Warhammer Math Calculator

1. What is a Warhammer Math Calculator?

A Warhammer Math Calculator is an indispensable tool for players of tabletop wargames like Warhammer 40,000, Age of Sigmar, and other systems that rely on dice rolls for combat resolution. It allows you to quickly and accurately determine the statistical probability of various combat outcomes, such as how many hits you'll land, how many wounds you'll inflict, and ultimately, how much damage your unit is likely to deal against an enemy target.

This Warhammer probability tool goes beyond simple dice rolling. It takes into account all the modifiers and special rules that affect combat in Warhammer – from your unit's Ballistic Skill (BS) or Weapon Skill (WS), to the Strength (S) of your weapons versus the Toughness (T) of your opponent, Armor Penetration (AP), various types of Saves (normal, invulnerable, ward/FNP), and re-roll mechanics.

Who Should Use It?

• Competitive Players: Gain a significant edge by understanding the most efficient unit matchups and weapon choices.
• List Builders: Optimize your army lists by ensuring your units have the statistical firepower to achieve their objectives.
• New Players: Demystify complex combat interactions and learn the core mechanics of dice rolls more quickly.
• Narrative Players: Appreciate the narrative impact of certain weapon profiles by seeing their statistical power.

Common Misunderstandings

Many players misunderstand that the calculator provides expected values, not guaranteed outcomes. Dice rolls are random, and while a calculator might predict 3.5 wounds, you'll roll either 3 or 4. Also, correctly applying re-rolls and understanding the interaction between normal saves, invulnerable saves, and 'Feel No Pain' mechanics are crucial for accurate results. Our Warhammer Math Calculator aims to clarify these interactions.

2. Warhammer Math Calculator Formula and Explanation

The core of Warhammer combat resolution follows a sequential probability chain. Each successful step feeds into the next, reducing the initial number of attacks down to the final damage dealt.

The Probability Chain:

1. Attacks: The initial number of dice rolled.
2. To Hit Roll: Each attack needs to meet or exceed a specific Weapon Skill (WS) or Ballistic Skill (BS) on a D6.
3. To Wound Roll: Each successful hit then needs to meet or exceed a specific roll on a D6, determined by comparing the attacker's Strength (S) to the target's Toughness (T).
4. Save Roll: Each successful wound grants the target a chance to save, needing to meet or exceed their Save (Sv) characteristic, modified by the attacker's Armor Penetration (AP). Invulnerable Saves ignore AP.
5. Feel No Pain (FNP)/Ward Save: If a wound is not saved, some units get a final chance to ignore it with a FNP or Ward Save.
6. Damage: For each wound that passes all saves, the specified damage is applied to the target.

Variable Explanations:

Our calculator simplifies these complex interactions, providing a clear statistical 40k damage calculator output for various scenarios.

3. Practical Examples

Let's look at some common Warhammer combat scenarios to demonstrate the power of this tool.

Example 1: Space Marine Intercessors vs. Necron Warriors

Imagine 5 Intercessors (10 attacks) shooting at a unit of Necron Warriors.

• Inputs:
  • Attacks: 10
  • To Hit (BS): 3+
  • Re-roll 1s to Hit: Yes (Chapter Tactic)
  • Attacker Strength (S): 4 (Bolt Rifle)
  • Target Toughness (T): 4
  • Re-roll 1s to Wound: No
  • AP: -1 (Bolt Rifle)
  • Target Save (Sv): 4+ (Necron Warrior)
  • Invulnerable Save: None
  • Re-roll 1s to Save: No
  • FNP: 5+ (Reanimation Protocol, simplified)
  • Damage per Wound: 1
• Results (Approximate):
  • Expected Hits: 7.78
  • Expected Wounds: 5.19
  • Expected Failed Saves: 3.46
  • Expected Wounds Taken (after FNP): 2.31
  • Total Damage: 2.31

  This means, on average, 10 Bolt Rifle shots with re-rolling 1s to hit will inflict about 2.31 damage to a unit of Necron Warriors, considering their Reanimation Protocols.

