Open Ended Dice

Not a type of dice, but a way of using them. Roll as normal, but if a maximum is rolled (eg a 6 on a D6), roll again and add the score to the six scored on the first roll. The second roll usually follows the same rule, allowing chains of rerolls; in this case, there is no upper bound to the possible score, although getting huge rolls is extremely unlikely.

For example (using a D6), Alice rolls a five; she scores five. Bob rolls a six; he rerolls, gets a two, and scores eight. Charles rolls a six, rerolls another six, rererolls yet another six, and then rolls a three; he scores 21. Charles is then lynched.

The point of all this is to augment normal (closed) dice with a small possibility of a huge score. This is congruent with the fantastic/heroic/comic-book aspect of many RolePlayingGames.

Note that OpenEndedDice as described above can never score a multiple of the maximum.

Mmm... 6-sided die. 1-5 are 1-5. 5 also means reroll and add. 6 is zero.

Good point. Alternatively, map each number N onto N-1, or repaint your dice with 0-5. It's even easier with a D10 - one of the faces is already zero. However, i don't think (but could be wrong) that this is how OpenEndedDice usually work.