and 4. 3,4,5 rolled 44% of all rolls (probability of that is 1 in 1000). Didn't expect this because there was another player at the table with higher elo, but it became obvious the dice would be biased against me after I didn't get any cards in the first five rolls of the dice.
As the highest elo player, I settled on every number except 11. Then 3 elevens were rolled in a row (1 in 6000 chance). Really painful loss (double as many 11's rolled as 5's)
boardgamearena.com/table?table=328738647
boardgamearena.com/gamereview?table=328752182
7 in 10,000 chance of so many 5's, 6's and 10's. This time the dice were hurting the player with the lowest elo.
boardgamearena.com/9/catan?table=329111691
boardgamearena.com/5/catan?table=329135601
8 rolled more than 6 and 9 combined. The numbers that were rolled more than expected corresponded to the settlements of the lowest elo player.
There were 3 ore hexes: 3,9, and 11. I settled 9 and 11. The lowest elo player settled 3. Then 3 was rolled more than 9 and 11 combined.
The elos of the players were 300, 308 and 102. The player with the elo of 308 ended up with one of the strongest positions I've ever seen in the game, with the highest sum of probabilities of getting cards, along with a 3-for-1 port. Yet he got last place and the lowest elo player won, with the weakest positioning.
This game rolled as if the dice had information about the game state. I (the highest elo player) settled on every number except 5,9,11. At one point in the game there was a string of 16 rolls where 14 of them were 5,7,9,11 (4 in 10,000 chance). That was enough to put me in last place. The moment I became last place, there was a string of 3's rolled in sequence (a number which only I was settled on).
The winner of the game was the lowest elo player, who never had a settlement on 6 or 8, and did not settle on ore until late in the game. The weird timing of the dice rolls caused his win.
boardgamearena.com/4/catan?table=331412953
boardgamearena.com/7/catan?table=331425862a
boardgamearena.com/7/catan?table=331431482
boardgamearena.com/7/catan?table=331503198
boardgamearena.com/8/catan?table=331713624
More 10's rolled than any other number. Is it a coincidence that the highest elo player settled on every number except 10?
Here's is an example of a rare game that doesn't fit into my usual observations. As the highest elo player, I settled on every number except 4 and 8. So I expected 4 and 8 to be rolled more than their expected probabilities. 8 was over-rolled. But 4 was rolled much less than it should. And 9 was over-rolled (the middle elo player did not settle on 9). Usually I find the over- and under-rolled numbers end up hurting or helping one particular player, but in this case, I don't see any of the usual correlations between extra rolls and elo.
Dice strongly supported the lowest elo player, who didn't settle on 6 and had two cities on 9.
6 rolled 6% (was less frequently rolled than 3)
9 rolled 19%
4 rolled 17%
(5 in 1000 chance of so many 4's and 9's)
Dice roll: rate of 2 (~3%) 2
Dice roll: rate of 3 (~6%) 6
Dice roll: rate of 4 (~8%) 19
Dice roll: rate of 5 (~11%) 8
Dice roll: rate of 6 (~14%) 2
Dice roll: rate of 7 (~17%) 21
Dice roll: rate of 8 (~14%) 19
Dice roll: rate of 9 (~11%) 8
Dice roll: rate of 10 (~8%) 10
Dice roll: rate of 11 (~6%) 4
Dice roll: rate of 12 (~3%) 0
I had similar distribution in my previous games. It seems that this is not random Gaussian distribution.
Notice a few things: in 48 rolls, one player ended with 11 points and one player only had 2 points. This was not because of robber play, but because of the random number generator. Both players started with the same probability of having their numbers rolled (19 out of 36 chance of getting a card on any single roll). Yet the middle elo player was doubly settled on 4 and 8 (which were rolled way out of proportion). The middle elo player's numbers (4,8,10) were rolled 50% of the time, when it should be about 30%. The highest elo player was doubly settled on 6 (which only rolled once in 48 rolls - a 3 in 500 chance). In the end, the middle elo player received THREE TIMES as many cards over the course of the game as the next player in spite of having the same starting position probability.
Must have been an incredibly frustrating game to play.
21% sixes when it should be 14%
boardgamearena.com/4/catan?table=338106225
Just as many 8's rolled as 11's
boardgamearena.com/5/catan?table=339274034
boardgamearena.com/4/catan?table=339656315
7
7
7
7
12
7
7
4
4
4
4
7
...
And then a mix of 7s all over the game....
Winning player rolled 7 seven out of their eighteen rolls. Myself and third player each rolled two 7's apiece. I'm salty because I thought I objectively had the best starting position and probability to win.
Lowest elo player was the only one to settle 4 and didn't settle 6.
Result: 24% fours!!! :o (1 in 10,000 chance) and only 1 six rolled in 45 total rolls.
Some matches have predictable dice rolls, like in our previous match.
I had the best odds (had all numbers except 6 and 2) but I ended with 0.6 resources per turn.
