In your most recent 8 games of Catan as of when I started on this post, 2 were cancelled, and the 6 completed games had a total of 425 rolls.
That gives a sample average of 70 + 5/6 rolls per game. The games can have 3 or 4 players, and (70+(5/6)) / (3+(1/2)) = 20 + (5/21) .
Accordingly,
in the three-7s-in-a-row paragraph, I pretend each game has 71 rolls
and
in the many-7s-by-users paragraph, I pretend each player gets 20 rolls
.
For any particular sequence of 3 rolls in a row, the probability of that sequence being all 7s is 1/216. A 71-roll game has 69 sequences of 3 rolls
in a row, and treating those as independent would give a probability of 215/216 ^ 69 that there is _no_ sequence of at least three 7s in a row.
That would give a probability of approximately 0.27 that there _is_ a sequence of at least three 7s in a row. Nearby events from those 69
are positively correlated (given that A,B,C is three 7s in a row, the conditional probability of B,C,D being three 7s in a row is 1/6), so 0.27 is an
an overestimate, but even restricting to the 23 non-overlapping sequences of three rolls in a row gives a probability of 0.1 . I ran Python code
to compute the exact probability for 71-roll games, and it's between 0.2370 and 0.2371 .
https://paste.ee/p/CVWVl has a paste of that run.
Sevens out of 20 rolls, on the other hand, is a simple binomial.
https://en.wikipedia.org/wiki/Binomial_distribution
I wrote Python code to compute the extremeness of the times you gave, and it reports that numbers at least as extreme as 5,6,7,8 have
total probability of approximately 0.3617 , 0.1279 , 0.03714 , 0.01125 respectively.
https://paste.ee/p/vIXc5 has a paste of that run.
Bear in mind that you have played over 10 games of Catan and in each of them, you had 2 or 3 opponents, rather than just 1 opponent .
Give us links to some of the games referred to in your resources sentence. Additionally, bear in mind
that the number of rolls per player varying from 20 will make it easier for players to get seven or eight 7s.
If you still think those have happened too much, then also give us links to games where those happen.
