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Independent Probability Tool
2 Dice • Range 2 - 40

2D20 Roller

Rolling 2D20 produces two independent 20-sided rolls. Depending on the ruleset, you can sum them (2 to 40, average 21) or evaluate Advantage (higher of the two) and Disadvantage (lower of the two).

Dice Tray
2d20
Click button or press Space to roll
Total Result
-- Ready
Roll Breakdown
Roll the dice to see outcome
Select Die Type Standard Polyhedral Set
Roll Configuration Quantity & Modifiers
1 – 100
2 – 1000
± bonus
âš™ Advanced Expression (NdM±K) â–¼
Shortcuts:
âš¡ Quick Dice Rolls 1-Click instant roll

Saved Presets

Roll History

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Exact Mathematical Probability

Combinatorial Engine

Calculates discrete binomial distributions, probability density, and cumulative odds for the active dice expression.

Range (Min - Max) --
Theoretical Average --
Most Likely (Mode) --
Total Permutations --
Query Target Probability
Exactly ( = X ) --%
At Least ( ≥ X ) --%
At Most ( ≤ X ) --%
Probability Density Distribution Hover / tap bar to view odds
View Full Probability Table & Combinations â–¼
Total Ways Exact % ≥ At Least ≤ At Most

Roll N Times (Multi-Trial Simulation)

Execute up to 10,000 repeated trials to calculate empirical distributions and statistics.

Trials --
Mean (Avg) --
Median --
Mode --
Min --
Max --
Sum --

Empirical Frequency Table

Roll Total Hits (Count) Frequency Bar Percentage
Click "Run Trials" to simulate rolls and generate frequency data.

Probability Curve & Mathematical Mechanics

Rolling 2D20 is the engine behind modern Advantage/Disadvantage mechanics in tabletop RPGs, as well as the proprietary 2d20 System (Dune, Star Trek Adventures, Fallout). It displays both individual rolls alongside the sum.

When summing 2D20, the outcomes range from 2 to 40 with average 21 (peaking at 21 with 5.00% probability). When rolling with Advantage (taking higher), the chance of rolling 15 or higher rises from 30% to 51%, and the chance of a Natural 20 jumps from 5.00% to 9.75%.

Prominent Tabletop Games Using 2D20

  • • Advantage and Disadvantage checks in modern 5th edition RPGs
  • • Modiphius 2d20 System tabletop games
  • • Simultaneous dual-attack resolution or contested grapple checks

2D20 Distribution Overview

Min Total 2
Max Total 40
Average 21
Most Likely 21 (5.00% probability for sum)
Total Sum Permutations Exact Probability
2 1/400 0.25%
10 9/400 2.25%
21 20/400 5.00%
30 11/400 2.75%
40 1/400 0.25%

Explore Related Dice Systems

D20 Roller → D100 Roller → Dice Probability →

Frequently Asked Questions About 2D20

How does Advantage change D20 odds?
When rolling two D20s and taking the higher result, the mathematical average increases from 10.5 to 13.82. The chance of a Natural 20 increases from 5.00% to 9.75%.
What is the chance of a critical failure (Natural 1) with Advantage?
You only get a 1 if both dice roll 1, which has an odds of (1/20) × (1/20) = 1 in 400, or just 0.25%.