Legion Dice Calculator
Legion Dice Probability Calculator
Analyze the odds of rolling specific outcomes in your Legion battles. Input your dice pool and see the probabilities for hits, critical hits, and misses.
Number of attack dice you are rolling.
The symbol on the dice that counts as a hit.
The symbol that counts as a critical hit (if different from Hit).
The symbol that counts as a blank (no effect).
Enter a special symbol if applicable (e.g., ‘surge’, ‘double-crit’). Leave blank if none.
Describe the effect of the special symbol (e.g., ‘cancel crit’, ‘add hit’). Leave blank if none.
Analysis Results
Probability of Rolling at Least One Hit: —
Average Hits Per Roll: —
Average Critical Hits Per Roll: —
Probability of No Hits: —
Formula: Prob(At least one Hit) = 1 – (Prob(No Hits))^NumDice. Prob(No Hits) = (1 – Prob(Single Hit)).
Dice Roll Distribution
See the probability of rolling exactly N hits or critical hits with your current dice pool.
| Dice Pool | Exact Hits | Exact Critical Hits | Exact Blanks | Exact Specials |
|---|---|---|---|---|
| Calculating… | ||||
What is a Legion Dice Calculator?
A Legion Dice Calculator is a specialized tool designed to help players of tabletop wargames, particularly those with dice-based combat systems like Star Wars: Legion, understand and predict the outcomes of their dice rolls. It quantifies the probability of achieving specific results – such as hits, critical hits, or misses – based on the number of dice rolled and the specific symbols on those dice that constitute each outcome. This allows players to make more informed strategic decisions during gameplay, optimize their unit activations, and better anticipate the effectiveness of their attacks or defenses.
This calculator is invaluable for:
- Players seeking a competitive edge: By understanding the true odds, players can deploy units more effectively and plan maneuvers with greater confidence.
- New players learning the game: It demystifies the dice mechanics and helps new players grasp the impact of different unit abilities or modifiers.
- Wargaming enthusiasts: Anyone who enjoys deep dives into game mechanics and probability will find this tool insightful.
Common Misconceptions about Legion Dice
A common misconception is that dice are purely random and unpredictable. While individual rolls are indeed random, the aggregate behavior of a large number of dice follows predictable statistical patterns. Another misconception is that a specific outcome is guaranteed if you roll enough dice; probability doesn’t work that way – it only increases the likelihood of certain outcomes. This Legion Dice Calculator helps to illustrate these statistical realities, moving beyond gut feelings to data-driven insights.
Legion Dice Calculator Formula and Mathematical Explanation
The core of the Legion Dice Calculator relies on binomial probability and its extensions. We’ll break down the calculations step-by-step.
Probability of a Single Die Outcome
Each die in Legion typically has a set of symbols. We need to determine the probability of a single die landing on a specific symbol. This is calculated as:
P(Symbol) = (Number of faces with Symbol) / (Total number of faces on the die)
For simplicity in this calculator, we assume a standard D6 where each face has an equal chance of appearing. However, the calculator focuses on the *definition* of the outcomes provided by the user.
Defining Outcomes
The user defines which symbols represent:
- Hit: The primary symbol for a successful attack.
- Critical Hit: A more potent success, often modifying or bypassing standard defenses.
- Blank: A symbol with no offensive effect.
- Special Symbol: A symbol that triggers a unique unit ability (e.g., surge, pierce).
The probabilities of these individual outcomes for a single die are denoted as:
- P(Single Hit)
- P(Single Crit)
- P(Single Blank)
- P(Single Special)
These probabilities are derived from the dice faces assigned by the user’s input, assuming each defined symbol occupies one face unless specified otherwise (which the basic calculator doesn’t account for, assuming standard D6-like distribution of defined outcomes).
Probability of No Hits (Binomial Probability)
If P(Single Hit) is the probability of a single die *not* being a hit (i.e., it’s a Blank, Crit, or Special), then the probability of *none* of the N dice hitting is:
P(No Hits) = (P(Not Single Hit))^N
Where N is the total number of attack dice.