Dice roll: rate of 2 (~3%) 2
Dice roll: rate of 3 (~6%) 8
Dice roll: rate of 4 (~8%) 6
Dice roll: rate of 5 (~11%) 9
Dice roll: rate of 6 (~14%) 21
Dice roll: rate of 7 (~17%) 11
Dice roll: rate of 8 (~14%) 20
Dice roll: rate of 9 (~11%) 6
Dice roll: rate of 10 (~8%) 9
Dice roll: rate of 11 (~6%) 6
Dice roll: rate of 12 (~3%) 3
boardgamearena.com/1/catan?table=343431035
boardgamearena.com/4/catan?table=343672786
It's just one of many examples, I really can't believe this anymore, you really need to do something, otherwise a premium version of this website is really pointless. Why should I pay to play when such statistics just take the fun away?
Imagine this: at one point in the game
I settled 3 (twice), 4, 5 (twice), 6 (twice), 8 (twice), 9, 10 (twice), 11 (twice), and 12
I realize the only way to get past the dice bias when I'm the highest elo player is to settle on as many numbers as possible.
At the same point in the game, the winner had
4, 6, 9 (twice), and 10
They ended up with just as many cards as me. This was all because of dice timing (my numbers rolled when the robber was there. 9 rolled 21% of the game 😲)
The other opponent had
4, 5, 6 and 8 (twice)
They both took a port on their initial placement. Probabilistically, I should have had waaaaay more cards than them. But I didn't. I ended with just 5 points.
WHAT IS POSSIBLE:
It is conceivable that a game implementation can use a pseudorandom number generator poorly, producing bias. For example, see en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#Potential_sources_of_bias and how implementation errors can cause it (this is not related to Catan, but is a general observation).
It is conceivable that a pseudorandom number generator can behave poorly, producing an uneven distribution over its expected range, or clustering numbers in a statistically invalid way over large numbers of samples.
WHAT IS NOT POSSIBLE:
Your elo is irrelevant. BGA implementations use a call like this, which is incredibly simple:
$new_value = bga_rand(1, 6);
This produces a new dice value that is either 1, 2, 3, 4, 5, or 6.
As a math professor you're well aware of function inputs and outputs. Note in this case, the API call has zero knowledge of elo, zero knowledge of which values might be good or bad, and zero knowledge of anything except for the minimum and maximum requested integer.
I tell you this to urge you, with respect, not to spread misinformation about PRNG values being related to rank. The source code is incredibly simple and easily verified.
What you COULD do, if you wish to do statistical analysis, is make a spreadsheet over a large number of games, tracking the dice results in each game WITHOUT considering elo, and determining the overall distribution of die results after (for example) 50 games. If such a large number of games still has an abnormal distribution, then this might be evidence to examine the bga_rand() API call more closely.
I KTO RZUCA KOŚĆMI ŻE TYLKO JEDEN GRACZ DOSTAJE 7 ? W KOŚĆIACH?
boardgamearena.com/1/catan?table=363134109
Turns out 19% of the rolls were 3 and 7% of the rolls were 8. How could I possibly know this at the beginning of the game?
boardgamearena.com/4/catan?table=363140553
At first glance the final game statistics look pretty "normal", but some things jump out
Blue settled only 5,9,10 at the initial setup. 5,9,10 then rolled much more than its expected value
White settled only 8,3,4, whose combined total rolls were just as expected.
I needed 11 to be rolled to win, but it only rolled 4%, while 3 rolled 8%
I've also been noticing that some players roll significantly more 7's in some games than other players. In this game, blue rolled 9 sevens, while white rolled only 1 seven.
As a note for myself, blue had the lowest elo at the table. These are observations. Observations and hypotheses can never, by definition, be "misinformation"
boardgamearena.com/1/catan?table=363340432
boardgamearena.com/4/catan?table=363369076
Table #370186736
Dice roll: rate of 2 (~3%)
4
Dice roll: rate of 3 (~6%)
4
Dice roll: rate of 4 (~8%)
11
Dice roll: rate of 5 (~11%)
6
Dice roll: rate of 6 (~14%)
8
Dice roll: rate of 7 (~17%)
23
Dice roll: rate of 8 (~14%)
21
Dice roll: rate of 9 (~11%)
8
Dice roll: rate of 10 (~8%)
8
Dice roll: rate of 11 (~6%)
9
Dice roll: rate of 12 (~3%)
0
More than double as many 10's as expected. This benefitted the orange player, who also happened to roll 10 sevens through the game while the other players only rolled 7 three and four times respectively. This pattern (where the person who rolls the most sevens also happens to get assistance from the dice on other numbers) has happened often enough that I would consider it noteworthy enough to examine more closely.
boardgamearena.com/4/catan?table=370928634
Same game as above
1 in 100,000 chance of a string of 5 threes in 7 rolls
4 in 100,000 chance of a string of 5 sixes in 8 rolls
Less than 1% chance of only two nines in 74 rolls
boardgamearena.com/4/catan?table=373547535
boardgamearena.com/table?table=373846133
4 rolled more than any other number
boardgamearena.com/8/catan?table=373850733
boardgamearena.com/5/catan?table=373899016
I had such a great setup - six was both wheat and ore. I settled both. I also settled the 8 ore. But I did not get as many cities as the lowest elo player who settled the 10 ore (that was their only ore source). Because 10 rolled way more than 6. In fact, 6 rolled just as rarely as 11. The other high elo player also settled both ore and wheat 6, but ended up with no cities. These dice make it impossible to play with normal basic strategy. My only winning strategy is "settle every number except 2 and 12"
table #373853551
Move #41
Progression 0%
21% fours! Ended in just 34 rolls. Has me wondering what the hypothetical smallest number of rolls is needed to win the game.
