Warhammer Math Calculator

Advanced Mathhammer probability engine for tabletop wargaming.

Phase	Roll Required	Probability	Expected Successes

What is a Warhammer Math Calculator?

A warhammer math calculator, often referred to as “Mathhammer,” is a specialized tool used by tabletop wargamers to predict the statistical outcomes of combat. Whether you are playing Warhammer 40,000, Age of Sigmar, or Horus Heresy, understanding the variance and expected values of your dice rolls is crucial for competitive play.

This warhammer math calculator takes the guesswork out of your command phase. Instead of wondering if your squad of Intercessors can take down a Chaos Knight, you can use the warhammer math calculator to determine the mathematical probability of success. Who should use it? Competitive tournament players, casual gamers looking to optimize their lists, and hobbyists interested in the underlying mechanics of wargaming.

Common misconceptions about the warhammer math calculator include the idea that “dice have no memory” or that math doesn’t matter because “anything can happen.” While a single roll is random, the law of large numbers ensures that over a 5-round game, your results will gravitate toward the averages calculated by this warhammer math calculator.

Warhammer Math Calculator Formula and Mathematical Explanation

The core logic behind our warhammer math calculator follows a sequential probability chain. Since each roll (Hit, Wound, Save) is independent, we multiply the probabilities together to find the final expected value.

The Step-by-Step Derivation

1. Hit Probability (P_hit): Calculated based on BS/WS. For a 3+, the chance is 4/6 (or 66.6%).
2. Wound Probability (P_wound): Determined by comparing Strength (S) vs Toughness (T).
   • If S >= 2T: 2+ (5/6)
   • If S > T: 3+ (4/6)
   • If S == T: 4+ (3/6)
   • If S < T: 5+ (2/6)
   • If S <= T/2: 6+ (1/6)
3. Save Failure Probability (P_fail): The target’s save is modified by AP. If a unit has a 3+ save and is hit with AP-2, they need a 5+. The probability of failing that save is 4/6.
4. Final Damage: Expected Damage = Attacks × P_hit × P_wound × P_fail × Damage characteristic.

Variable Definitions Table

Variable	Meaning	Unit	Typical Range
Attacks (A)	Total dice rolled for the attack	Integer	1 – 100+
Skill (WS/BS)	Accuracy of the attacker	D6 Target	2+ to 6+
Strength (S)	Power of the attack	Statistic	3 to 16
Toughness (T)	Resilience of the defender	Statistic	3 to 12
AP	Armor Penetration	Modifier	0 to -6

Practical Examples (Real-World Use Cases)

Example 1: Space Marine Bolt Rifle vs. Ork Boy

In this scenario, we input 10 attacks from a squad of Intercessors using a warhammer math calculator. The Intercessors have a BS of 3+, S4, and AP-1. The Ork Boy has T5 and a 6+ save.
The warhammer math calculator shows:
– Hits: 6.67
– Wounds (S < T): 2.22 - Failed Saves (6+ save becomes 7+ due to AP-1): 2.22 - Total Damage: 2.22. This tells the player they are likely to kill 2 Orks per volley.

Example 2: Lascannon vs. Rhino Transport

A single Lascannon shot (1 attack) hitting on 3+, with S12 against a T9 Rhino. The Rhino has a 3+ save, and the Lascannon is AP-3.
The warhammer math calculator determines:
– Hit chance: 0.67
– Wound chance (S > T): 0.44 (approx 0.67 * 0.67)
– Save: 3+ becomes 6+ (fail on 1-5, so 5/6 chance).
– Average damage (D6+1 is roughly 4.5): The warhammer math calculator yields an expected 1.68 damage per shot.

How to Use This Warhammer Math Calculator

Using the warhammer math calculator is simple and designed for quick adjustments during army list building or active play.

1. Enter Attacks: Input the total number of shots or swings your unit makes.
2. Select Skill: Use the dropdown to set the required hit roll (e.g., 3+ for most elites).
3. Input S and T: The warhammer math calculator automatically determines the wound roll based on these two values.
4. Set Armor Stats: Enter the AP and the target’s base Save. The warhammer math calculator handles the arithmetic of modifiers.
5. Analyze Results: View the expected damage and the probability funnel chart to see where your efficiency is lost.

Key Factors That Affect Warhammer Math Calculator Results

• Volume of Fire: Increasing the number of attacks is the most reliable way to mitigate bad luck, as shown by the warhammer math calculator.
• Strength/Toughness Thresholds: Reaching the “Double Strength” (S >= 2T) threshold is a massive boost in efficiency.
• Armor Penetration (AP): AP is vital against high-save targets. The warhammer math calculator shows that AP-2 against a 3+ save is a 100% increase in damage compared to AP0.
• Damage Variance: Weapons with D6 damage are swingy. Use the warhammer math calculator with average values (3.5) to see the long-term trend.
• Re-rolls: (Advanced) Re-rolling 1s or all failed hits significantly shifts the warhammer math calculator output upward.
• Invulnerable Saves: Remember that AP cannot worsen a save beyond a target’s invulnerable save. Always use the better of the two in the warhammer math calculator.

Frequently Asked Questions (FAQ)

Does the warhammer math calculator account for re-rolls?

This version of the warhammer math calculator calculates raw averages. You can simulate re-rolls by manually adjusting the skill or attack count based on common probability modifiers (e.g., +16% for re-rolling 1s).

Why is my “expected damage” a decimal?

Dice results are whole numbers, but the warhammer math calculator provides an average. If the result is 2.5, it means in half your games you might do 2 damage and in the other half 3.

What does “Mathhammer” actually mean?

It is a portmanteau of “Math” and “Warhammer,” representing the community’s practice of using a warhammer math calculator to optimize gameplay.

Can I use this for Age of Sigmar?

Yes, the warhammer math calculator logic applies to AoS, though you may need to interpret “Strength vs Toughness” as the “To Wound” characteristic directly.

Is higher AP always better?

Not always. If the target has a 6+ save, AP-1 makes it impossible to save. AP-2 would be wasted points. Use the warhammer math calculator to find these “points of diminishing returns.”

How does cover affect the warhammer math calculator?

Cover usually improves a save by 1. Simply adjust the “Target Save” in the warhammer math calculator (e.g., change 4+ to 3+).

Does this calculator work for Mortal Wounds?

Mortal wounds skip the wound and save rolls. You can simulate them by setting the save to “None” and adjusting the wound roll accordingly in the warhammer math calculator.

What is the most important stat in the warhammer math calculator?

Usually, the number of attacks (Volume). More dice mean more consistency and fewer “whiffed” combat phases.