You are referring to the common mistake of confusing randomness and uniformity. Your players are thinking: "Dice rolls are equiprobable, so I should roll evenl

You are referring to the common mistake of confusing randomness and uniformity. Your players are thinking: "Dice rolls are equiprobable, so I should roll evenly-distributed results." That only starts being true after a great number of rolls. Random distributions will be uneven and present clumps, strands and voids. For the same reason, during WWII, British intelligence thought that the Germans were bombing specific targets in London, while they were just dropping bombs at random. Source recently posted on HN: http://www.wired.com/wiredscience/2012/12/what-does-randomness-look-like/ http://www.wired.com/wiredscience/2012/12/what-does-randomne...