1 in 500 chance of so few 5, 9 and 11. I settled every number but 10. Then 10 rolled way more than expected. 3 was double its expected value. It just so happened that the player who benefitted from the 3's and 10's also rolled double as many 7's as the rest of us. I've noticed this pattern in other games as well. This time one difference from the norm is that the dice bias went towards the player with the highest elo.
Really weird distribution (double as many 11's rolled as 6's)
1 in 10,000 chance of so few 6's and 7's
This is another example of a game where it's really obvious that the way that the roll distribution is different from a pure normal distribution is strongly correlated to the players' initial placements (and in this case, penalized the player with the highest elo, by chance perhaps, or for whatever reason)
boardgamearena.com/5/catan?table=380188073
boardgamearena.com/1/catan?table=382466496
boardgamearena.com/7/catan?table=382703627
1 in 10,000 chance of so few 3, 8 and 9
boardgamearena.com/8/catan?table=382713595
24% sixes
The only two numbers the highest elo player did not settle on initially were 6 and 11. Coincidence again??
boardgamearena.com/7/catan?table=384272045
Is it a coincidence once again that the highest elo player was the only player who settled 6?
boardgamearena.com/table?table=384288729
11% 5's and 6's (and most of those only at the end of the game)
boardgamearena.com/7/catan?table=384402695
More 2's than 9's
More 11's than 7's
boardgamearena.com/table?table=384415171
More 3's than 8's
Actually 6 times as many 3's rolled as 4's
boardgamearena.com/community
Twice as many 10's as 7's
All incidentally helping the lowest elo player at the table
boardgamearena.com/1/catan?table=385062522
This is one of the worst skews I've seen in a long time. Less than 1 in 1000 chance of so many 8,5,10 (all benefitting one player) and so few 6,7
A pattern I've noticed is that when one player benefits from the dice skew, they also tend to roll more sevens. This is a good case in point. The winner rolled 8 sevens while the rest of us each rolled one 7.
As soon as I picked my initial settlements, I commented that my choices pretty much guaranteed that 4 would not roll (I was the highest elo at the table and I settled on two 4's, one of which was the highest source of brick on the board). Sure enough, 12 rolled more than 4 (until the very end, when they ended with the same percentage of rolls). The person who had one settlement on an 11 brick had more brick throughout the game than my two settlements on 4 and one on 3.
Question: how could I possibly know this would happen??
How did I know this would happen?
boardgamearena.com/4/catan?table=385372698
In this game 11 rolled more than 8. The player who settled an 11 ore (and had an elo of 100ish) easily won over the player who settled 8 ore and 8 wheat, as well as 10 brick and 10 wood (and had an elo of 325ish - one of the top 100 players).
One of the patterns I've noticed happened in this game as well - that the 100ish elo player who benefited from a disproportionate number of 3's, 4's and 11's also rolled the majority of the 7's (four 7's compared to one and two 7's for the other players).
Based on that theory, what should happen when the highest elo player settles every number except 2 and 12 (a common strategy of mine, given my observations)? We should see a lot more 2 and 12 than usual.
Here, the lowest elo player settled the 2 ore, while the highest elo player settled 10 ore.
2 rolled 7% of the time, while 10 rolled 4% of the time, as predicted.
boardgamearena.com/8/catan?table=385383356
In this game, the dice strongly favored me, the middle ELO at the table, and hurt the lowest ELO player. I have never averaged so many cards per roll before (1.5!!).
Six was rolled 36% of the time. The probability of that occuring is 1 in 10,000.
boardgamearena.com/5/catan?table=386335131
7 was rolled 5 times in a row. At first I was excited for the robber to finally move off my 8 (which I had 2 settlements on and a port for), but after all the dust settled, the robber was back on my 8. 7 did not get rolled after that for the remainder of the game. A lot of 8's were rolled, but I did not use that port once the entire game :(
1. You had the highest elo at the table
2. The fact that the dice might be biased against you was evident after you only got one card in the first eight rolls of the dice (and that from an 11), in spite of a strong choice of initial settlements
3. By the end of the game, you had a settlement on every number except 12. And yet, you only averaged 0.5 cards per roll...
4. The string of five 7's in a row happened when you had the monopoly card in your hand (I feel this is not a coincidence as I have seen this before). The chance of five 7's in a row is 1 in 10,000
Three 11's rolled before the first 6.
All in all, 13% 11's and 8% 6's.
I was the highest ELO player at the table. I settled every number except 8, 11 and 10. I eventually settled every number except 2. My initial settlements gave me a 23/36 probability of getting a card on any given dice roll.
The lowest ELO player settled 2,5,8 and 10 at the beginning of the game. That's it! They chose 2 ports! And one had a 2! Their probability of getting a card on any given dice roll was 13/36 - almost half my chances. Yet they ended up with a fist full of cards while I sat patiently waiting and waiting for the first 6 to roll, as 8 rolled over and over.
By the end of the game, the lowest ELO player received on average 1 card per turn, while I got 0.7 cards per turn - this was all due to the biased dice.
The highest elo player ended the game with a 56/36 chance of getting a card on any given roll (based on settlements).
