Games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is a tension between a level of randomness that makes the game interesting and contributes to the player enjoyment of a game, and a level at which the outcome itself is effectively random and the game becomes dull. The optimal level for a game will depend on the design goals and target audience. We introduce a new technique to quantify the level of randomness in game outcome and use it to compare 15 tabletop games and disentangle the different contributions to the overall randomness from specific parts of some games. We further explore the interaction between game randomness and player skill, and how this innate randomness can affect error analysis in common game experiments.