We were playing Settlers of Catan the other day. If you don't know it, you should immediately go out and buy it, because it is a fantastic game... one of the best strategy / board games ever. But back to my topic... The game relies on die randomness. From basic math / probability, we know that when rolling two dice, the sum of 7 has the highest probability of getting rolled. Next, the sums of 6 and 8 would have the next best chance. More importantly, the 6 and the 8 would have equal chance of getting rolled. Then 5 and 9 and so on. This is easily shown with a table (sample space) displaying all the possible outcomes of rolling two dice and then counting the number of possible outcomes of getting a sum of 7, sum of 6, sum of 8 etc.
But when we were playing our board game, it seemed that these random rules didn't apply all that well. The higher numbers seemed to come up way more than the lower ones. For instance 9 came up way more than 5. First we thought that our dies are not well balanced, so we traded them from a set from Monopoly, but the same trend continued. Unhappy with this (I lost the game because I chose lower numbers in Settlers and they hardly came up) I decided to look into this more.
