How to Roll Dice for Tabletop Games (Notation Guide)

Tabletop role-playing games and board games rely on dice to inject randomness into outcomes. Whether you’re rolling a d20 to attack a dragon in Dungeons & Dragons, rolling 2d6 for movement in Monopoly, or rolling a pool of d10s in World of Darkness, understanding how dice work gives you a clearer picture of your odds. You don’t need to be a mathematician—just knowing a few core concepts will change how you evaluate risks at the table.

This guide covers dice notation, probability basics, the standard RPG dice set, advantage/disadvantage mechanics, and practical rolling strategies. Need to roll some dice right now? Use our Free Online Dice Roller.

Dice Notation Explained: XdY+Z

Tabletop games use a universal shorthand to describe dice rolls. Once you learn it, you can read any game’s rules without confusion.

Format: XdY+Z

X = Number of dice to roll
d = “dice” (just a separator)
Y = Number of sides on each die
Z = A flat modifier added to (or subtracted from) the total

Examples:

Notation	Meaning
1d20	Roll one 20-sided die
3d6	Roll three 6-sided dice and add them together
2d8+5	Roll two 8-sided dice, add them, then add 5
1d12-2	Roll one 12-sided die, subtract 2
4d6 drop lowest	Roll four d6, remove the lowest die, sum the rest
1d100 (or d%)	Roll a 100-sided die (or two d10s for tens and ones)

The notation scales to any situation. A greatsword in D&D 5th Edition deals 2d6 slashing damage. A fireball spell deals 8d6 fire damage. A healing potion restores 2d4+2 hit points. Each tells you exactly which dice to grab and what math to do.

The Standard RPG Dice Set

A typical set for tabletop RPGs includes seven dice. Each has a specific use:

d4 (tetrahedron): Four triangular faces. Used for small damage (daggers), minor healing, or random tables. Range: 1-4, average: 2.5.

d6 (cube): The classic die everyone knows. Used for ability score generation (3d6 or 4d6 drop lowest), many weapon damages, and countless board games. Range: 1-6, average: 3.5.

d8 (octahedron): Eight triangular faces. Common for medium weapon damage (longsword, rapier) and some healing spells. Range: 1-8, average: 4.5.

d10 (pentagonal trapezohedron): Ten faces numbered 0-9 (where 0 = 10). Used for percentile rolls (paired with another d10) and some weapon damages. Range: 1-10, average: 5.5.

d12 (dodecahedron): Twelve pentagonal faces. Used for heavy weapon damage (greataxe) and barbarian hit dice. Often considered the most underused die. Range: 1-12, average: 6.5.

d20 (icosahedron): Twenty triangular faces. The signature die of D&D and many other RPGs. Used for attack rolls, ability checks, and saving throws. Range: 1-20, average: 10.5.

d100 (percentile): Rolled using two d10s—one for the tens digit and one for the ones digit. A roll of 40 and 7 equals 47. Double zeros (00 and 0) equals 100. Used for random encounter tables and percentile-based systems.

Probability Basics for Dice

Single Die Probability

Every face on a fair die has an equal chance of landing. The probability of rolling any specific number is:

$P = \frac{1}{number \ of \ sides}$

d6: Each face has a 1/6 (16.67%) chance. d20: Each face has a 1/20 (5%) chance.

The probability of rolling at or above a target (common in RPGs):

$P(\geq target) = \frac{(max - target + 1)}{max}$

Example: What are the odds of rolling 15 or higher on a d20?

(20 - 15 + 1) / 20 = 6/20 = 30%

Example: What are the odds of rolling 8 or higher on a d12?

(12 - 8 + 1) / 12 = 5/12 = 41.7%

Multiple Dice: The Bell Curve Effect

When you roll multiple dice and sum them, the results cluster around the average. This is because there are many more combinations that produce middle values than extreme values.

2d6 probability distribution:

Total	Combinations	Probability
2	1 (1+1)	2.78%
3	2	5.56%
4	3	8.33%
5	4	11.11%
6	5	13.89%
7	6 (most common)	16.67%
8	5	13.89%
9	4	11.11%
10	3	8.33%
11	2	5.56%
12	1 (6+6)	2.78%

Rolling a 7 on 2d6 is six times more likely than rolling a 2 or 12. This bell curve means that 2d6 damage is far more predictable than 1d12 damage, even though both have the same average (7 vs. 6.5) and similar ranges.

Key insight: More dice = more consistency. 3d6 produces results heavily concentrated between 9 and 12. A single d18 (if it existed) would be equally likely to produce any number from 1-18. Game designers choose multiple dice when they want reliable outcomes and single dice when they want wild swings.

The Effect of Modifiers

A modifier (+Z or -Z) shifts the entire distribution without changing its shape.

