WOLFRAM|DEMONSTRATIONS PROJECT

Open Dice Rolls

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open rolls
sides
4
10
6
2
8
5
10
1
12
4
20
8
normal rolls
sides
4
10
6
6
8
5
10
3
12
2
20
4
reroll
dice
open rolls
normal rolls
{2,1,1,1,5,2,3,2,2,11}
30
{1,3,3,3,1,4,1,3,3,4}
26
{5,4}
9
{3,3,3,5,1,3}
18
{6,3,7,2,1}
19
{6,4,6,8,6}
30
{5}
5
{2,4,6}
12
{1,2,5,28}
36
{6,8}
14
{16,7,8,16,5,13,14,3}
82
{10,19,5,4}
38
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.