Yet the lowest elo player got 0.9 cards per roll and the highest elo player got, on average, 0.6 cards per roll.
boardgamearena.com/7/catan?table=388236876
Lowest elo players settled 3 ore and 11 ore
6 ore should roll more than 3 ore and 11 ore combined
And yet... 22% 11's and 3's (should be 11%)
7% sixes (should be 14%)
There were three times fewer sixes than 11's and 3's
boardgamearena.com/10/catan?table=388569894
Then 3 rolled less than any other number, in fact twice as many 2's rolled as 3's. (Also strange was 43% of all rolls were 6 or 8 when it should be 28%)
boardgamearena.com/5/catan?table=388589607
for me it's not plausible only 8 and 4.
table #388655356
Dadi: percentuale di 2 (~3%)
9
Dadi: percentuale di 3 (~6%)
2
Dadi: percentuale di 4 (~8%)
22
Dadi: percentuale di 5 (~11%)
7
Dadi: percentuale di 6 (~14%)
11
Dadi: percentuale di 7 (~17%)
11
Dadi: percentuale di 8 (~14%)
22
Dadi: percentuale di 9 (~11%)
11
Dadi: percentuale di 10 (~8%)
0
Dadi: percentuale di 11 (~6%)
0
Dadi: percentuale di 12 (~3%)
4
The randomizer REALLY didn't want me to win (I had the highest elo at the table)
More 11's rolled than 5's or 6's (the only numbers I didn't settle were 3,4, and 11. 4 also rolled more than 5 or 6).
I only needed a knight or a victory point to win (19/25 chance at start of game). Instead I pulled both monopolies, the road builder and year of plenty!
Thank you for posting. This game fits a lot of patterns I've been observing.
Notice that there were no 10's or 11's rolled (1in 1000 chance).
You were the highest ELO at the table. You also had the strongest starting settlements, with a 21/36 probability of getting a card on any given roll. Yet you ended the game with only 0.5 cards per roll on average.
The lowest ELO player had the weakest starting position, with a 19/36 probability of getting a card on any given roll. Yet they ended the game with 1.4 cards per roll on average.
This is the sort of initial settlements that encourage dice bias, in my experience: when one of the lower elo players at the table doubles up on a number on their initial choice of settlements (here one player doubled up on both 8 and 4, and then they rolled a combined total of 44% 😳). When I am not the highest elo at the table, I try to double up on a number in the initial settlements - this strategy has been working for me. When I'm the highest elo, I settle every possible number except 2 and 12.
table=388822860 (for exemple)
I apologize to the developper for "Repeatedly reporting the same thing after it being explained that this is not a bug and that the dice work with a very fair algorythm is aggressive towards the developer and causes unnecessary work for them. The dice are fairly balanced".
i did'nt saw your response (i though i will me notified in my profil)
I was very frustrated because i love this game and did'nt thought dreaming.
Very happy to see this bug report... that i just discovered.
Thank You all for that ! I'll sleep better.
One of the best inspiration : If you can't fix this problem . I'll stop playing permanently
I thank you and the other developers for this incredible site
I have no doubt that Catan calls
$new_value = bga_rand(1,6)
every time it rolls the dice. I've done enough coding myself to realize how much easier it is to program a simple random dice call than something more complicated. I doubt that the bga_rand function is non-random enough to explain all the weirdness we're all observing.
I actually don't blame the catan developers.
I'm wondering if there might be another function at play at a more site-wide meta-level that encourages low ELO players to keep playing by purposely giving them a little extra luck every now and again. I only say this because I have observed similar weirdness in the randomizer (working as a function of relative elos at the table, but not uniformly (i.e. occasionally the highest elo player will get the extra luck)) while playing Viticulture on this platform. I have no idea how such a meta-level function would be coded - it seems extremely complicated. In Catan, it seems to know where the ore hexes are, where the sheep hexes are, at what moments a 7 would be devastating and at what moments it would be beneficial, and sometimes what development card I need next.
In Viticulture, it seemed to know which mamas and papas were best, which set of vines cards would destroy your chances, and which order cards did not synch with which vine cards. It also seemed to know the best visitor cards.
I have not observed this yet in other games on this platform, but it might be especially evident in Catan...
A lot of these observations could simply be the luck of the draw. In any given game, one player will be lucky and the others unlucky, by default. The reason I stop and wonder is because too often the luck in one dimension goes hand in hand with luck in other dimensions, to the point where I can predict how the final distribution will differ from the normal. I should not be able to make such predictions (which are correct about ,80% of the time) if there is no mistake in the randomizer.
As the highest elo player at the table, I settled every number except 8 and 12, after I got my third settlement.
Sure enough, 8 rolled 23% of the time (should be close to 14%)
I had the highest elo and settled every number except 11 and 12. I had a wheat 6, an ore 5 and a sheep 3.
Before I was able to settle the 8, it rolled like crazy. As soon as I settled the 8 (meaning I had settled every number except 11 and 12), there were a string of times interesting rolls: 7 (for opponent), 7 (for opponent), 11 (for me), 7, 3 - i.e. in the six rolls after I settled every number, I managed to lose cards rather than gain.
