Catastrophe Dice is a concept whereby each dice represents a level of difficulty. The original impetus was a game based upon environmental catastrophe (hence the name). At low levels of danger, a player would roll a red die, which has 1 pip on it, and has less of a chance of getting a "hit" (negative event). But as the danger levels go up, you add more dice to the pool, and the danger levels increase, giving a greater chance to hit. Here's an image, along with a little table that a kind user on boardgamegeek calculated out for me.