Probability of At Least One Hit
The complementary event to “no hits” is “at least one hit”. Therefore:
P(At Least One Hit) = 1 – P(No Hits)
P(At Least One Hit) = 1 – (P(Not Single Hit))^N
Average Number of Hits
The expected value (average) of hits from N dice is simply:
Average Hits = N * P(Single Hit)
Average Number of Critical Hits
Similarly, the expected value of critical hits is:
Average Crits = N * P(Single Crit)
Handling Special Symbols
The probability of a special symbol appearing is P(Single Special). The calculator notes this probability but does not directly integrate its *effect* into the hit/crit calculation unless the user specifies a trigger that modifies hits or crits (e.g., “surge to hit” would increase the effective P(Single Hit)).
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Attack Dice Pool (N) | The total number of dice rolled for an attack. | Count | 1 – 10+ |
| Hit Symbol | The primary symbol on a die that counts as a hit. | Symbol Type | Hit, Crit |
| Crit Symbol | The symbol on a die that counts as a critical hit. | Symbol Type | Crit, Hit, Blank |
| Blank Symbol | The symbol on a die that counts as a blank (no effect). | Symbol Type | Blank, Hit, Crit |
| Special Symbol | An optional symbol triggering a unique ability. | Symbol Type / Name | e.g., Surge, Pierce, Double-Crit |
| Special Trigger | The effect of the special symbol. | Text Description | e.g., Add Hit, Cancel Crit |
| P(Single Hit) | Probability of one die rolling a hit. | Probability (0 to 1) | 0 – 1 |
| P(Single Crit) | Probability of one die rolling a critical hit. | Probability (0 to 1) | 0 – 1 |
| P(Single Blank) | Probability of one die rolling a blank. | Probability (0 to 1) | 0 – 1 |
| P(Single Special) | Probability of one die rolling a special symbol. | Probability (0 to 1) | 0 – 1 |
| P(No Hits) | Probability of none of the dice rolling a hit. | Probability (0 to 1) | 0 – 1 |
| P(At Least One Hit) | Probability of rolling one or more hits. | Probability (0 to 1) | 0 – 1 |
| Average Hits | Expected number of hits per roll. | Count | 0+ |
| Average Crits | Expected number of critical hits per roll. | Count | 0+ |
Practical Examples (Real-World Use Cases)
Example 1: Standard Rebel Trooper Attack
A unit of Rebel Troopers fires their E-11 blaster rifles. Each trooper rolls 1 attack die. Let’s assume the E-11 dice have the following symbols: 2 Blanks, 2 Hits, 1 Crit, 1 Special (Surge). A standard E-11 die has 6 sides.
- Attack Dice Pool: 4 (for 4 troopers)
- Hit Symbol: Hit
- Crit Symbol: Crit
- Blank Symbol: Blank
- Special Symbol: Surge
- Special Trigger: (Let’s assume Surge allows re-rolls or converts to hits, but for this base calculation, we note its presence)
Calculator Inputs:
- Attack Dice Pool: 4
- Hit Criteria: Hit
- Crit Criteria: Crit
- Blank Criteria: Blank
- Special Symbol: Surge
- Special Trigger: (Left blank for basic calculation)
Calculator Outputs:
- P(Single Hit) = 2/6 = 0.333
- P(Single Crit) = 1/6 = 0.167
- P(Single Blank) = 2/6 = 0.333
- P(Single Special) = 1/6 = 0.167
- P(Not Single Hit) = P(Blank) + P(Special) = 0.333 + 0.167 = 0.500
- P(No Hits) = (0.500)^4 = 0.0625
- P(At Least One Hit): 1 – 0.0625 = 0.9375 (or 93.75%)
- Average Hits Per Roll: 4 * 0.333 = 1.33
- Average Critical Hits Per Roll: 4 * 0.167 = 0.67
- Probability of No Hits: 0.0625 (or 6.25%)
- Chance of Special Symbol: 0.167 (or 16.7%)
Interpretation: With 4 Rebel Troopers, you have a very high chance (over 93%) of scoring at least one hit. On average, you expect about 1.33 hits and 0.67 critical hits per roll. This demonstrates the reliability of the E-11 for basic damage output, though the special symbol’s utility needs separate consideration.