All in all, 5 and 6 rolled 13% of the time (about half as much as the 25% that they should roll) and 3 rolled 13% of the time (double the expected 6%). I was still able to win, but felt like I was playing against a fourth invisible player: the dice.
boardgamearena.com/4/catan?table=389259270
12 rolls double as much as it should (6% instead of 3%)
boardgamearena.com/4/catan?table=389447053
Hmmm... I see the highest ELO player settled both ore and wheat on 5's? I know! Let's make 11 roll double as often as 5 and let's make 12 roll as much as 5! That'll do the trick. And while we're at it, why not let the lowest ELO player roll 7 twelve (!!!) times while the highest ELO player never rolls the robber? Oh look, it worked! The player with an ELO of 130 and a weaker starting position actually beat the players with ELO's in the 200's and 300's. Another underdog victory for the records. Yippee!
boardgamearena.com/7/catan?table=389875137
This game was a real joke (I was the third Elo level)
Durée de la partie 58 min
Niveau moyen des joueurs 150
Score moyen 6.25
Cartes développement restantes 21
Lancer de dés : taux de 2 (~3%) 3
Lancer de dés : taux de 3 (~6%) 2
Lancer de dés : taux de 4 (~8%) 5
Lancer de dés : taux de 5 (~11%) 15
Lancer de dés : taux de 6 (~14%) 6
Lancer de dés : taux de 7 (~17%) 29
Lancer de dés : taux de 8 (~14%) 19
Lancer de dés : taux de 9 (~11%) 18
Lancer de dés : taux de 10 (~8%) 2
Lancer de dés : taux de 11 (~6%) 2
Lancer de dés : taux de 12 (~3%) 0
with a specific series :
X lance les dés : 4,5
Y lance les dés : 4,5
Z lance les dés : 5,4
W lance les dés : 5,2
X lance les dés : 4,5
Y lance les dés : 5,4
I was nearbe two "6" tiles.
Hope there was no relation due to the -30 Karma for opening many bug reports
Positive message : we had many laught ...
No (other) comment.
24% nines
Five times as many 11's as 5's.
I was the highest elo at the table. I settled every number except 11. I knew the dice would be biased against me when two 11's rolled in the first 3 rolls. Lowest elo player easily won.
1. The lowest ELO player at the table rolled the most 7's
2. The only number the lowest ELO player did not settle was nine. Then nine rolled as infrequently as 2
3. The lowest ELO player doubly settled 4. Then 4 rolled way more than expected.
4. The lowest ELO player had the highest number of cards per roll (1.1) in spite of not having the strongest starting position.
I'm working on quantifying these observations statistically over the set of all 3-player games that I've played (over 500 games). Hopefully that's enough. If anyone knows where I can go to find all 3-player Catan games ever played, I would love the info to improve my stats.
boardgamearena.com/5/catan?table=391345403
1. The winner did not settle 10. Then 10 rolled half as much as expected
2. The winner rolled the most 7's
This time these advantages went to the highest elo player at the table (it happens occasionally).
boardgamearena.com/4/catan?table=391351548
1. There will be more 4's than 9's
2. 3 and 6 will be quite rare
Sure enough, more 4's than 9's and 3 and 6 both rolled about half as much as expected.
boardgamearena.com/4/catan?table=391369459
37 min
Niveau moyen des joueurs
180
Score moyen
6.25
Cartes développement restantes 17
Lancer de dés : taux de 2 (~3%) 4
Lancer de dés : taux de 3 (~6%) 2
Lancer de dés : taux de 4 (~8%) 4
Lancer de dés : taux de 5 (~11%) 10
Lancer de dés : taux de 6 (~14%) 13
Lancer de dés : taux de 7 (~17%) 13
Lancer de dés : taux de 8 (~14%) 15
Lancer de dés : taux de 9 (~11%) 29
Lancer de dés : taux de 10 (~8%) 6
Lancer de dés : taux de 11 (~6%) 2
Lancer de dés : taux de 12 (~3%) 2
more 11s than 6...
47 min
Niveau moyen des joueurs
170
Score moyen 8
Cartes développement restantes 15
Lancer de dés : taux de 2 (~3%) 1
Lancer de dés : taux de 3 (~6%) 1
Lancer de dés : taux de 4 (~8%) 7
Lancer de dés : taux de 5 (~11%) 14
Lancer de dés : taux de 6 (~14%) 9
Lancer de dés : taux de 7 (~17%) 17
Lancer de dés : taux de 8 (~14%) 10
Lancer de dés : taux de 9 (~11%) 16
Lancer de dés : taux de 10 (~8%) 10
Lancer de dés : taux de 11 (~6%) 12
Lancer de dés : taux de 12 (~3%) 1
Each time i choose the position with 6, it's just a calamity ...
very strange "Random" : it's just incredible (see precedent post)
11 in second position ...
Lancer de dés : taux de 2 (~3%) 0
Lancer de dés : taux de 3 (~6%) 2
Lancer de dés : taux de 4 (~8%) 12
Lancer de dés : taux de 5 (~11%) 12
Lancer de dés : taux de 6 (~14%) 6
Lancer de dés : taux de 7 (~17%) 10
Lancer de dés : taux de 8 (~14%) 18
Lancer de dés : taux de 9 (~11%) 12boardgamearena.com/bug?id=66082#
Lancer de dés : taux de 10 (~8%) 12
Lancer de dés : taux de 11 (~6%) 14
Lancer de dés : taux de 12 (~3%) 4
it's time for me to stop playing this awfull game.
