Dice notation step by step

At the table

Tabletop games write rolls as XdY (X dice, Y sides), sometimes with a bonus or drop lowest. This lesson walks from the smallest form to 4d6dl1 ability scores.

Try it

In the playground, open this lesson in the playground and click Run (or press Shift+Enter). Output lists five distributions in order—one per stage below.

Stage 1: one die (1d4)

↗output("one_d4", 1d4)

• 1d4 — roll one four-sided die (faces 1–4). Same pattern as 1d6, 1d20, etc.
• Omitted count means one die: d4 and 1d4 are the same idea (the tool expands both).

Mean ≈ 2.5.

Stage 2: add dice (2d6)

↗output("two_d6", 2d6)

• 2d6 — roll two six-sided dice and add them.
• Sum of two independent d6 (same idea as lesson 2); the engine expands this to dice_pool(2, 6) and then sums. For pools you keep separate, see lesson 6.

Mean ≈ 7.

Stage 3: flat bonus (2d6 + 3)

↗output("two_d6_plus_3", 2d6 + 3)

• + 3 adds 3 to every total on the roll—like a fixed stat bonus on the sum (lesson 3).
• Equivalent to shift(2d6, 3) when you already have a DieRoll in a variable.

Mean ≈ 10 (7 + 3).

Stage 4: many dice (4d6)

↗output("four_d6", 4d6)

• 4d6 — roll four d6 and sum all of them (no drops).

Mean ≈ 14 (four times the mean of one d6).

Stage 5: drop lowest (4d6dl1)

↗output("four_d6dl1", 4d6dl1)

• dl1 — drop lowest 1 die before summing (classic ability-score roll).
• The tool expands this to drop_lowest(4, 6, 1).
• 4d6dl2 would drop the two lowest; 3d6dl1 is three dice drop one—same dlN pattern.

Mean ≈ 12.24 (higher than straight 4d6 because the worst die never counts).

Stage 6: drop highest (4d6dh1)

↗output("four_d6dh1", 4d6dh1)

• dh1 — drop highest 1 die, then sum the rest (the opposite of dl1).
• Expands to drop_highest(4, 6, 1).

Mean ≈ 8.76.

Stage 7: keep highest N (4d6kh2)

↗output("four_d6kh2", 4d6kh2)

• kh2 — roll four d6, keep the highest 2, sum only those (advantage-style “best two”).
• Expands to keep_highest(4, 6, 2). Not the same as dl2 (which drops two lows and sums the other two dice).

Mean ≈ 9.34.

Stage 8: keep lowest N (3d12kl1)

↗output("three_d12kl1", 3d12kl1)

• kl1 — keep the lowest 1 die and sum it (here, just that single die).
• Expands to keep_lowest(3, 12, 1).

Mean ≈ 3.52 (average of the minimum of three d12).

Suffix cheat sheet

Reading the result

Eight named outputs in the sample script, each with mean and a probability table (or truncated table for large supports).

Try this

• Change 1d4 to a die your game uses (1d8, 1d12).
• Compare 2d6 + 3 and shift(2d6, 3)—means should match.
• Try 4d6kh3 vs 4d6dl1—both sum three dice, but different sets of faces count.

one_d4 · DieRoll · mean 2.500

two_d6 · DieRoll · mean 7.000

two_d6_plus_3 · DieRoll · mean 10.000

four_d6 · DieRoll · mean 14.000

four_d6dl1 · DieRoll · mean 12.245

four_d6dh1 · DieRoll · mean 8.755

four_d6kh2 · DieRoll · mean 9.344

three_d12kl1 · DieRoll · mean 3.521