Example 2: Heavy Weapon Unit – AT-RT Laser Cannon
An AT-RT equipped with a Laser Cannon fires. Let’s say the Laser Cannon die has: 3 Hits, 2 Crits, 1 Blank.
- Attack Dice Pool: 2 (for 2 dice)
- Hit Symbol: Hit
- Crit Symbol: Crit
- Blank Symbol: Blank
- Special Symbol: None
Calculator Inputs:
- Attack Dice Pool: 2
- Hit Criteria: Hit
- Crit Criteria: Crit
- Blank Criteria: Blank
- Special Symbol: (Left blank)
Calculator Outputs:
- P(Single Hit) = 3/6 = 0.5
- P(Single Crit) = 2/6 = 0.333
- P(Single Blank) = 1/6 = 0.167
- P(Not Single Hit) = P(Blank) = 0.167
- P(No Hits) = (0.167)^2 = 0.02789
- P(At Least One Hit): 1 – 0.02789 = 0.9721 (or 97.21%)
- Average Hits Per Roll: 2 * 0.5 = 1.0
- Average Critical Hits Per Roll: 2 * 0.333 = 0.67
Interpretation: The AT-RT’s Laser Cannon is highly likely to score at least one hit (over 97%). It averages exactly 1 hit and 0.67 critical hits per roll. This indicates a potent and reliable offensive platform, capable of dealing significant damage.
How to Use This Legion Dice Calculator
Using the Legion Dice Calculator is straightforward. Follow these steps to get your probability analysis:
- Input Your Dice Pool: Enter the total number of dice you are rolling for your attack in the “Attack Dice Pool” field.
- Define Hit Symbols: Select the symbol from the dropdown that represents a standard “Hit” on your dice.
- Define Critical Hit Symbols: Select the symbol that represents a “Critical Hit”. This might be the same as the Hit symbol if your dice have symbols that count as both, or a separate symbol.
- Define Blank Symbols: Select the symbol that represents a “Blank” or a result with no offensive impact.
- Add Special Symbols (Optional): If your dice have a special symbol (like “Surge”, “Pierce”, etc.), enter its name in the “Special Symbol” field.
- Describe Special Trigger (Optional): If you entered a special symbol, briefly describe its effect in the “Special Trigger” field (e.g., “Add Hit”, “Cancel Crit”). This is primarily for informational purposes within the calculator’s context.
- Calculate: Click the “Calculate Probabilities” button.
Reading the Results
- Primary Result (Probability of Rolling at Least One Hit): This is your main indicator of success. A higher percentage means you are very likely to deal some damage.
- Average Hits Per Roll: The expected number of hits you’ll get over many rolls. Useful for comparing unit damage output.
- Average Critical Hits Per Roll: The expected number of critical hits. Crucial for understanding potential damage against heavily armored targets.
- Probability of No Hits: The chance you’ll roll absolutely no hits. A low percentage indicates reliability.
- Intermediate Values: These show the underlying probabilities for a single die, essential for understanding how the overall probabilities are derived.
- Dice Roll Distribution Table & Chart: These provide a more granular view, showing the exact probability of rolling specific counts of hits, crits, blanks, and specials.
Decision-Making Guidance
Use these results to:
- Choose Units: Compare the average hits and crits of different units to select the best tools for your strategy.
- Position Units: Understand which units are reliable damage dealers and position them accordingly.
- Target Priority: Identify units that are likely to deal significant damage (high average crits) and prioritize eliminating them.
- Manage Risk: If a crucial attack has a low probability of hitting (e.g., due to modifiers), you might adjust your strategy or seek ways to improve the odds.
