D20 Probability: Understanding D&D Odds

Understanding d20 probabilities makes you a better D&D player. Here's the math.

Base Probabilities

On 1d20:

• Natural 1: 5% chance.
• Natural 20: 5%.
• Natural 10: 5%.
• Any specific number: 5%.
• 10 or higher: 55%.
• 15 or higher: 30%.
• 20: 5%.

With Modifiers

Adding +5:

• 10+ on d20 = 15+ total. 30% chance.
• 15+ on d20 = 20+ total. 5% chance.

Your attack bonus = probability of hitting certain ACs.

Advantage

Roll 2d20, take higher.

• Probability of at least one natural 20: 1 - (19/20)^2 = 9.75%.
• Roughly +4 to +5 bonus compared to straight.

Disadvantage

Roll 2d20, take lower.

• Probability of at least one natural 1: 9.75%.
• Roughly -4 to -5 bonus compared to straight.

Save Success Rates

• Need 10+ on a save: 55%.
• Need 15+: 30%.
• Need 20: 5%.

Fail rates: (100% - success rate).

Crit Hit Rate

• Normal: 5%.
• Advantage: 9.75%.
• Champion (19-20): 10% normal, 19% advantage.
• Champion 15+ (18-20): 15% normal, 28% advantage.

Multiple Attacks

Probability of at least one hit across multiple attacks:

• 1 attack at 60% = 60%.
• 2 attacks at 60% each = 84%.
• 3 attacks at 60% each = 94%.

More attacks = more reliable damage.

Multiple Saves

Probability of failing at least one save:

• 1 save at 70% success = 70% pass.
• 2 saves (e.g., Fireball then Hold Person) = 49% pass both.
• 3 saves = 34% pass all.

Multiple save exposure compounds.

Lucky Feat

Reroll three times per long rest. Each reroll:

• If you rolled low, rerolling gives you effectively advantage on that specific roll.

Halfling Lucky

Reroll natural 1s automatically. Saves approximately 5% of your rolls from bad results.

Expected Damage

Average d20 roll: 10.5.

So average attack roll: 10.5 + modifier.

For damage estimation: Roll + modifier vs. target AC.

In The Endlessness

Our AI Dungeon Master uses genuinely random d20 rolls. No fudging.

For related reads, our advantage and disadvantage, critical hits guide, and transparent dice rolling cover more.

Final Takeaway

Understand the math. Plan accordingly. Accept randomness.

Roll at The Endlessness with full probability transparency.