Oh, I'm definitely agreeing with the person. I was just being a little snarky at that one statement.
I am also trying to ask a question that is extremely relevant to the author's "study".
"Are the original dice fair?"
That was never asked, it was assumed. It is a pretty hefty assumption too. I think everyone that has played a game of Catan has, at some point, questioned the fairness of the dice. I'm not saying they are unfair, but because of manufacturing methods, it is quite possible to get a pair of dice with an ever so slight bias.
ALWAYS ALWAYS ALWAYS find the bias in the instruments you are using to perform an experiment. THEY ALL HAVE THEM. NEVER NEVER NEVER assume your instruments are accurate without first verifying.
> I think everyone that has played a game of Catan has, at some point, questioned the fairness of the dice.
This is why a lot of people play with a set of 36 cards (one 2, two 3's, three 4's...one 12). There really aren't that many rolls in a game, and there's a lot of variation that may result in a 5 never coming up, which adds more chance to the game than I like. Cards mean that while the order is random, you get each number in the deck eventually.
I've never heard of anyone playing like that before actually. And it seems to completely mess with the statistical nature of the game. Even if you shuffled them each time, shuffling methods are bad and you probably wouldn't get a nice normal distribution. Which fair dice produce.
If you don't shuffle until you run out of cards, you mess with the instantaneous probability of any particular draw, but you hardcode the distribution. You are guaranteed to get the distribution you put in the deck, and I think that's a better measure of fairness than having a constant instantaneous probability.
As the deck becomes smaller, your ability to predict the next draw scales with your skill at counting cards. I think that's a good feature for a random number generator to have, as it's what allows games like poker and blackjack to be about more than simply getting lucky.
Well, I agree that a game needs to have more than luck. But something like blackjack is a horrible example because there's a lot of skill that can be applied even without counting cards. Not only that, but blackjack still has a large amount of luck involved with it even when you are highly skilled.
Personally, I find that the best games are ones that have a good balance of luck and skill. Too much luck and there is no skill, you might as well play a slot machine (some people enjoy games candy land). Too much skill, and winning distributions become too low. A highly skilled player will ALWAYS win, and creates too high of a barrier to entry (connect 4 or dots and squares are an example here). There are (a few) exceptions to the latter like Go, which has so many possible moves that you might as well have an element of randomness, but there is still a steep learning curve.
Catan is one of my favorite games introduction to Euro Games, because the learning curve is low, and there is enough luck that an intelligent novice can win. I don't actually believe the dice are unfair, but the low number of rolls makes each game different. This means the skilled player needs to be highly adaptive to the changing environment.
Dice create a nice normal distribution that are independent. While over a large number of games, 6 and 8 are great choices, there will be games where you just don't do well (they are rare). By not shuffling the cards, you are creating a flat distribution and really removing the vast majority of luck in the game (you still have luck in the order of the cards, order of placement, and order of turn). You now have a dependent probability function, and I think you could make great arguments that you remove all the things that (I believe, and laid out above) make the game great. I think you could also make arguments that the setup is the most important part of the game (when your cards are dependent events). But it is a game, and these are just opinions.
I am also trying to ask a question that is extremely relevant to the author's "study".
"Are the original dice fair?"
That was never asked, it was assumed. It is a pretty hefty assumption too. I think everyone that has played a game of Catan has, at some point, questioned the fairness of the dice. I'm not saying they are unfair, but because of manufacturing methods, it is quite possible to get a pair of dice with an ever so slight bias.
ALWAYS ALWAYS ALWAYS find the bias in the instruments you are using to perform an experiment. THEY ALL HAVE THEM. NEVER NEVER NEVER assume your instruments are accurate without first verifying.