Warhammer Dice Calculator

Reviewed by: David Chen, Wargame Analyst. This calculator is based on the Expected Value (EV) model for sequential D6 rolls.

The **Warhammer Dice Calculator** helps you quickly determine the average expected damage output of an attack sequence in popular wargames, allowing for better tactical planning and unit assessment.

1. Number of Attacks (A)

2. To Hit Roll Required (H – 2+ to 6+)

Re-roll Hit Rolls of 1

3. To Wound Roll Required (W – 2+ to 6+)

4. Target Armor Save (S – 2+ to 6+)

5. Target Invulnerable Save (I – Enter 7 for None)

6. Damage per Unsaves Wound (D)

Expected Total Damage:

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Detailed Calculation Steps

Enter values and click 'Calculate' to see the steps.

Warhammer Dice Calculator Formula:


                    P_Success = (7 - Required Roll) / 6

                    P_Hit = P_Success(H) * (1 + (1/6 * Reroll\_1s))

                    E_Hits = Attacks * P_Hit

                    E_Wounds = E_Hits * P_Success(W)

                    P_Save = MAX(P_Success(S), P_Success(I))

                    E_Damage = E_Wounds * (1 - P_Save) * Damage

Formula Sources: Math StackExchange on Rerolls, Wargaming Math Hammer

Variables:

Number of Attacks (A): The total dice rolled in the initial phase. Must be a positive integer.
To Hit Roll Required (H): The minimum D6 score needed to hit the target (typically 2, 3, 4, 5, or 6).
Re-roll Hit Rolls of 1: A toggle that increases the expected number of hits by allowing the re-roll of ‘1’ results.
To Wound Roll Required (W): The minimum D6 score needed for a successful wound, given a successful hit.
Target Armor Save (S): The minimum D6 score needed to negate a wound using standard armor (often 2+ through 6+).
Target Invulnerable Save (I): The minimum D6 score needed to negate a wound using an invulnerable field. Enter ‘7’ if the target does not have one.
Damage per Unsaves Wound (D): The total damage inflicted for each wound that passes all save rolls.

Related Calculators:

Compound Interest Calculator | Expected Value Sequence Tool | D&D Advantage Calculator | Monte Carlo Simulation Tool

What is the Warhammer Dice Calculator?

The Warhammer Dice Calculator is a utility built on **Mathhammer** principles, designed to convert complex sequences of dice rolls into a single, predictable Expected Value (EV) damage number. In wargames like Warhammer 40,000, an attack usually involves three sequential rolls: the Hit roll, the Wound roll, and the Save roll. The cumulative probabilities of these sequential events determine the average damage a unit can inflict.

Understanding expected damage is crucial for competitive play. Instead of relying on lucky rolls, this tool provides the mathematical baseline, allowing players to compare the damage efficiency of different weapons, units, and army compositions. For instance, it can quickly show if 10 shots hitting on 4+ with a re-roll of 1s is statistically better than 5 shots hitting on 3+ with no re-roll.

The formula correctly accounts for the most common tactical variables, such as re-rolls on ones, and the target’s ability to choose the better of their standard and invulnerable save rolls, ensuring the output is as accurate to game mechanics as possible.

How to Calculate Expected Damage (Example):

Define the Inputs: Start with 10 Attacks (A=10), requiring 3+ to Hit (H=3), with Re-roll 1s active, requiring 4+ to Wound (W=4), and saving on a 5+ (S=5), with no Invulnerable Save (I=7), and 1 Damage (D=1).
Calculate Hit Probability (P_Hit): Base probability for 3+ is (7-3)/6 = 0.6667. With Re-roll 1s, the final P_Hit is 0.6667 * (7/6) = 0.7778.
Calculate Expected Hits (E_Hits): $10 \text{ Attacks} \times 0.7778 \text{ P\_Hit} = 7.78 \text{ Hits}$.
Calculate Wound Probability (P_Wound): The base probability for 4+ is (7-4)/6 = 0.5.
Calculate Expected Wounds (E_Wounds): $7.78 \text{ Hits} \times 0.5 \text{ P\_Wound} = 3.89 \text{ Wounds}$.
Determine Save Probability (P_Save): Target has a 5+ save, which is (7-5)/6 = 0.3333. The Invulnerable save (7+) is 0. The max is 0.3333.
Calculate Expected Damage (E_Damage): $3.89 \text{ Wounds} \times (1 – 0.3333) \text{ Save Fail} \times 1 \text{ Damage} = 2.59 \text{ Total Damage}$.

Frequently Asked Questions (FAQ):

What is the difference between a normal save and an invulnerable save? A normal save can be modified (reduced) by a weapon’s Armor Penetration (AP) characteristic. An invulnerable save (often called an Invuln or Invul) cannot be modified or reduced by AP, meaning it is often a unit’s last line of defense against powerful weapons.

Why does the calculator use Expected Value (EV)? The calculator uses EV because it represents the mathematical average result over an infinite number of identical attacks. While your next single roll might be extremely lucky or unlucky, the EV gives the most reliable figure for comparing unit effectiveness across an entire game.

How do I handle critical hits (6s to hit)? This simple calculator uses expected probability only. For specific critical hit rules (e.g., a 6 to hit causes two hits), you must manually adjust the ‘Number of Attacks’ field based on the expected number of 6s (Attacks / 6) and run the calculation multiple times.

What should I enter for a ‘7+’ save roll? A 7+ save means the save is impossible on a D6, resulting in a 0% chance of success. You should enter ‘7’ in the input field, which the calculator treats as an automatic failure for the save roll.