Example 2: Lascannon vs. Leman Russ Battle Tank

A single Lascannon shot against a heavily armored tank.

• Inputs:
  • Attacks: 1
  • To Hit (BS): 3+
  • Re-roll 1s to Hit: No
  • Attacker Strength (S): 12 (Lascannon)
  • Target Toughness (T): 8 (Leman Russ)
  • Re-roll 1s to Wound: No
  • AP: -3 (Lascannon)
  • Target Save (Sv): 3+ (Leman Russ)
  • Invulnerable Save: None
  • Re-roll 1s to Save: No
  • FNP: None
  • Damage per Wound: 6 (Lascannon)
• Results (Approximate):
  • Expected Hits: 0.67
  • Expected Wounds: 0.56
  • Expected Failed Saves: 0.37
  • Expected Wounds Taken (after FNP): 0.37
  • Total Damage: 2.22

  Despite its high damage, a single Lascannon shot only has an expected damage output of 2.22 against a Leman Russ, due to the low number of attacks and the tank's resilience. This highlights why multiple high-strength, high-AP shots are often preferred against durable targets.

4. How to Use This Warhammer Math Calculator

Using this wargaming odds calculator is straightforward. Follow these steps for accurate results:

1. Input Number of Attacks: Enter the total number of attacks your unit will make. This is often the number of models multiplied by their attacks characteristic, or the number of shots from a weapon.
2. Select Roll to Hit (BS/WS): Choose the D6 roll your unit needs to hit. This is usually determined by your unit's Ballistic Skill (for shooting) or Weapon Skill (for melee).
3. Apply Re-roll 1s to Hit (Optional): Check this box if your unit has an ability to re-roll failed hit rolls of 1.
4. Input Attacker Strength (S): Enter the Strength characteristic of your weapon or unit.
5. Input Target Toughness (T): Enter the Toughness characteristic of the enemy unit you are attacking.
6. Apply Re-roll 1s to Wound (Optional): Check this box if your unit has an ability to re-roll failed wound rolls of 1.
7. Input Armor Penetration (AP): Enter the AP value of your weapon (e.g., -1, -2). A value of 0 means no AP.
8. Select Target Save (Sv): Choose the basic D6 roll the target unit needs to make a successful save.
9. Select Target Invulnerable Save (Invul Sv, Optional): If the target has an Invulnerable Save, select it here. The calculator will automatically use the better of the modified normal save or the invulnerable save.
10. Apply Re-roll 1s to Save (Optional): Check this box if the target unit can re-roll failed save rolls of 1.
11. Select Feel No Pain / Ward Save (FNP, Optional): If the target has a FNP or Ward Save, select the required roll.
12. Input Damage per Wound: Enter the amount of damage each successful, unsaved wound inflicts. For weapons with variable damage (like D3 or D6), use the average value (e.g., 2 for D3, 3.5 for D6).
13. Click "Calculate": The results will appear, showing expected hits, wounds, failed saves, and total damage.
14. Interpret Results: The results are expected averages. Use them for strategic planning, not as a guarantee for any single game turn.

5. Key Factors That Affect Warhammer Math

Several variables significantly influence the outcome of combat calculations in Warhammer:

1. Number of Attacks: This is the most fundamental factor. More attacks generally lead to more hits and wounds, scaling linearly. It's often better to have many lower-quality attacks than a few high-quality ones against hordes.
2. To Hit Roll (BS/WS): The base chance to hit. Improving this (e.g., from 4+ to 3+) has a substantial impact, especially when combined with re-rolls. Each +1 modifier can increase hit probability by 16.67%.
3. Strength vs. Toughness Comparison: This directly dictates the 'To Wound' roll. Wounding on 2+ is vastly superior to 6+. The sweet spot is often having Strength equal to or greater than double the target's Toughness.
4. Armor Penetration (AP): AP directly reduces the target's armor save. Even a small amount of AP (like -1) can dramatically increase failed saves against units with good armor, making a 3+ save effectively a 4+ save.
5. Save Characteristic (Sv): A unit's natural resilience. A 2+ save is incredibly strong, while a 6+ save is very weak. AP interacts heavily with this.
6. Invulnerable Saves: Crucial for durable units, as they ignore AP. This makes them highly resilient against high-AP weapons that would otherwise bypass their normal armor.
7. Re-rolls: Re-rolls (especially re-rolling 1s or all failures) significantly boost consistency and expected outcomes. They reduce the impact of bad luck and are a cornerstone of many powerful unit abilities.
8. Feel No Pain (FNP) / Ward Saves: These provide a final layer of defense, allowing units to ignore wounds that have already bypassed all other saves. They are particularly effective against high-damage weapons.
9. Damage per Wound: While not a probability, higher damage per wound means fewer successful wounds are needed to incapacitate a target. This makes high-damage weapons essential for taking down multi-wound models like vehicles and monsters.
10. Modifiers (+/- to Hit/Wound): External factors, such as aura abilities or psychic powers, can modify hit and wound rolls, shifting the probabilities in your favor or against you.

Understanding these factors helps in building effective armies and making informed tactical decisions on the battlefield, making this a useful tabletop dice roller aid.

6. Frequently Asked Questions (FAQ)

Q: Why are my results not whole numbers?

A: The calculator provides "expected values" or averages. For instance, if you have a 50% chance to hit with 3 attacks, you'd expect 1.5 hits. In reality, you'll either get 0, 1, 2, or 3 hits. The calculator helps you understand the average outcome over many dice rolls.

Q: How do re-rolls work in the calculation?

A: Re-rolls increase the probability of success. For example, re-rolling 1s to hit means any 1s rolled initially get a second chance to become a hit. This effectively increases the chance of success for those specific dice. Our miniature combat simulator incorporates this by adjusting the base probability.

Q: What about modifiers like +1 to hit or -1 to wound?

A: These modifiers directly change the target roll. If you need a 3+ to hit and have a +1 modifier, you now need a 2+ to hit. If you have a -1 modifier, you'd need a 4+. You should adjust the "Roll to Hit" or "Roll to Wound" (implicitly via S vs T) inputs in the calculator to reflect these modifiers.

Q: How do I handle weapons with variable damage (e.g., D3, D6)?

A: For this calculator, we recommend using the average damage value. For D3, use 2 (average of 1, 2, 3). For D6, use 3.5 (average of 1-6). For more complex scenarios, you might need a dedicated AoE wound calculator that handles dice pools.

Q: What's the difference between a normal Save and an Invulnerable Save?

A: A normal Save is modified by Armor Penetration (AP). An Invulnerable Save, however, ignores AP. If a weapon has AP-3 and your unit has a 3+ Save and a 5+ Invulnerable Save, you would use the 5+ Invulnerable Save because your normal save would be reduced to a 6+ (3+ Save + 3 AP = 6+).

Q: What is a "Feel No Pain" (FNP) or Ward Save?

A: A FNP or Ward Save is an additional roll made after a unit has failed its normal or invulnerable save. If successful, the wound is ignored. It's a last line of defense against incoming damage.

Q: Does this calculator work for Age of Sigmar or other wargames?

A: While designed with Warhammer 40,000 in mind, many wargames share similar dice mechanics. You can often adapt the inputs for Age of Sigmar or other systems that use sequential D6 rolls for combat, as long as you understand the equivalent stats. Always check specific game rules.

Q: Can this tool help me build better army lists?

A: Absolutely! By comparing the expected damage output of different units and weapons against various target profiles, you can make informed decisions about which units to include in your army list to fulfill specific tactical roles. It's a powerful wargaming odds planning tool.