Rarity and Frequency

If we consider the simple example of tossing 2d6 then we can make some observations.

• The outcome Two {1,1} is rare, being only 1 of 36 possible outcomes
  
• The frequency of the outcome Two tends toward the average of to once every 36 rolls at infinite rolls
  

During game design, the dev might want an event to occur at a frequency related to other game properties, such as time in-game, expected useful lifespan of a level-dependent item, or visually pleasing distribution. So it's useful to consider the frequency as a variable, and the probability as the inverse interpretation. For example the variable might be populationSize in which the given result is expected to occur, and then the roll would be 1/populationSize.

Lady Luck is Lawful Neutral, and her every dance step is an expression of the laws of physics, of which we are privy to only a portion.