Key Factors That Affect Legion Dice Results
While the core calculator determines probabilities based on dice symbols, real Legion gameplay involves numerous factors that can alter the effective outcome of a roll. Understanding these is key to strategic play:
-
Unit Abilities & Keywords:
This is paramount. Many units have keywords like “Surge,” “Pierce,” “Critical,” or specific abilities that modify dice results *before* or *after* the initial roll. For example, a “Surge to Hit” ability effectively increases the P(Single Hit) if the player chooses to spend a token to activate it. This calculator provides the base probability; actual results depend on ability usage.
-
Terrain:
Cover often provides defensive bonuses (e.g., increasing the number of defense dice needed to score a hit), but some units might have abilities to ignore cover or penetrate defenses more easily.
-
Range:
Certain weapons might have different dice pools or effects at different ranges. Some weapons might be less effective at close range or more effective at optimal ranges.
-
Suppression:
Suppressed units often suffer penalties, which can include rolling fewer dice or having their dice results modified negatively.
-
Commander/Emperor:
Specific unit abilities, like those granted by commanders or leaders, can provide re-rolls, bonus dice, or other beneficial modifications to units within range.
-
Line of Sight (LoS) & Line of Fire (LoF):
Even if a unit has a powerful attack, they must be able to see their target to shoot. Obstacles can block LoS, preventing attacks entirely.
-
Dice Pool Size & Quality:
The number of dice (N) is a direct input. However, the *quality* of those dice – meaning the distribution of hits, crits, blanks, and specials – significantly impacts the probabilities. A die with more hits is inherently better than one with more blanks, all else being equal.
-
Player Skill & Decision Making:
Knowing when to use limited resources like surge tokens, when to focus fire, and when to play defensively are critical skills that leverage probabilistic understanding. The calculator provides the odds; the player decides how to act upon them.
Frequently Asked Questions (FAQ)
“Hit” symbols are the standard success indicators for an attack, typically used to overcome a unit’s defense value. “Crit” (Critical Hit) symbols usually represent a more potent success. They often bypass standard defense values or inflict additional negative effects, making them crucial against heavily armored targets.
It depends on the specific dice design for the unit’s weapon. Some dice might have symbols that count as both a Hit and a Crit simultaneously, while others might have distinct symbols for each. The calculator allows you to specify separate criteria if needed, but for simplicity, it often assumes distinct outcomes unless your dice explicitly combine them.
The calculator notes the presence and probability of “Special Symbols” like Surge. However, the *effect* of Surge (e.g., converting blanks/hits to crits, or hits to crits) is applied *after* the initial roll. To account for Surge, you would typically calculate the base probabilities, then consider how spending a surge token might improve the outcome based on the specific rule.
No, this calculator focuses solely on the *offensive* dice roll probabilities – what your attacking unit is rolling. Defense is a separate mechanic involving the defending unit rolling their own dice to cancel incoming hits and crits. You would need a separate calculator or analysis for defensive probabilities.
This calculator uses a single “Attack Dice Pool” input. For weapons with variable dice pools based on range, you should run the calculator twice: once with the dice pool for short range, and again with the dice pool for long range.
These are expected values based on probability. Over a large number of rolls (hundreds or thousands), the average outcome will converge towards these numbers. In a single game, actual results will fluctuate due to natural randomness.
While the underlying probability principles are similar, this calculator is specifically designed for offensive dice pools in Legion. For defense, you’d need to input the defensive dice symbols and the number of defense dice rolled by the target unit.
A high probability (e.g., 90%+) means that it is extremely likely you will score at least one successful hit on your target, assuming no defensive measures are taken. This indicates a reliable offensive unit.
This calculator focuses on offensive outcomes (hits, crits, blanks, specials). Symbols like “Dodge” or “Block” are purely defensive and do not factor into the attacker’s probability calculation. You would define them as ‘blank’ or simply ignore them when setting up the offensive calculation.