It's just ... insane.
Durée de la partie
52 min
Niveau moyen des joueurs
144
Score moyen
7.5
Cartes développement restantes 8
Lancer de dés : taux de 2 (~3%) 5
Lancer de dés : taux de 3 (~6%) 5
Lancer de dés : taux de 4 (~8%) 8
Lancer de dés : taux de 5 (~11%) 15
Lancer de dés : taux de 6 (~14%) 16
Lancer de dés : taux de 7 (~17%) 14
Lancer de dés : taux de 8 (~14%) 9
Lancer de dés : taux de 9 (~11%) 11
Lancer de dés : taux de 10 (~8%) 4
Lancer de dés : taux de 11 (~6%) 11
Lancer de dés : taux de 12 (~3%) 2
Total rolls: 102
Total 9 appeared: 1 time
What is the probability of this happening?
The probability of one 9 in 79 rolls is 0.099029% (about 1 in 1000)
The end game stats give the (rounded) percentage of 9's rolled, not the total. In your game there were 79 rolls rather than 102 (which is the sum of the percentage from the rolls table)
Notice that you had the highest ELO at the table and settled twice on 9, and they were both ore hexes.
The other two players settled every number on the board between the two of them, except 2, 12 and 9. Is this still a coincidence??
You had the strongest starting position in the game. Probabilistically, you should have won.
Other experts like myself have noticed these issues (example comment pasted below)
I will continue the slow and tedious task of trying to analyze thousands of games and provide concrete evidence that this is the case (but I am a mathematician and not a statistician, so I may need to consult my statistician brother for support, and I also have other things to do with my time, so it may take a while).
"I'm a Statisical expert, Inmho. and others. I concur with others as above.
I've developed Medical software $ 1 Million install +\-, for multiple departments in large hospitals and research ctrs, medical records for diseases difficult to track, advise, schedule, supplies auto ordered, interfaced with other vmajor vendor, at point of contact. multiple advisories, appropriately offer algorithms for Risk Assessment of Death if patient goes to surgery chemo, radiation, etc. For patients with complicated diseases, Heart, Cancer, Diabetes, Orthopedics, High Risk Pregnancy, etc
7 graduate semesters in statistics. Invited speaker to International, National, State, Local agencies, CDC, NIH, NCI, co-laborated & presented to: with FBI, FEMA, LLNL, UCSF, UCB, EMSA, OSHA, NIOSH, CSTE, APHA, DOT, DOL, FDA....
I like game, but clearly NOT random.
I've been doing statistics since 1970s Mainframe, UNIX, PC, Mac, HP, IBM, Sun, SAS, SPSS, BMDP, MUMPS (used by VA and NASA).& currently Sr Epidemiologist III, working on Covid19.
It's a fun game- My thanks for all"
2 - 3 rolls
3 - 0 rolls
4 - 16 rolls
5 - 8 rolls
6 - 29 rolls
7 - 8 rolls
8 - 8 rolls
9 - 11 rolls
10 - 0 rolls
11 - 16 rolls
12 - 3 rolls
The chance of so many 4's, 6's and 11's in a game is 3 in 100,000 😯
This greatly benefitted the middle elo player and hurt the lowest elo player
As an aside, the end fame stats show the percentage of rolls, not the total number of rolls (so there was 1 two rolled in a total of 38 rolls for the game)
In this game, 12 rolled more than 4, 9 or 10.
5 rolled 6x more often than 4 when they should be roughly similar in their number of rolls.
Again, these are not shockingly unexpected. What is weird is to be able to predict this dice behavior before the first roll.
boardgamearena.com/4/catan?table=398003901
It is not uncommon for surprising rolls to happen even in tabletop Catan with real dice: four rolls of the same number, 11s being rolled more than 6s, four Development Card with victory points being drawn one after the other... all of this can happen on a game of Catan using real dice and paper cards. There is nothing surprising about these things happening too in BGA's Catan.
See also boardgamearena.com/bug?id=64097, where a suggestion about a widget to show dice statistics has degenerated into lots of players complaining that the random number generator is buggy (when it is not).
Agreed, there are many people who complain about random number generators who don't understand stats.
However in this case, there are multiple complaints by experts in stats (see July 1 post above). I myself have a graduate degree in math.
There are also a lot of people in the forums, myself included, complaining that the dice act strongly in their favor, making the game less fun (see Jun 11 post above).
If I can predict in advance the way in which the dice rolls will differ from a normal distribution, then the random number generator cannot possibly be working properly, right?
0 rolls of 6. 23 rolls of 8
I invested heavily in two 6 resources at the beginning, and could not build a single thing!
9 came up repeatedly to the point one player thought another was hacking.
boardgamearena.com/1/catan?table=427058192
A couple things to note:
1. The player who won with 11 points started the game with the lowest probability of getting a card on a given roll. (The other two players ended the game with 2 and 3 points).
2. The winner started the game with the lowest elo. The player with the highest elo settled two 6's and 6 never rolled for the whole game
3. The lowest elo player settled two 8's and two 9's which both rolled like crazy. I have noticed in three player Catan games when a player settles two hexes with the same number at the beginning of the game that those numbers roll either in relatively extreme overabundance or underabundance (relative to the expected number of rolls)
I had 8 ore and 5 wheat and should have had the most cities on the board (probabilistically), but 11 rolled more than 5, and both 9 and 10 rolled more than 8, to the advantage of the lowest elo player at the table.
boardgamearena.com/4/catan?table=463224316
Even very good Catan players can't achieve a high ELO because the result depends a lot on the rolls, just don't play it if you can't handle that. I personnally can't handle that much luck so I don't play it, neither IRL nor online.
