Open Dice Rolls

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.
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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+