Open Dice Rolls
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A variety of gaming systems use open rolls, where a maximal value prompts the roll of a new die. This Demonstration allows you to make both open rolls and normal rolls on the standard dice of gaming.[more]
An open roll on a cube (six-sided) starts by rolling it. If 1 to 5 shows up, that is the final value of that open roll. If the maximal value appears (in this case 6) the die is rolled again and 6 is added to the result. If 1 to 5 shows up, that gives a roll of 7 to 11 (6 + 1 to 5). If it is a 6 again, the die is rolled again and again, until a non-6 appears, and the last roll is added to all the 6's that occurred. Other dice have other maximal values that trigger extra rolls.
Compare the 10 open tetrahedron (four-sided) rolls to the ten normal four-sided rolls. About 94% of the time, one of the ten open four-sided rolls will be above 4. This Demonstration is meant as a gaming aid, prompted by hearing someone asking for a website that gave open dice rolls.[less]
Contributed by: Ed Pegg Jr (August 2011)
Open content licensed under CC BY-NC-SA
"Open Dice Rolls"
Wolfram Demonstrations Project
Published: August 3 2011