Don't look up excuses with randomness or conspiracy theories.
en.wikipedia.org/wiki/Law_of_averages
Picking and choosing games that one feels are "unfair" while ignoring others shows a distinct lack of understanding of probability.
@cboers18: Please, PLEASE stop posting random games as though they prove something. They do not. You are not engaging in rigorous scientific study methods, which makes me severely doubt your claims of expertise and authority. You are engaging in apophenia.
If you want to prove that the randomizer is broken in some way, play ten thousand games, diligently record EVERY roll across those games, and submit that.
But, like I've said before, if I can predict within the first three rolls, how the end game stats will differ from a normal distribution, then something has to be up with the randomizer. Designing an experiment to prove it is not straightforward.
Like 'The starting 6 numbers of the player with the highest elo will be rolled in average less than usual compared to all others numbers'.
Then in all of your next 100 games, note like the 10 games where something weird happen about this event. Then share it on the forum, here, or in mp.
That will force you to choose a specific event, force the number of game to be definite, which will remove most of the cherry picking.
Severeal numbers didn't come at all. Not only the 2 and the 12, but also numbers Like the 4 and the 10.
擲骰:2 的比率 (~3%)
0
擲骰:3 的比率 (~6%)
6
擲骰:4 的比率 (~8%)
11
擲骰:5 的比率 (~11%)
16
擲骰:6 的比率 (~14%)
11
擲骰:7 的比率 (~17%)
23
擲骰:8 的比率 (~14%)
10
擲骰:9 的比率 (~11%)
11
擲骰:10 的比率 (~8%)
3
擲骰:11 的比率 (~6%)
3
擲骰:12 的比率 (~3%)
5
There must be something wrong.
It also seems this problem apears since 2022 and no one cares.
That's a pity, because this online version is awsome.
I lost significant skill points due to 2 recent crazy games and am tempted to not play the game any more.
boardgamearena.com/table?table=557463015 15% 12 rolls
boardgamearena.com/table?table=556660512 44% of rolls were 4 or 5
I see the solution as offering the Traders and Barbarians Event Deck (maybe not with the events) so that dice are *shuffled* with a reset instead of *randomly generated*. This would be HUGE for Catan.
Ход #209
Кубики: частота 2 (~3%) 2
Кубики: частота 3 (~6%) 5
Кубики: частота 4 (~8%) 7
Кубики: частота 5 (~11%) 8
Кубики: частота 6 (~14%) 13
Кубики: частота 7 (~17%) 8
Кубики: частота 8 (~14%) 11
Кубики: частота 9 (~11%) 5
Кубики: частота 10 (~8%) 18
Кубики: частота 11 (~6%) 10
Кубики: частота 12 (~3%) 13. !!!!!!!!!!!!!!!!!!!!!!
It’s just not the right thing to do. These are systematic mistakes and they’re not logical. Mathematical statistics from a world of pairs. Developers, do something. Respect your users. Get rid of the algorithms. Hire the right people if you can’t do it yourself.
This game had 4, 6 and 7 over and over again. Makes the game seem unbalanced. I know this can happen, but there does seem to be a pattern of dice sticking on certain numbers. Other games recently had 4 or 10 once or twice each four turns.
In the first, I got virtually no resources for the last 2/3rds of the game - maybe 2 - while my opponents racked up score after score. In the second, same thing. Even worse, I had a wheat field that was supposed to produce on 8's. I think only one 8 was rolled for the game! but lots of consecutive 7's for both games.
Something has got to be wrong for your randomizer ... at least when it comes to real time games.
Dice roll: percentage of 3 (~6%)
4
Dice roll: percentage of 4 (~8%)
4
Dice roll: percentage of 5 (~11%)
19
Dice roll: percentage of 6 (~14%)
15
Dice roll: percentage of 7 (~17%)
14
Dice roll: percentage of 8 (~14%)
13
Dice roll: percentage of 9 (~11%)
10
Dice roll: percentage of 10 (~8%)
9
Dice roll: percentage of 11 (~6%)
8
Dice roll: percentage of 12 (~3%)
1
Can you please look into it?
There is no way the dice randomization is correct.
I just got a game with 8+ times number 12......
There is a cluster on a few numbers.
I play a this game daily and I got to see 5 times in a row 11 and other strange things.
The feeling is shared with lots of players.
Some have stopped this game due to that....
6 consecutive 7's, starting from move 46: boardgamearena.com/gamereview?table=584453091
Overall, 7 was thrown 28% of the times, instead of 16,67%
Doesn't look like the rolls are independent of each other.
boardgamearena.com/13/catan?table=590449529 Here's another game I played where one player (who started the game with the lowest probability of getting a card on a single roll) doubled up on two numbers (8 and 10) and ended up winning the game in a landslide.
Played through an entire game without a single 7 rolled.
