Board Game Arena

This is the 3rd time since yesterday I had a clear lead only to see it squashed by an abnormal number of dice rolls.
https://boardgamearena.com/table?table=607601755

The second player (who had 2 1/2 x my ELO) had a few settlements on 4, and that number got rolled 21 times in this game.
Can anyone calculate the chances of that happening in a reasonable game?

Just venting my frustration

This is what Chat GPT had to say about it:
A rough way to decide “significance” is to compare how many standard deviations away your result is from the expected. For large nnn, each category’s count can be approximated by a binomial distribution with parameters (n,p)(n, p)(n,p) (where ppp is the theoretical probability).
• For example, the theoretical probability of rolling a 4 is p=8.33%p = 8.33\%p=8.33%.
• The standard deviation for that binomial is roughly np(1−p)\sqrt{np(1 - p)}np(1−p).
o Here n=100n = 100n=100, p≈0.0833p \approx 0.0833p≈0.0833.
o σ≈100×0.0833×0.9167≈2.76%\sigma \approx \sqrt{100 \times 0.0833 \times 0.9167} \approx 2.76\%σ≈100×0.0833×0.9167≈2.76% in percentage points.

Comparing the difference of +12.67%+12.67\%+12.67% for sum=4 to σ≈2.76%\sigma \approx 2.76\%σ≈2.76% suggests that sum=4 is roughly 4.6 standard deviations above the expected value—a strong indication it is a statistical outlier.

Sum=5’s difference of −7.11%-7.11\%−7.11% is also around 2.6 standard deviations below expectation, which might also be considered unusually low (though sum=4 is the more extreme outlier).

Having also raised concern about dice fixing, cheating, or just dice being otherwise rigged/broken, I promise the forums here usually doesn't have an ear to hear it. you got a little team of "it's all random" guys that pounce on anyone who gets hosed.

But I hear you. I believe you. I've been the guy on the other end plenty of times. It isn't just numbers, it's numbers combined with player behavior. When a player "plays" normally and gets lucky, great. Normal play reflects players who do not know (or control) the dice rolls. Rigged play reflects players who do know or control dice rolls, and it sucks. I often wonder what "fun" players have in rigging a friendly online game. I don't see the point, but some people just revel in it I guess. BGA has and will say nothing on the topic. I for one salute you adding another voice.

Adriaticvs wrote: ↑29 December 2024, 00:59 This is the 3rd time since yesterday I had a clear lead only to see it squashed by an abnormal number of dice rolls.
https://boardgamearena.com/table?table=607601755

The second player (who had 2 1/2 x my ELO) had a few settlements on 4, and that number got rolled 21 times in this game.
Can anyone calculate the chances of that happening in a reasonable game?

Just venting my frustration

actually the number of rolls where
{1, 2, 11, 2, 8, 9, 8, 6, 3, 2, 0}
for {2,3,4,5,6,7,8,9,10,11,12} outcome respectively, so 4 got rolled 11 times and not 21

four is indeed the worst outlier with a probability of 3.27 per mille
the probability to observe an outlier smaller or equal than this is about 3 %.

Unlucky but certainly not abnormal

tylerjwarren wrote: ↑29 December 2024, 01:39 Having also raised concern about dice fixing, cheating, or just dice being otherwise rigged/broken, I promise the forums here usually doesn't have an ear to hear it. you got a little team of "it's all random" guys that pounce on anyone who gets hosed.

That's because most post don't explain what is wrong, or can just be dismissed with fast calculations.
Here on that subject, first they didn't said the dice was rigged which is extremely nice, and secondly asked a math question.
And so answers should be way nicer here

They didn't rolled 21 times, it got rolled 11 times out of 52 rolls.
What you have read is a percentage.

This has a probability of 0.327%.
But you can make that claim for every number and for telling that number is too much or too few rolled, so I will """multiply""" it by 2*11.

We now get (1-((1-0.00327)^22))*100=6.95% .

So one game out of 14,4 you should have one number too much or too few rolled as unlikely than that 4 of that game.

tylerjwarren wrote: ↑29 December 2024, 01:39 I often wonder what "fun" players have in rigging a friendly online game.

Exactly !! There are absolutely zero reason that would explain why would BGA do such a thing. So the most obvious answer is : it's not rigged and players just can't handle the randomness, but it's always easier online to blame the program than the lack of luck/skill.

To play should be fun! If you a have to cry, don't play. If you don't like luckbased games, play chess. Catan is a luckbased game... and statistic doesn't work on single game.