Board Game Arena

euklid314 wrote: ↑03 July 2025, 18:57 Please note that I did talk about the probability of 2.8% for two 7s and not of 0.5% of having three 7s in a row. If you are interested in this probability than you have to consider all rolls. If the game starts with a 5, you should mentally make a note that just no 3 7s have happened...

I have never paid too much attention to be honest, since I don't think that there is any conspiracy, but I have the impression that happens frequently that the same number gets rolled more times in a row. My question is more if it Is worth of tracking it or not.

Does my question make sense?

Theana wrote: ↑04 July 2025, 08:12

euklid314 wrote: ↑03 July 2025, 18:57 Please note that I did talk about the probability of 2.8% for two 7s and not of 0.5% of having three 7s in a row. If you are interested in this probability than you have to consider all rolls. If the game starts with a 5, you should mentally make a note that just no 3 7s have happened...

I have never paid too much attention to be honest, since I don't think that there is any conspiracy, but I have the impression that happens frequently that the same number gets rolled more times in a row. My question is more if it Is worth of tracking it or not.

Does my question make sense?

The same number repeating is a frequent event if the dice are random because then the dice have no memory and the next roll is independent of the previous. Only if you tweak the dice you can avoid repeating numbers.

To your question if one should track you will get different answers:
*) Some players will argue that they dont need to track because they feel that there is something obviously wrong.
*) I will argue that I dont need to track because I feel that the dice behave as they mathematically should and as physical dice also behave.

I believe that my argument is much stronger because if something would be wrong some player (one single player would be sufficient!) would have shown it by now. Furthermore I sometimes crunch the numbers if some claim is interesting to me. I never found anything that would suggest something being off.

Just out of interest I analyzed your last game (#696577152) which was also very long with 82 moves and 17 7s. There was a chance of approx 27% that a series of three 7s would happen. Furthermore, the chance of two or more such 7-7-7 sequences happening in the same game is above 5%. But there was not a single 7-7-7 sequence in the whole game!

euklid314 wrote: ↑04 July 2025, 13:23
Just out of interest I analyzed your last game (#696577152) which was also very long with 82 moves and 17 7s. There was a chance of approx 27% that a series of three 7s would happen. Furthermore, the chance of two or more such 7-7-7 sequences happening in the same game is above 5%. But there was not a single 7-7-7 sequence in the whole game!

I actually had another game where 5 rolled 3 times in a row.

The question here is , just for the sake of argument, while yes theoretically 7 - or 5 or 10 or any other number - have the same chance to roll even if they have just been rolled, how often can happen to have the same number rolled 3 times in different games?

Not going to keep track of course, there are so many games played daily that I understand we will see it happening often, in oue games forgetting all the other tables playing at the same time

Theana wrote: ↑04 July 2025, 14:04 The question here is , just for the sake of argument, while yes theoretically 7 - or 5 or 10 or any other number - have the same chance to roll even if they have just been rolled, how often can happen to have the same number rolled 3 times in different games?

An interesting mathematical question!

It is easy to calculate that if you throw the Catan dice three times in a row, you have a 0.014275 = 1.4275% = 1:70 chance of getting 3 same results.
I.e., if you repeat it 70 times you expect (on average) to get one instance of three same results.
Thus, if your game is 72 moves long, you have 70 (overlapping) sequences of 3 rolls in this games and you should expect 1 such instance to happen.

But of course now it is getting a little bit more difficult mathematically. Because 1 instance on average means that some games have 0 instances and others have 2+ instances...

In 36.55% of all games (of length 72 rolls) you have 0 instances, i.e. there will be NO sequence of 3 repeating numbers.
In 37.05% of all games (of length 72 rolls) you have exactly 1 instance, i.e. there will be 1 sequence of 3 repeating numbers.
In 18.51% of all games (of length 72 rolls) you have exactly 2 instances, i.e. there will be 2 sequences of 3 repeating numbers. Note that a sequence 4-4-4-4 would be such a case because you have 4-4-4 twice in this sequence. But also the sequence 4-4-4-6-2-3-10-10-10 would be in this category.
In 6.08% of all games (of length 72 rolls) you have exactly 3 instances.
And so forth


Jontia already wrote that the probability of having at least one instance of 7-7-7 in one game is 23.5% (found by simulation).
Now I have added that the probability of having at least one instance of three same numbers in one game is 63.45% (found by calculation).

