Game #633614948

[Parténope y Ulises]

It is ridiculous. This match finished without any 8. Zero. In all the match. Honestly, it is against statistics.
Just a comment.

#633614948

[Jellby]

With only 36 dice rolls, it's not that unlikely (31/36)^36 = 0.5%, or one in 200. Even with 50 rolls it would be one in 2000.

[JohnnyCyclops]

Randomness gonna random

[Meeplelowda]

Honestly, it is against statistics.

If it NEVER happened, THAT would be "against statistics."

People just want to round things like 0.5% down to zero and act like they're never supposed to happen, BUT IT'S NOT 0% and it's going to happen and SHOULD happen.

[Jellby]

I forgot to say: that's of course the chance of "no 8" being rolled. There's an equivalent chance of "no 6" being rolled, and if that had happened, you'd also have come and complain. So the probability is actually 1%, or even higher.[*]

[*] Probabilities cannot be simply added, because there's also a chance of "no 8 and no 6", but this is a reasonable approximation. I'm also ignoring the probabilities of "no 5" or "no 9", or any other "weird" result that would have triggered your suspicions.

[gmrsmrt]

Actually the probability is much higher than this.
(31/36)**37 = 0.4% (I count 37 rolls) is indeed the probability to get zero 8 out of 37 rolls.
However there is nothing special about 8.
One should count the probability to get X rolls with the outcome 2 and add up all the outcomes which are at least as weird as
the one in question.
Then do the same with the outcome 3, and so on until 12
The total will be at least ten times larger than the original 0.4% something in the few per cent range. Certainly nothing uncommon and found
many times a day on the BGA platform, given the amount of played games.

[Gulchen]

One should perhaps do that for ​ ​ ​ no 7s ​ , ​ ​ ​ but for X in ​ {2,3,4,5,9,10,11,12} , ​ ​ ​ no Xs ​ is strictly less
surprising than ​ ​ ​ no 8s ​ , ​ ​ ​ since the probability of X should be strictly less than the probability of 8.

[GamerJilli]

I find it hard to trust this site

[gmrsmrt]

An outcome can be "weird" (low probability) either because it's too low or because it's too high.
For the case under discussion
too low can occur only for 6,7,8 (for the other outcomes the probability will be higher)
however too high can occur basically for all numbers. This lead to an increase of a factor larger than ten of the probability to have an outlier at least as large as the observed one.
The actual number need to be computed inspecting all the cases separately since the probability of the various outcomes jump
discontinuously between different outcomes. A naive sum would result, as jellby was noticing, to a slight overcount (two numbers can be
way off SIMULTANEOUSLY), however if the outlier is large (low probability) the probability of multiple outliers will turn out very small
and the estimate with the naive sum will be pretty accurate.

[euklid314]

An outcome can be "weird" (low probability) either because it's too low or because it's too high.
For the case under discussion
too low can occur only for 6,7,8 (for the other outcomes the probability will be higher)
however too high can occur basically for all numbers. This lead to an increase of a factor larger than ten of the probability to have an outlier at least as large as the observed one.
The actual number need to be computed inspecting all the cases separately since the probability of the various outcomes jump
discontinuously between different outcomes. A naive sum would result, as jellby was noticing, to a slight overcount (two numbers can be
way off SIMULTANEOUSLY), however if the outlier is large (low probability) the probability of multiple outliers will turn out very small
and the estimate with the naive sum will be pretty accurate.

Well, a "too low" occurrence could also be found if a game had not a single 10 AND no 11 AND no 12. Or not a single 2 AND no 3 AND no 4. Both these events are exactly equally likely as having not a single 7.

There are almost infinitely many "weird events" a human might detect if they analyze a small set of dice throws. That is probably the main reason why there are so many "rigged dice" threads. Many people just dont want to accept that you have to expect heavy outliers in the random distribution of such a short game like CATAN. There will be heavy outliers in almost every game if the dice rolls are random!