Dice Probability Calculator
Calculate dice roll probabilities and odds for D&D, RPGs, and tabletop games - Percentage chance calculator
Calculate the probability of any dice roll outcome with our dice odds calculator. Perfect for D&D players planning character builds, game masters balancing encounters, or anyone curious about dice mathematics. Our calculator supports all standard RPG dice (D4, D6, D8, D10, D12, D20, D100) and multiple dice combinations with accurate probability calculations.
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About Dice Probability Calculator
Calculate the probability of any dice roll outcome with our dice odds calculator. Perfect for D&D players planning character builds, game masters balancing encounters, or anyone curious about dice mathematics. Our calculator supports all standard RPG dice and multiple dice combinations.
Practical Applications: Use this calculator to determine your actual chance of hitting with an attack (d20+modifier vs AC), succeeding on a saving throw, or dealing lethal damage. Understanding these odds helps you make better tactical decisions in D&D and other RPGs.
Dice Probability Calculator Configuration Options
Quick Scenarios
Dice Configuration
Comparison Types
Probability Distribution
How to Use the Dice Probability Calculator
[STEP 1] Choose Quick Scenario or Configure Manually
Select a pre-configured scenario like "D20: Natural 20" or "D20+5: Beat AC 18" for instant results, or manually configure your dice type, number of dice, and modifiers for custom calculations.
[STEP 2] Set Your Target Number
Enter the target number you want to analyze. The calculator automatically shows the minimum and maximum possible rolls based on your dice configuration.
[STEP 3] Select Comparison Type
Choose how to compare against your target: exactly (for specific values), at least (≥ for meeting or exceeding), at most (≤ for staying under), greater than (>), or less than (<).
[STEP 4] View Probability Results
Click CALCULATE to see your probability as a percentage, odds ratio (1 in X), and detailed statistics including average roll. For 3 or fewer dice, view the complete probability distribution chart.
Dice Probability Best Practices
- _ Accurate Calculations - Uses precise probability mathematics for all dice combinations, no approximations or simulations
- _ D&D Applications - Perfect for calculating attack hit chances, saving throw odds, and damage ranges in D&D 5e and other RPG systems
- _ Multiple Dice Support - Handles complex probability calculations with up to 10 dice, including modifiers and different comparison types
- _ Quick Scenarios - Use presets for common D&D situations like advantage rolls, natural 20s, or beating specific armor classes
- _ Strategic Planning - Make informed tactical decisions based on actual probabilities rather than intuition or guesswork
- _ Educational Tool - Great for teaching probability and statistics concepts using familiar gaming scenarios
Understanding Advantage in D&D
Advantage is one of D&D 5e's most powerful mechanics. When you have advantage, you roll 2d20 and take the higher result. This dramatically improves your success rate for mid-range target numbers.
Notice how advantage provides the biggest improvement for mid-range targets (around 11-15). For very easy or very hard checks, the improvement is smaller but still significant.
Dice Probability Algorithm
Our probability calculator uses exhaustive enumeration for precise calculations. For single dice, it counts favorable outcomes directly. For multiple dice, it generates the complete probability distribution using recursive combinatorics, then calculates exact probabilities from the distribution.
// Dice probability calculation algorithm
Algorithm: Exhaustive Enumeration with Distribution Analysis
Input Parameters:
- dice_sides: Number of sides on each die (D4=4, D6=6, D20=20, etc.)
- num_dice: Number of dice to roll (1-10)
- modifier: Value to add to total roll (-50 to +50)
- target: Target number to compare against
- comparison: Type of comparison (exactly, at-least, at-most, greater, less)
Single Die Calculation (num_dice = 1):
1. Total possible outcomes = dice_sides
2. For each face value f ∈ [1, dice_sides]:
- Calculate result = f + modifier
- If result matches comparison with target:
* Increment favorable_outcomes
3. Probability = favorable_outcomes / total_outcomes
Multiple Dice Calculation (num_dice > 1):
1. Generate Complete Distribution:
- Initialize empty distribution map
- Use recursive function RollDice(dice_remaining, current_sum):
* Base case (dice_remaining = 0):
> total = current_sum + modifier
> distribution[total] += 1
* Recursive case:
> For each face value f ∈ [1, dice_sides]:
- RollDice(dice_remaining - 1, current_sum + f)
- Call RollDice(num_dice, 0)
2. Calculate Probability from Distribution:
- total_outcomes = Σ(all distribution values)
- favorable_outcomes = Σ(distribution[value]) where value matches comparison
- Probability = favorable_outcomes / total_outcomes
Comparison Matching:
- exactly: value = target
- at-least: value ≥ target
- at-most: value ≤ target
- greater: value > target
- less: value < target
Odds Calculation:
- If probability = 0: odds = "0 in 1"
- If probability = 1: odds = "1 in 1"
- Otherwise: odds = "1 in " + round(1/probability)
Distribution Chart (for num_dice ≤ 3):
- For each possible outcome value v:
* Calculate: percentage = (distribution[v] / total_outcomes) × 100
* Display bar chart with width proportional to percentage
* Highlight target value for visual reference
Example Calculations:
1. D20 Natural 20:
- favorable = 1, total = 20
- probability = 1/20 = 0.05 (5%)
- odds = 1 in 20
2. 2D6 ≥ 7:
- Distribution: {2:1, 3:2, 4:3, 5:4, 6:5, 7:6, 8:5, 9:4, 10:3, 11:2, 12:1}
- favorable = 6+5+4+3+2+1 = 21
- total = 36
- probability = 21/36 = 0.583 (58.33%)
3. D20+5 ≥ 18 (Beat AC 18):
- Need to roll 13+ on D20
- favorable = 8 (rolls 13-20)
- probability = 8/20 = 0.40 (40%)
Complexity Analysis:
• Single die: O(d) where d = dice_sides
• Multiple dice: O(d^n) where n = num_dice
- Limited to 10 dice max to maintain reasonable computation time
- For 10 D20s: 20^10 = 10.24 trillion combinations (handled efficiently)
API Access for Developers
Calculate dice probabilities programmatically using our free REST API. Send a POST request with your dice configuration to receive exact probability calculations.
Example request body: {"dice_type": "d20", "num_dice": 1, "target": 15, "modifier": 5, "comparison": "at-least"}
Response includes probability (decimal), percentage, odds ratio, min/max possible values, average roll, and complete distribution data for analysis.