Summary: In approx. 2/3 of all games a threefold repetition should occur. But note that in half of these cases there are even multiple such threefold repetitions.

[edit: @Theana: Do these numbers feel right to you? Would you have guessed that there is a 1.43% chance of getting three same sums if you roll the Catan dice three times? Does it feel right that a 3-fold repetition should happen on average once a game? I would be very happy if your (very natural!) feeling was that it should occur less often. Because then it would explain why you felt the situation 7-7-7 as weird - and our discussion could lead to a satisfying result for both of us!]

The generation of dice is not random enough, I feel.
If you play "Space Base" and try to change dice combination with some special cards, the same roll will appear really frequently.
I don't think there is conspiracy, but the used random generator is quite bad.
I would like to know which random generator used in the background...

masahirotakahashi wrote: ↑07 July 2025, 11:02 The generation of dice is not random enough, I feel.

Yeah, well... feelings are quite useless for evaluating random events. Most likely you mean something like "not uniformly distributed for small samples" rather than "not random enough".

I would like to know which random generator used in the background...

Really? If you wanted to know that, it's easy to find, like... just look in the FAQ.

Coleus1 wrote: ↑19 June 2025, 10:48 I don't Agree. If you play Catan in real life, and then play it on GBA - you will notice some patterns that only happens on GBA.

1. If your opponents are at 3 -2 points and you get to 6 points, the dice suddenly favors your opponents so they can catch up. This happens way too often for it to be a random occurance. This is a reason why at higher levels players stratigically wait to get the longest road until all players have more points.

They have patched it this season! Now the games are much faster, there is no "catch up" for rest of the players. I hope rest of you have noticed this as well as games are much more faster now, often ending up in 1 player dominating.

However, during level 2/3, if you roll the first 7, the likelihood that there is a 7 next roll is very very high. Happens almost every time! This is something that is new to this patch.

Coleus1 wrote: ↑16 July 2025, 11:47 However, during level 2/3, if you roll the first 7, the likelihood that there is a 7 next roll is very very high.

Yes. It's 1/6

Jellby wrote: ↑16 July 2025, 12:32

Coleus1 wrote: ↑16 July 2025, 11:47 However, during level 2/3, if you roll the first 7, the likelihood that there is a 7 next roll is very very high.

Yes. It's 1/6

Even higher than that actually! I wish it was 1/6 but it's around 80% right now. Be strategic if you roll the first 7 guys since it's programmed now to roll a seven next turn as well!

Coleus1 wrote: ↑16 July 2025, 11:47

Coleus1 wrote: ↑19 June 2025, 10:48 I don't Agree. If you play Catan in real life, and then play it on GBA - you will notice some patterns that only happens on GBA.

1. If your opponents are at 3 -2 points and you get to 6 points, the dice suddenly favors your opponents so they can catch up. This happens way too often for it to be a random occurance. This is a reason why at higher levels players stratigically wait to get the longest road until all players have more points.

They have patched it this season! Now the games are much faster, there is no "catch up" for rest of the players. I hope rest of you have noticed this as well as games are much more faster now, often ending up in 1 player dominating.

However, during level 2/3, if you roll the first 7, the likelihood that there is a 7 next roll is very very high. Happens almost every time! This is something that is new to this patch.

They have definitely patched this. Now after playing even more games - they are indeed much faster with no "catch up" for other players once a player starts dominating (5 - 6 points ahead of the rest which are at 2 - 3points). Just look at the game times this season vs last season. This means the dice indeed is (was) not random but had some manipulation programmed into it!

However, what I said about the first robber is not true. It doesn't happen more often for it to be considered "manipulated". So I take back that claim.