On Dice-Rolls and Results

Dungeon Fodder had a loot table which operated on a dice-roll. One issue was that the odds for “Leveling Up!” were too ridiculously difficult so I had to think about why. A player only levels up on a roll of 3 or 18 but what were the odds? I had a look around and this site explained it pretty thoroughly to me;

3 dice or 3d6 equates to 6 to the power of 3 which comes up to 216 possibilities. Typically a 3d6 would yield you only 16 possibilities (3 to 18) so from there one can calculate the odds of getting a specific number. While not something astronomically new, it does highlight the fact that game designers must have a strong understanding of mathematics to handle data, probability and statistics. Therefore the odds for 3 dice would be as follows;

Probability of a sum of 3: 1/216 = 0.5%
Probability of a sum of 4: 3/216 = 1.4%
Probability of a sum of 5: 6/216 = 2.8%
Probability of a sum of 6: 10/216 = 4.6%
Probability of a sum of 7: 15/216 = 7.0%
Probability of a sum of 8: 21/216 = 9.7%
Probability of a sum of 9: 25/216 = 11.6%
Probability of a sum of 10: 27/216 = 12.5%
Probability of a sum of 11: 27/216 = 12.5%
Probability of a sum of 12: 25/216 = 11.6%
Probability of a sum of 13: 21/216 = 9.7%
Probability of a sum of 14: 15/216 = 7.0%
Probability of a sum of 15: 10/216 = 4.6%
Probability of a sum of 16: 6/216 = 2.8%
Probability of a sum of 17: 3/216 = 1.4%
Probability of a sum of 18: 1/216 = 0.5%

Also on an unrelated note, the designs for an Orientation type activity is underway and there are thoughts of using comparison tables such as the one below. It has been a long time since I’ve seen one used but it is a fun and visual way to figure out the results of a dice roll. I might also try to integrate this into Dungeon Fodder if the need arises and it helps by visually explaining concepts on the game.