Game duration
27 min
Players' average level
80
Average score
5.5
Remaining development cards
19
Dice roll: percentage of 2 (~3%)
3
Dice roll: percentage of 3 (~6%)
11
Dice roll: percentage of 4 (~8%)
8
Dice roll: percentage of 5 (~11%)
16
Dice roll: percentage of 6 (~14%)
27
Dice roll: percentage of 7 (~17%)
0
Dice roll: percentage of 8 (~14%)
11
Dice roll: percentage of 9 (~11%)
11
Dice roll: percentage of 10 (~8%)
11
Dice roll: percentage of 11 (~6%)
3
Dice roll: percentage of 12 (~3%)
0
I would not expect people playing a game for enjoyment to, as you suggest, "play ten thousand games, diligently record EVERY roll across those games, and submit that" in order to contribute to a bug report. Nor would I describe other posters contributions as "worthless nonsense."
Please remember, we're talking about the minutiae of engineering code here. Not the probability of dice rolls.
There is no contribution here which won't help a software engineer look at and understand the issue.
My best guess, based on the behaviour reported is that to aid with performance the dice rolls are being determined at load time rather than run time from a random number generator which is seeded from the current time in milliseconds. The issue with this is that, depending on the OS the code is running on, the system clock won't be updating every millisecond. This will lead produce the clustering that's being reported.
what the hell, you see that you have 1 million complaints about this and you don't do anything. I PROPOSE THAT NO ONE BUYS PREMIUM AGAIN UNTIL THE DICE GENERATOR IS REPLACED. IF YOU PLAY US - Then we have to cut your invested money. or to move to another online gaming platform
boardgamearena.com/table?table=631239836
20% of rolls were 2, 11 or 12 (should be 11% of rolls). And this was even after a bunch of 5s, 4s and 10s finally rolled at the end of the game. Interestingly, one player settled on every number except 2,3,11,12.
would you mind expanding on your statement please?
When you say 'random,' do you mean:
- The set of dice rolls for a game is not predictable prior to any visibility of the set;
- OR The set of of dice rolls for a game is not predictable even after a small subset of the set has been observed?
boardgamearena.com/11/catan?table=646391502
boardgamearena.com/5/catan?table=648719540
in game
651846181
the number 9 was rolled 31 times....
Less than 1% chance if no 6 in the first 31 rolls, favoring the lowest elo player (half of the first 16 rolls were 8). Also, many more 7s rolled by the player with the lowest elo.
38 TIMES THE NUMBER 8!!!!! only 3 times the number 6. This is insane!
This game seems really bugged dice-wise.
I made a table showing the results for each game (table ID, counts of each sum from 2 to 12, χ² statistic, and p-value), and I included my Python calculations for anyone curious:
colab.research.google.com/drive/1Cmyp6RRjgLr0XbXgf9lrj_37zQXoc1MZ?usp=sharing
In short: I compared what actually happened in each game to what should happen with fair dice. The p-value tells you the probability of seeing results as far from the expected ones, assuming the dice are fair. If the p-value is above 0.05, the dice are likely fair; below that, it’s statistically unusual.
In my 15 games, 6 had p-values low enough to suggest the dice weren’t fair. The most extreme case was table #715991625 — I’ve never seen dice so biased before!
Honestly, it’s frustrating when the dice are this unfair — something should really be done about it.
25 min
Durchschnittliches Spielerniveau
142
Durchschnittliche Punktezahl
6.66667
Verbliebene Entwicklungskarten
13
Würfelwurf: % der 2 (~ 3 %)
3
Würfelwurf: % der 3 (~ 6 %)
10
Würfelwurf: % der 4 (~ 8 %)
5
Würfelwurf: % der 5 (~ 11 %)
14
Würfelwurf: % der 6 (~ 14 %)
12
Würfelwurf: % der 7 (~ 17 %)
27
Würfelwurf: % der 8 (~14%)
5
Würfelwurf: % der 9 (~ 11 %)
10
Würfelwurf: % der 10 (~ 8%)
7
Würfelwurf: % der 11 (~ 6 %)
3
Würfelwurf: % der 12 (~ 3 %)
3
l
das kann nicht sein und macht keinen spass, weiss nicht was geaendert wurde aber sowas passiert am laufenden band !!! Das die 11 oder 3 oefter kommen als 6 oder 8 und das extrem oder es kommt 5 mal hintereinader dieselbe zahl ...das passiert in wirklichkeit auch nicht vielleicht einmal bei 10 partien... bin von einem elo 290 zurueckgefallen weil da ws geandert wurde ...bitte tut was
The dice in this game are so unnatural, in about 70% of the games (I played) there are specific numbers (different in every game ) that roll extremely often, others nearly never.
Change the dice programming - this game is no fun that way.
Just ask the Catan- people on "catanuniverse.de" how thes do it, the dice there are natural.
These dice are ridiculous, really!
The Space Base dice are really random and natural, they roll like RL.
Catan dice do not, no way !
Is it possible to get this topic addressed? I see that I am not alone in noting the issue.
הוסף לדוח הזה
- מספר שולחן/מהלך אחר
- האם לחיצה על F5 פתר את הבעיה?
- האם הבעיה הופיע כמה פעמים? בכל פעם? באופן אקראי?
- אם יש לך צילום מסך (מומלץ) אתה יכול להשתמש ב Imgur.com כדי להעלות אותו להדביק קישור לכאן.
