Warhammer Dice Calculator

Analyze probabilities and optimize your strategy with Mathhammer.

What is a Warhammer Dice Calculator?

A Warhammer Dice Calculator, often referred to by the community as a “Mathhammer” tool, is a statistical engine designed to predict the average outcomes of combat in Warhammer 40,000, Age of Sigmar, and similar tabletop wargames. By applying the laws of probability to the various dice rolls required during a game turn—hitting, wounding, and saving—players can determine the efficiency of their units before ever placing them on the table.

Who should use a Warhammer Dice Calculator? Competitive tournament players use it to build optimized lists, while casual players use it to understand why certain units seem to underperform. A common misconception is that a Warhammer Dice Calculator predicts exactly what will happen in your next turn. In reality, it provides the expected value, which is the average result if the scenario were repeated thousands of times. Understanding the variance around this mean is the hallmark of a veteran strategist.

Warhammer Dice Calculator Formula and Mathematical Explanation

The core logic of the Warhammer Dice Calculator relies on sequential probability. Since each step in the combat sequence (Hit -> Wound -> Save) is independent, we multiply the probability of success for each stage together.

The mathematical derivation follows these steps:

1. Hit Probability: P(Hit) = (7 – Ballistic/Weapon Skill) / 6.
2. Wound Probability: Depends on the ratio of Strength (S) to Toughness (T).
   • If S >= 2T: 5/6 (2+)
   • If S > T: 4/6 (3+)
   • If S == T: 3/6 (4+)
   • If S < T: 2/6 (5+)
   • If S <= 0.5T: 1/6 (6+)
3. Save Probability: P(Fail Save) = 1 – [ (7 – (Armor Save + AP)) / 6 ]. This is capped by the Invulnerable Save if applicable.

Table 1: Variables Used in Warhammer Dice Calculator Calculations

Variable	Meaning	Unit	Typical Range
Attacks (A)	Number of shots or swings	Integer	1 – 100
Skill (BS/WS)	Target number to hit on D6	Threshold	2+ to 6+
Strength (S)	Attacker’s power rating	Rating	1 – 16
Toughness (T)	Defender’s resilience rating	Rating	1 – 16
AP	Armor Penetration	Modifier	0 to -6
Damage (D)	Wounds lost per failed save	Integer	1 – D6+3

Practical Examples (Real-World Use Cases)

Example 1: Space Marine Intercessor Shooting at an Ork Boy

In this scenario, we use the Warhammer Dice Calculator to see how effective a Bolt Rifle is. The Intercessor has 2 attacks at BS 3+. The Bolt Rifle is Strength 4, AP -1. The Ork Boy is Toughness 5 with a 5+ save.

• Inputs: Attacks: 2, Hit: 3+, S: 4, T: 5, AP: 1, Save: 5+, Damage: 1.
• Output: The Warhammer Dice Calculator shows an average of 0.44 wounds. This means you need roughly 3 Intercessors to guarantee killing a single Ork Boy in one round of shooting.

Example 2: Anti-Tank Lascannon vs. a Heavy Tank

A Lascannon has 1 attack at BS 3+, Strength 12, AP -3, and Damage 1 (for simplicity, we assume 1 damage, though it’s usually variable). The target tank is Toughness 12 with a 2+ save.

• Inputs: Attacks: 1, Hit: 3+, S: 12, T: 12, AP: 3, Save: 2+, Damage: 1.
• Output: The Warhammer Dice Calculator calculates: P(Hit)=0.66, P(Wound)=0.5, P(Fail Save)=0.66. Result: 0.22 average damage per shot. You realize you’ll need multiple Lascannons to bring down the behemoth.

How to Use This Warhammer Dice Calculator

Using our Warhammer Dice Calculator is straightforward. Follow these steps to get precise combat analytics:

1. Enter Attacks: Input the total number of dice you are rolling for the unit’s attacks.
2. Select Skill: Choose the Weapon Skill or Ballistic Skill from the dropdown.
3. Compare S vs T: Enter the weapon’s Strength and the target’s Toughness. The Warhammer Dice Calculator automatically determines the required wound roll.
4. Account for Armor: Input the AP (as a positive number) and the target’s base Save.
5. Invulnerable Saves: If the target has an invulnerable save, select it. The calculator will use the best possible save for the defender.
6. View Results: The expected damage and intermediate steps update instantly.

Key Factors That Affect Warhammer Dice Calculator Results

Several factors can swing the results predicted by a Warhammer Dice Calculator:

• Rerolls: Rerolls to hit or wound significantly increase reliability and “floor” performance.
• Critical Hits: Rules like Lethal Hits or Sustained Hits add extra layers that a basic Warhammer Dice Calculator must account for.
• Damage Variance: Weapons with D6 damage have high variance. While the Warhammer Dice Calculator shows the average (3.5), the actual result could be 1 or 6.
• Modifers: -1 to hit or +1 to wound modifiers shift the probabilities by 16.6% per step.
• Target Selection: Using a high-strength weapon against a low-toughness target is often “overkill” and inefficient in terms of points.
• Defensive Buffs: Feel No Pain rolls occur after the save, acting as a final filter for damage that the Warhammer Dice Calculator can further process.

Frequently Asked Questions (FAQ)

Q: Does this Warhammer Dice Calculator work for both 40k and AOS?
A: Yes, the core mechanics of hit, wound, and save are identical enough that this Warhammer Dice Calculator serves both systems effectively.

Q: How do I handle AP -1 in the calculator?
A: Simply enter “1” in the AP field. The Warhammer Dice Calculator subtracts this from the armor save.

Q: What if my weapon does D6 damage?
A: For an average result, enter 3.5. For a more conservative estimate, enter 2 or 3.

Q: Why does the calculator show 0.33 wounds instead of a whole number?
A: The Warhammer Dice Calculator provides a statistical average. 0.33 wounds means you have a 33% chance of dealing 1 wound.

Q: Does this include “Feel No Pain” saves?
A: This version calculates up to unsaved wounds. To account for Feel No Pain, multiply the final result by the chance of failure (e.g., for a 5+++, multiply by 0.66).

Q: Is a 1 on a dice always a failure?
A: Yes, in most Warhammer rulesets, an unmodified roll of 1 always fails, regardless of modifiers. The Warhammer Dice Calculator assumes standard rule conventions.

Q: How can I calculate 2D6 attacks?
A: Enter 7 as the number of attacks, which is the average result of a 2D6 roll.

Q: Can this calculator help with list building?
A: Absolutely. Use the Warhammer Dice Calculator to compare two different weapon options against various “meta” targets to see which is more efficient.

Related Tools and Internal Resources

• Combat Probability Calculator – A deeper look at variance and bell curves in gaming.
• Points Efficiency Tool – Calculate damage per point spent on a unit.
• Standard Deviation in Wargaming – Why averages aren’t everything in the Warhammer Dice Calculator.
• Unit Comparison Table – Pre-calculated data for popular 40k factions.
• Dice Rolling Simulator – Run 10,000 simulations to see the range of outcomes.
• Mathhammer Strategy Guide – Advanced tactics using the Warhammer Dice Calculator.