D20 Combat Statistics

Advanced D&D combat analysis using Monte Carlo simulation with accurate dice rolling, critical hit mechanics, and full D&D rule compliance.

This tool simulates 100,000 combats to provide precise statistical distributions for "time to kill" scenarios. Each simulation rolls actual dice and follows complete D&D combat rules, including natural 1s, natural 20s, and critical damage with doubled dice.

In D&D combat, understanding the statistical distribution of outcomes helps optimize character builds and strategy. This tool uses Monte Carlo simulation to model actual dice rolling, providing accurate probability distributions that account for the full complexity of D&D combat mechanics.

Attack Distribution Visualization

This chart shows the probability distribution of combat length using Monte Carlo simulation with 100,000 trials. Each simulation actually rolls dice and follows D&D rules precisely, providing highly accurate results.

Chart will appear here once valid parameters are entered

Configure Your Character

Adjust the parameters below to see how combat statistics change in real-time.

Attack Bonus (+)

Your total attack bonus

Damage

Dice notation or flat number

Enemy AC

Enemy's armor class

Enemy HP

Enemy's hit points

Include Critical Hit Mechanics (20 = double damage dice)

Combat Statistics

Statistical analysis will appear here once valid parameters are entered.

The Mathematics

This tool uses Monte Carlo simulation to model D&D combat with complete accuracy. Each analysis runs 100,000 simulated combats, rolling actual dice and following all D&D rules precisely.

The Simulation

• Each attack rolls a d20 and adds your attack bonus vs. target AC
• Natural 1s always miss, Natural 20s always hit (when enabled)
• Critical hits (Natural 20s) roll damage dice twice plus modifiers
• Damage is rolled with actual dice (1d8, 2d6+2, etc.) not averages
• Combat continues until target reaches 0 HP or below

Why Monte Carlo?

• Accurate dice rolling: Simulates actual randomness, not averages
• Complex interactions: Handles critical hits, variable damage, and edge cases
• Realistic results: Accounts for all D&D mechanics exactly as played
• High precision: 100,000 trials provide statistically robust results

Why This Matters

• Character Optimization: Compare different build choices mathematically
• Encounter Design: Balance combat difficulty with precise probability
• Understanding Variance: See how random the d20 system really is
• No Simulation Needed: Get exact answers instantly

Technical Features

• Exact PMF: Precise probability mass function calculation
• Natural 1/20 Rules: Enforces 5% minimum miss/hit rates
• Real-time Updates: Instant recalculation as you adjust parameters
• Interactive Visualization: D3.js charts of the probability distribution