Coins & dice
Dice roll
d4, d6, d8, d10, d12, d20, or d100 — roll a single die or a whole handful.
What is a d20 and how to read a roll notation
Recording 2d6 It is read simply: two dice with six sides. The first number is the number of dice, the second is how many sides each has. d20 — a twenty-sided die from board games, d100 — 'hundred': a die that gives a value from 1 to 100. This site offers d4, d6, d8, d10, d12, d20, and d100, from one die up to fifty.
An honest roll: each value from 1 to N is equally likely. For a d6, that's 1/6 ≈ 16.7% per face, for a d20 — 5%, for a d100 — 1%. Combinations are added, so the sum of two dice is no longer uniformly distributed.
How the modifier is calculated
Modifier — a number that is added to the roll total. In tabletop games, this accounts for a skill bonus, weapon strength, or a penalty for difficult conditions. The result is calculated using the formula sum of all dice + modifier. The range here is from −20 to +20: a negative value reduces the result, a positive value increases it.
The average result of a single d6 is 3.5, so for 2d6 the average sum is 7, and with a +3 modifier — 10. This helps to understand how much the result is above or below average.
Advantage and interference
In 'advantage' mode, two full sets of dice are rolled and the set with big result. "With disadvantage" — on the contrary, with less. The modifier is added to each roll before comparison. This is a simplified version of the rule from D&D: there, for advantage, you roll two d20s and take the best one, and here it works the same for any set of dice.
Probability on a d6
For a single d6, all six faces are equally likely. For the sum of two d6, the distribution is triangular: 7 occurs most often — 6 combinations out of 36, that is, 16.7%. The extreme values 2 and 12 occur once each out of 36 — about 2.8%. On a histogram, this looks like a 'hill' with its peak in the middle.
The more dice are rolled, the closer the distribution of the sum is to normal — extreme results become rare, while the middle of the range becomes the most frequent.
Where dice come in handy
- rolls in board games and role-playing systems;
- checking probabilities and distributions in class;
- random selection of a number from 1 to 20 or up to 100;
- a fair resolution of a dispute when there are more than two options;
- generation of random values for tests and prototypes.