Rolling 1d20+5 to beat a target of 15 is mathematically identical to rolling 1d20 to beat a target of 10. The modifier moves your floor and ceiling:

1d20 range: 1-20 (average 10.5)
1d20+5 range: 6-25 (average 15.5)
1d20-3 range: -2 to 17 (average 7.5)

In D&D, a character with a +8 attack modifier rolling against an Armor Class of 18 needs to roll a 10 or higher on the d20. That is an (20-10+1)/20 = 55% hit chance.

Advantage and Disadvantage

D&D 5th Edition introduced a clean mechanic for situational bonuses and penalties:

Advantage: Roll 2d20 and keep the higher result
Disadvantage: Roll 2d20 and keep the lower result

The Math Behind Advantage

The probability of rolling at least N with advantage (keeping higher of two d20 rolls):

$P_{adv}(\geq N) = 1 - P(\lt N)^2 = 1 - \left(\frac{N-1}{20}\right)^2$

Example: Probability of rolling 15+ with advantage:

Normal: 6/20 = 30%
With advantage: 1 - (14/20)^2 = 1 - 0.49 = 51%

Advantage nearly doubled the odds. The effect is strongest in the middle of the range and weakest at the extremes:

Target	Normal	Advantage	Disadvantage
2+	95%	99.75%	90.25%
6+	75%	93.75%	56.25%
11+	50%	75%	25%
16+	25%	43.75%	6.25%
20	5%	9.75%	0.25%

Advantage is roughly equivalent to a +3.5 to +5 bonus, depending on the target number. Disadvantage is the mirror image.

Dice Rolling Strategies

Character Creation: 4d6 Drop Lowest

The most popular method for generating D&D ability scores is rolling 4d6 and dropping the lowest die. This produces a range of 3-18 with an average of about 12.24 (compared to 10.5 for a straight 3d6).

Example roll: You roll 4, 3, 6, 2. Drop the 2. Your score is 4 + 3 + 6 = 13.

This method biases toward higher scores, which is intentional—it makes characters feel more heroic than average. The distribution skews right, making scores of 14-16 common and scores below 8 rare.

Risk Assessment at the Table

When your character faces a choice, quick probability estimates help you decide:

Need a 5+ on d20? That is 80%. Go for it.
Need a 15+ on d20? That is 30%. Have a backup plan.
Need a 19+ on d20? That’s 10%. Only attempt this if failure isn’t catastrophic.
Dealing 3d6 damage? Expect 9-12 most of the time. You will almost never roll below 5 or above 16.

Dice Pools: Counting Successes

Some systems (Shadowrun, World of Darkness) use dice pools where you roll a handful of dice and count how many meet a threshold.

Example: Roll 6d6, each die showing 5+ counts as a success. Expected successes:

$Expected = N \times P = 6 \times \frac{2}{6} = 2 \ successes$

The probability of getting at least 1 success with a pool of N dice (target 5+ on d6):

$P(\geq 1) = 1 - \left(\frac{4}{6}\right)^N$

With 6 dice: 1 - (4/6)^6 = 1 - 0.088 = 91.2% chance of at least one success.

Test out different dice combinations and see the results with our Dice Roller.

Frequently Asked Questions

What does “drop lowest” or “keep highest” mean?

These instructions modify a standard roll. “4d6 drop lowest” means roll four six-sided dice, remove the single lowest result, and add the remaining three. “2d20 keep highest” (advantage) means roll two d20s and use only the better result. The dropped dice are ignored entirely—they don’t count as negative modifiers or anything else.

Are digital dice rollers truly random?

Quality digital dice rollers use pseudo-random number generators (PRNGs) that are statistically indistinguishable from true randomness for gaming purposes. Some use cryptographic-grade randomness. Physical dice, ironically, are often less fair than digital ones due to manufacturing imperfections, worn edges, and inconsistent throwing techniques. For any practical tabletop gaming purpose, a good digital roller is perfectly fair.

Why do some games use 2d6 instead of 1d12?

The distributions are different. 1d12 gives each result (1-12) equal probability. 2d6 creates a bell curve where 7 is six times more likely than 2 or 12. Game designers choose 2d6 when they want predictable, average-clustering outcomes (like Monopoly movement or Powered by the Apocalypse skill checks). They choose 1d12 when they want equal unpredictability across the full range.

How do I calculate the average for any dice expression?

Multiply the number of dice by the average of one die, then add the modifier. The average of one die is (1 + number of sides) / 2. For 3d8+4: average of d8 = 4.5, so 3 x 4.5 + 4 = 17.5. For 2d10-1: average of d10 = 5.5, so 2 x 5.5 - 1 = 10.

What is a critical hit and how likely is it?

In D&D, a natural 20 on a d20 attack roll is a critical hit, which doubles your damage dice. The probability is 1/20 = 5%. With advantage, the chance of at least one natural 20 rises to 1 - (19/20)^2 = 9.75%. Some class features extend the critical range to 19-20 (10% normally, 19% with advantage) or even 18-20 (15% normally, 27.75% with advantage).