Open Dice Rolls

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.