On the topic of die rolls (Lucky no. 7)

[Smith]

A lot of people (both inside the game and here in the forum) are complaining about the high amount of 7s that are rolled in the game. Now this should be basic knowledge and a no-brainer to everyone who went to school for a couple of years, but at this point I kinda feel the need to explain it anyway:

These are all the combinations you can roll with two dice:

1+1
1+2
1+3
1+4
1+5
1+6
2+1
2+2
2+3
2+4
2+5
2+6
3+1
3+2
3+3
3+4
3+5
3+6
4+1
4+2
4+3
4+4
4+5
4+6
5+1
5+2
5+3
5+4
5+5
5+6
6+1
6+2
6+3
6+4
6+5
6+6
(It's 36 options, in case you don't wanna count)

Now, as we all know, the number of dots on one single die isn't what we use in CATAN. It's the sum of dots on both dice that counts.

Which means that these are the actual numbers you can roll:

2
3
4
5
6
7
3
4
5
6
7
8
4
5
6
7
8
9
5
6
7
8
9
10
6
7
8
9
10
11
7
8
9
10
11
12
(Still 36 options)

If you look at those results a little more closely, you'll notice that the numbers 2 and 12 can only be achieved by one combination each (2 is 1+1 and 12 is 6+6).
The numbers 3 and 11, however, can be achieved by two possible combinations each (for example 3 is 1+2 and also 2+1). There are three different ways of achieving a sum of 4 or 10, four different ways to get a 5 or 9 and five different combinations each if you want to roll a 6 or 8 (which is why those numbers are red in the game). And then of course there is 7, which can be achieved in six different ways (1+6, 2+5, 3+4, 4+3, 5+2 and 6+1).

That means that six out thirty-six different combinations produce a 7. It's the most likely number to get with two dice.

Does this mean that you'll always roll more 7s than any other number? No, it doesn't. It's just the most likely result. It's completely possible (though unlikely) to play a whole game without ever rolling a 7. It is also possible (though extremely improbable) to play a whole game and always roll a 7. Both are possibilities that do exist but are, I would think, unheard of. The most likely outcome when playing with two dice is that you roll a lot of 7s, quite some 6s and 8s and very few 2s and 12s. I'm not saying that's always the case. It's just the most probable distribution.

The argument that "Well, when I play the REAL game with my aunt on the weekends, we don't have that many 7s, but we do have a lot of 5s!" is childish and doesn't change the facts. Maybe your aunt is cheating. Maybe her dice aren't perfectly balanced (as all things should be). Maybe it's just a coincidence.

Statistically speaking, 1 out of 6 die rolls should result in a 7.
If it doesn't, well, that's just life.

[USM [CM]]

Hahahahahaha! Thank you so much :D

[dota matthäus]

more people should read this.
you basically say "everything should be perfectly balanced" after explaining why the dice rolls AREN'T balanced at all. scnr :-P
i'm fine with usually two different numbers being rolled the most in every match (yes 5, i'm looking at you!), but it also results in a lot of anger being thrown at each other, people who think it's all rigged and the occasional ragequit. not excluding myself from all of that ¯\_(ツ)_/¯
i wish it was more about skill and less about luck, but after all it's just a board game.

[Smith]

I hate losing a game because of bad luck just like the next person. Doesn't mean everything's rigged. Although I can't prove that it isn't. ;)

[Smith]

Originally posted by beatfux:

more people should read this.
you basically say "everything should be perfectly balanced" after explaining why the dice rolls AREN'T balanced at all. scnr :-P

A Gaussian distribution curve looks pretty symmetrical to me ;)

[Smith]

Now since this discussion is going on and on and some people claim that in many rounds one number is featured uncharacteristicly often, I decided to pick up some dice (the wooden variety) and just roll a couple of games with 50 rolls each. See what happens. And this is what happened:


GAME 1:

2 0x
3 2x
4 6x
5 5x
6 6x
7 14x
8 8x
9 7x
10 1x
11 1x
12 0x


GAME 2:

2 0x
3 2x
4 6x
5 8x
6 5x
7 4x
8 8x
9 7x
10 5x
11 3x
12 2x


GAME 3:

2 2x
3 1x
4 7x
5 4x
6 8x
7 5x
8 12x
9 5x
10 2x
11 2x
12 2x


GAME 4:

2 0x
3 4x
4 8x
5 10x
6 10x
7 5x
8 2x
9 7x
10 2x
11 2x
12 0x


Are some numbers discriminated against? Are my dice broken? Who knows. Who cares.

[steady10]

This is a joke haha.

The issue isnt that the dice arent varied, its the facts that in a whole game numbers such as 5/6/7/8/9 DO NOT ROLL.

I have played games on this "app" where number 6 hasnt rolled in over 100 rolls of the dice.

Your "explanation" is flawed and short sighted. Real dice are random. This "app" is based on an algorithm created by human beings.

7 should roll. So should 6. So should 5. So should 8. So should 9.

The issue isnt they are rolling continuously and proves that you havent understood the issue at all.

You have actually proven the games dice is broken through your experiment with real dice. Did any number with a statistically higher probability (5/6/7/8/9) not roll during your 4 games?

No it didnt.So thank you for your attempt to defend the delevopers, but unfortunately you are picking facts out to suite your argument, much like many "experts".

[Smith]

Maybe you are a student of higher mathematics and I don't get your glorious insights into probability, but your argument doesn't make any sense to me.

[Chaz.M.Sandcrags]

Originally posted by Smith:

Now since this discussion is going on and on and some people claim that in many rounds one number is featured uncharacteristicly often, I decided to pick up some dice (the wooden variety) and just roll a couple of games with 50 rolls each. See what happens. And this is what happened:

...[YADA YADA YADA]...


Are some numbers discriminated against? Are my dice broken? Who knows. Who cares.

I'm with Smith on this - the distribution of numbers in an individual game may be weird, but that just may be fate (i.e. me getting screwed when my particular high-probability numbers never get rolled, or 7 gets rolled with more frequency than we'd like). I first noticed it in the actual table top board game and thought there was something wrong with the way we were rolling the dice (in a container vs in the hand, vigorously shaking vs barely shaking, rolling the dice vs dropping the dice, etc etc etc). But I realized after a few games that it made hardly any difference how we rolled.

It seems to me that that same randomness is inherent in the Catan Universe dice rolls.

But that also doesn't mean that every game I play, a 7 is rolled every other turn, or 6's and 8's never get rolled. Sometimes you get three 7's in a row. Sometimes you get three 6's in a row... or two 8's, or four 3's. It may strike you as weird or "rigged"... but if you want to test it... start rolling some real dice and see how it plays out.

[Eclipsis Tenebris]

My issue is more that the AI is ♥♥♥♥♥♥♥ cheating. Not as bad as the previous Catan game, but still there.

[Eclipsis Tenebris]

The only way to avoid this btw, is to play using the 'card stak'. Though they use two card stacks and remove halve of the cards at random, this is still MUCH closer to actual probability. Though you will never get outlier games... which can be a bit boring, but it's better than nothing.

The AI still cheats though by basically shuffling the cards in their favour... but still much easier to deal with.